Hobe
/
Ginger


								%%

								%% IEEEtran.cls 2002/11/18 version V1.6b

								%%

								%% NOTE: This text file uses MS Windows line feed conventions. When (human)

								%% reading this file on other platforms, you may have to use a text

								%% editor that can handle lines terminated by the MS Windows line feed

								%% characters (0x0D 0x0A).

								%%

								%%

								%% This is the official IEEE LaTeX class for authors of the Institute of

								%% Electrical and Electronics Engineers (IEEE) Transactions journals and

								%% conferences.

								%%

								%% The latest version and documentation of IEEEtran can be obtained at:

								%% http://www.ieee.org

								%% and/or

								%% http://www.ctan.org/tex-archive/macros/latex/contrib/supported/IEEEtran/

								%%

								%% The CTAN page may have additional files related to obscure,

								%% non-IEEE standard and/or platform dependent use of this tool.

								%%

								%% Based on the original 1993 IEEEtran.cls, but with many bug fixes

								%% and enhancements (from both JVH and MDS) over the 1996/7 version.

								%%

								%%

								%% Contributors:

								%% Gerry Murray (1993), Silvano Balemi (1993),

								%% Jon Dixon (1996), Peter N"uchter (1996),

								%% Juergen von Hagen (2000), and Michael Shell (2001-2002)

								%%

								%%

								%% Copyright (c) 1993-2002 by Gerry Murray, Silvano Balemi,

								%%                         Jon Dixion, Peter N"uchter,

								%%                         Juergen von Hagen and Michael Shell

								%%

								%% Current maintainer (V1.3 to V1.6): Michael Shell

								%%                                    mshell@ece.gatech.edu

								%%                                    See the CTAN website above

								%%                                    for current contact information.

								%%

								%% Special thanks to Peter Wilson (CUA) and Donald Arseneau

								%% for allowing the inclusion of the \@ifmtarg command

								%% from their ifmtarg LaTeX package.

								%%

								%%**********************************************************************

								%% Legal Notice:

								%% This code is offered as-is without any warranty either

								%% expressed or implied; without even the implied warranty of

								%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE!

								%% User assumes all risk.

								%% In no event shall IEEE or any contributor to this code

								%% be liable for any damages or losses, including, but not limited to,

								%% incidental, consequential, or any other damages, resulting from the

								%% use or misuse of any information contained here.

								%%

								%% All comments are the opinions of their respective authors and are not

								%% necessarily endorsed by the IEEE.

								%%

								%% This code is distributed under the Perl Artistic License

								%% ( http://language.perl.com/misc/Artistic.html )

								%% and may be freely used, distributed and modified.

								%% Retain the contribution notices and credits.

								%%

								%% Major changes to the user interface should be indicated by an

								%% increase in the version numbers. If a version is a beta, it will

								%% be indicated with a BETA suffix, i.e., 1.4 BETA.

								%% Small changes can be indicated by appending letters to the version

								%% such as "IEEEtran_v14a.cls".

								%% In all cases, \Providesclass, any \typeout messages to the user,

								%% \IEEEtransversionmajor and \IEEEtransversionminor must reflect the

								%% correct version information.

								%% The changes should also be documented via source comments.

								%%**********************************************************************

								%%

								%

								% Available class options

								% (e.g., \documentclass[10pt,conference]{ieeeconf}

								%

								%             *** choose only one from each category ***

								%

								% 9pt, 10pt, 11pt, 12pt

								%    Sets normal font size. The default is 10pt.

								%

								% conference, journal, technote, peerreview, peerreviewca

								%    determines format mode - conference papers, journal papers,

								%    correspondence papers (technotes), or peer review papers. The user

								%    should also select 9pt when using technote. peerreview is like

								%    journal mode, but provides for a single-column "cover" title page for

								%    anonymous peer review. The paper title (without the author names) is

								%    repeated at the top of the page after the cover page. For peer review

								%    papers, the \IEEEpeerreviewmaketitle command must be executed (will

								%    automatically be ignored for non-peerreview modes) at the place the

								%    cover page is to end, usually just after the abstract (keywords are

								%    not normally used with peer review papers). peerreviewca is like

								%    peerreview, but allows the author names to be entered and formatted

								%    as with conference mode so that author affiliation and contact

								%    information can be easily seen on the cover page.

								%    The default is journal.

								%

								% draft, draftcls, draftclsnofoot, final

								%    determines if paper is formatted as a widely spaced draft (for

								%    handwritten editor comments) or as a properly typeset final version.

								%    draftcls restricts draft mode to the class file while all other LaTeX

								%    packages (i.e., \usepackage{graphicx}) will behave as final - allows

								%    for a draft paper with visible figures, etc. draftclsnofoot is like

								%    draftcls, but does not display the date and the word "DRAFT" at the foot

								%    of the pages. If using one of the draft modes, the user will probably

								%    also want to select onecolumn.

								%    The default is final.

								%

								% letterpaper, a4paper

								%    determines paper size: 8.5in X 11in or 210mm X 297mm. CHANGING THE PAPER

								%    SIZE WILL NOT ALTER THE TYPESETTING OF THE DOCUMENT - ONLY THE MARGINS

								%    WILL BE AFFECTED. In particular, documents using the a4paper option will

								%    have reduced side margins (A4 is narrower than US letter) and a longer

								%    bottom margin (A4 is longer than US letter). For both cases, the top

								%    margins will be the same and the text will be horizontally centered.

								%    For final submission to IEEE, authors should use US letter (8.5 X 11in)

								%    paper. Note that authors should ensure that all post-processing

								%    (ps, pdf, etc.) uses the same paper specificiation as the .tex document.

								%    Problems here are by far the number one reason for incorrect margins.

								%    IEEEtran will automatically set the default paper size under pdflatex

								%    (without requiring a change to pdftex.cfg), so this issue is more

								%    important to dvips users. Fix config.ps, config.pdf, or ~/.dvipsrc for

								%    dvips, or use the dvips -t papersize option instead as needed. See the

								%    testflow documentation

								%    http://www.ctan.org/tex-archive/macros/latex/contrib/supported/IEEEtran/testflow

								%    for more details on dvips paper size configuration.

								%    The default is letterpaper.

								%

								% oneside, twoside

								%    determines if layout follows single sided or two sided (duplex)

								%    printing. The only notable change is with the headings at the top of

								%    the pages.

								%    The default is oneside.

								%

								% onecolumn, twocolumn

								%    determines if text is organized into one or two columns per page. One

								%    column mode is usually used only with draft papers.

								%    The default is twocolumn.

								%

								% nofonttune

								%    turns off tuning of the font interword spacing. Maybe useful to those

								%    not using the standard Times fonts or for those who have already "tuned"

								%    their fonts.

								%    The default is to enable IEEEtran to tune font parameters.

								%

								%

								%*******

								% 11/2002 V1.6b (MDS) changes:

								%

								% 1) Fixed problem with figure captions when using hyperref. Thanks to

								%    Leandro Barajas and Michael Bassetti for reporting this bug.

								%

								% 2) Provide a fake nabib command \NAT@parse so that hyperref will not

								%    interfere with the operation of cite.sty. However, as a result citation

								%    numbers will not be hyperlinked. Also, natbib will not be able to work

								%    with IEEEtran. However, this is perhaps the best solution until cite.sty

								%    and hyperref.sty are able to co-exist with each other.

								%    It easy enough to override the fake command via:

								%    \makeatletter

								%    \let\NAT@parse\undefined

								%    \makeatother

								%

								% 3) Revised font selection method so as not to have problems when used

								%    with setspace.sty. Thanks to Zhang Yan for reporting this bug.

								%

								% 4) Added \special to feed papersize to dvips. Thanks to Moritz Borgmann

								%    for suggesting this feature.

								%

								% 5) In addition to the IEEE IED lists, the original IED style list

								%    environments (as is done in article.cls) are now provided as

								%    LaTeXitemize, LaTeXenumerate, and LaTeXdescription. Also, users can

								%    now redefine \makelabel within IEEE IED list controls. There may be

								%    some use for this in specialized applications. Thanks to Eli Barzilay

								%    for suggesting this feature.

								%

								% 6) \table* now defaults to \footnotesize text like \table.

								%

								% 7) The draft modes now no longer force a pagebreak after the title.

								%    Thanks to Christian Peel for suggesting this change.

								%

								% 8) New draftclsnofoot mode is like draftcls, but does not display the

								%    date and the word "DRAFT" at the foot of the page. Thanks to

								%    Christian Peel for suggesting this feature.

								%

								% 9) New peerreview and peerreviewca modes with \IEEEpeerreviewmaketitle

								%    command allows for a "cover" titlepage for anonymous peer review.

								%    Except for the cover titlepage, peerreview is much like journal mode.

								%    peerreviewca is like peerreview, but allows the author names to be

								%    entered and formatted as under conference mode so that author

								%    affiliations and contact information can be easily seen on the cover

								%    page. Thanks to Eric Benedict for suggesting this feature.

								%

								%

								%*******

								% 7/2002 V1.6 (MDS) changes:

								%

								% 1) Added conference mode via conference option. Defaults to the traditional

								%    journal mode. i.e., \documentclass[conference]{IEEEtran}

								%

								% 2) Added support for A4 paper via new a4paper option. Pdflatex's paper size

								%    lengths are now automatically set to the proper paper size being used.

								%

								% 3) Revised margins again. Page text is now horizontally centered.

								%    Conference mode increases the top and bottom margins with the bottom

								%    margin being slightly larger. For A4 paper, the top margin and text

								%    typesetting will not change from those of US letter paper, but the side

								%    margins will be smaller and the bottom margin will be larger than that of

								%    US letter. All per IEEE specs.

								%

								% 4) Fixed footnote line spacing anomaly in draft mode.

								%    Thanks to Alberto Rodriguez for reporting this bug.

								%

								%    Also, slightly revised footnote and \thanks note spacing.

								%    Set \interfootnotelinepenalty=10000 to prevent LaTeX

								%    from breaking footnotes across multiple pages or columns.

								%

								% 5) Fixed bug that caused overwritten photo areas and sometimes anomalous

								%    spacing when a new paragraph was started within a biography. Also,

								%    the presence of \par's, new lines or spaces at the beginning of

								%    abstract, keywords, biography, or biographynophoto will no longer

								%    affect the first word spacing.

								%    Thanks to Eric Durant for reporting this bug.

								%

								%    The biography environment now does a better job in preventing

								%    a biography photo area from being broken across pages or columns.

								%

								% 6) Fixed whitespace between \cite entries bug. i.e.,

								%    both \cite{einstein24, knuth84} and \cite{einstein24,knuth84}

								%    are now valid. \cite is now a robust command as it should be.

								%    IEEEtran now no longer defines the old non-standard \shortcite or

								%    \citename.

								%

								%    The base IEEEtran.cls does not sort citation numbers or produce ranges

								%    for three or more consecutive numbers. However, V1.6 of IEEEtran.cls

								%    now pre-defines the following format control macros to facilitate easy

								%    use with Donald Arseneau's cite.sty package (tested with cite.sty V3.9):

								%

								%    \def\citepunct{], [}

								%    \def\citedash{]--[}

								%

								%    cite.sty is standard on most LaTeX sytems and can be obtained from

								%    www.ctan.org. Thanks to Donald Arseneau for creating cite.sty, providing

								%    the required format arguments to produce the IEEE style. and

								%    designing a cite interface capable of handling the IEEE citation

								%    style.

								%

								%    Note: Historically, IEEE has wanted authors to "hardcode" symbolics.

								%    (i.e., replace all \cite{} with fixed [x]). However, it now seems that

								%    most electronic manuscript submissions to IEEE are in .pdf format, and

								%    as such, do not require the LaTeX document reference numbers to be hard

								%    coded. If an author is required to submit actual LaTeX files, I do

								%    recommend that the bibliography file (.bbl) be copied into the .tex

								%    document and the \bibliographystyle{} and \bibliography{} commands be

								%    commented out so that the .tex file does not depend on (potentially

								%    lengthy and/or confidential) external bibliography database files.

								%

								% 7) Adjusted some spacing parameters. The spacing above and below equations

								%    has been revised (to a typical IEEE value). \jot now has a decent value.

								%    The title text is now exactly 24pt. (On a related note, \fontsubfuzz has

								%    been increased to 0.9pt to prevent annoying font substitution warnings

								%    when using the Computer Modern fonts that use the 24.88pt size.)

								%    In V1.6, \small is now 8.5pt in 9pt docs because \footnotesize is 8pt.

								%    For 9pt docs, you should probably go ahead and use \footnotesize when you

								%    need text a little smaller than \normalsize.

								%    The interword spacing has been adjusted to be extremely close to that

								%    which IEEE uses. You can use a new class option, nofonttune, if you need

								%    to disable the adjusting of the interword spacing. This adjustment and

								%    an increase to \hyphenpenalty have greatly reduced the amount of

								%    hyphenation in a typical paper.

								%       The baselineskip for the normalsize fonts has been tweaked to reduce

								%    underfull vboxes on journal paper columns with only paragraphs.

								%    Conference mode does the same thing but by also tweaking the \textheight

								%    slightly off 9.25in (IEEE spec) to ensure an integer number of lines per

								%    page. Draft (also draftcls) mode has also been revised to reduce

								%    underfull vbox warnings. However, draft mode can still produce underfull

								%    vboxes (a direct result of the increase in line spacing and margins) if:

								%    A non-normalsize font occupies an entire column (abstract and index terms

								%    take up a whole column by themselves); or the beginning of a section

								%    occurs near the end of a column and cannot be squeezed into the bottom,

								%    etc. This is normal as draft mode's liberal spacings cannot guarantee

								%    perfect formatting.

								%

								% 8) New biographynophoto environment for biographies without photos.

								%    Usage:

								%

								%    \begin{biographynophoto}{author name}

								%    biography text here

								%    \end{biographynophoto}

								%

								% 9) Fixed bug that produced multiple table of contents entries for papers

								%    with more than one biography. Also, biography now works better with

								%    hyperref.

								%

								%10) New \sublargesize font size command provides for 11pt text in a 10pt

								%    document. (Needed for things like author names.) For documents not

								%    using 10pt normal size text, \sublargesize is currently identical

								%    to \large.

								%

								%11) New \IEEEmembership command to provide correct font to indicate IEEE

								%    membership for journal papers.

								%

								%12) Fixed author name line overflow problem when in journal mode. This

								%    problem had been introduced in V1.5 in my rush to get \and to work for

								%    conferences. \and is unneeded (and invalid) in journal mode. For

								%    conference mode, \and will work as expected and features an optional

								%    spacing argument. i.e., \and[\hspace{5ex}]

								%    \and will default (recommended) to using \hfill which will result in

								%    equal spacing between author blocks.

								%

								%13) New \authorblockN, \authorblockA and \authorrefmark commands to

								%    facilitate easy formatting of author names, affiliations and cross

								%    reference symbols, respectively, when in conference mode. These

								%    three commands are to be used only for conference papers.

								%    In conference mode, \author text is placed within a modified tabular

								%    environment (somewhat like article.cls). So, within \author in conference

								%    mode, you should not try to enclose multiple \\ within an environment or

								%    command (other than the argument braces of \authorblockX{}). For example:

								%

								%    \author{\authorblockN{{John Doe \\ Jane Doe}}} % WRONG!

								%

								%    will generate an error.

								%

								%    Note that font size/attribute changes will now persists across \\ within

								%    \author. (But, not across author blocks nor across \and.)

								%    However, with the new commands, there should be no need to alter any

								%    font attributes within \author. All text sizing and spacing within

								%    \author{} and the author block commands is per IEEE specs for both

								%    conference and journal modes. (In conference mode, the author names

								%    are only very slightly larger than the affiliations which are in normal

								%    size.) For specialized applications you can alter the justification of

								%    author lines by placing \hfill at the beginning or at the end of a line.

								%    The interline spacing within \author is determined by the font attributes

								%    that are in effect at the end of each line within author.

								%

								%14) Because the titles and author name blocks use different font sizes/styles

								%    from the main text, it was possible that two column papers with titles that

								%    span both columns (standard journal and conference papers, but not technotes)

								%    with certain numbers of lines for the title and authors' name/affiliations

								%    can cause underfull vbox problems (paragraphs with large spacings between

								%    them) in the second column of the main text on the title page - if there were

								%    no new sections, equations or figures in this column (they would provide some

								%    needed rubber spacing). The use of things like special paper notices and

								%    publisher ID marks also affected this issue. The problem could not happen

								%    in the first column because the first column has a rubber length around the

								%    heading of the first section. Furthermore, problems seldom occurred on pages

								%    after the first as the margins had been chosen not to cause it with the popular

								%    font sizes. Rubber lengths after the author names would not fix this problem.

								%       Auto-calculating a "good" spacing after the title is a tad difficult

								%    to do in LaTeX. However, I am pleased to report that V1.6 has this new

								%    capability - "dynamically determined title spacing". IEEEtran will now

								%    measure the height of all the title and author text in \maketitle

								%    and then calculate a rigid (non-rubber) spacer to follow that meets

								%    IEEE specs and also produces a \textheight on the title page that ensures

								%    an integer number of normalsized lines on the rest of the page. Single

								%    column  papers, and two column papers with the title entirely in column

								%    one (technotes) do not need dynamic rigid spacing and therefore use

								%    standard rubber spacers.

								%

								%    Note: This problem can still crop up if you use floats that span both

								%    columns (i.e., figure*). It has been a decade+ long limitation with LaTeX

								%    that the stretchable portion of \dbltextfloatsep is ignored.

								%    If you get a problem with underful vbox warnings and paragraphs that "are

								%    pulled apart" on page with a float that spans both columns, tweak the

								%    space between the figure and the main text a little:

								%

								%    \vskip 5pt

								%    \end{figure*}

								%

								%    If you can't find a value that fixes both columns, you are going to

								%    have to put a rubber spacer somewhere in one or both of the columns.

								%

								%15) Because of change #14 above, those of you using \pubid will, as of V1.6,

								%    have to place it *before* \maketitle in order for it have the intended

								%    affect. The dynamic spacer algorithm must see if you are using \pubid when

								%    \maketitle is called. \pubidadjcol works as before except that it now

								%    has additional logic to prevent it from doing anything if \pubid was never

								%    called.

								%

								%16) In some unusual, non-standard circumstances, an author may desire to

								%    alter the spacing after the title area or put some unusual text above

								%    the main text. For instance, to stop a bad break when a new section

								%    occurs right at the start of the second page. This is difficult to do

								%    when the title spans both columns of two column text since LaTeX treats

								%    such title text as a type of float. A new command, \IEEEaftertitletext{},

								%    gives access to the end of that produced by \maketitle. The types of

								%    things that can go into \IEEEaftertitletext are the same as those into

								%    \twocolumn[] - no \par, but \\ are OK. There is no restriction on the

								%    range of spacings that can be used.

								%    i.e., \IEEEaftertitletext{\vspace{-100pt}} will push the main text well

								%    into the title and \IEEEaftertitletext{\vspace{100pt}} will push it far down

								%    the page. You will have complete control. If used, place

								%    \IEEEaftertitletext{} before \maketitle like \title and \author. IEEEtran's

								%    dynamic title spacing intentionally does not take into consideration the

								%    contents of \IEEEaftertitletext{} when determining the spacer after the title

								%    area (otherwise it would try to second guess you), so the user will have

								%    manually adjust the height of the contents in \IEEEaftertitletext{} if the

								%    problem discussed in #14 above should develop. A safe bet is to keep

								%    the height of contents of \IEEEaftertitletext{} to integer multiples of

								%    \baselineskip, i.e., \IEEEaftertitletext{\vspace{-1\baselineskip}}

								%

								%    Because it can result in an IEEE nonstandard format, the use of

								%    \IEEEaftertitletext{} is discouraged. Possible uses include (1) the use of

								%    IEEEtran for non-IEEE work with different title spacing requirements,

								%    or (2) as an emergency manual override if a problem should develop in

								%    IEEEtran's automatic spacing algorithm.

								%

								%17) completely rewritten \PARstart to:

								%    a. no longer have problems when the user begins an environment

								%       within the paragraph that uses \PARstart.

								%    b. auto-detect and use the current font family

								%    c. revise handling of the space at the end of the first word so that

								%       interword glue will now work as normal.

								%    d. produce correctly aligned edges for the (two) indented lines.

								%

								%    Because the current font family is now auto-detected, there is no

								%    longer any need for \CMPARstart - it is now the same as \PARstart.

								%

								%18) There is now a new "open box" Q.E.D. symbol (\QEDopen) as well as the

								%    original default (\QED) closed one (\QEDclosed). Some journals use

								%    the open form. To make \proof use the open form, just do:

								%    \renewcommand{\QED}{\QEDopen}

								%

								%19) Additional \typeout{} notices added to warn the user when unusual

								%    settings/commands are detected or as reminders to avoid common errors

								%    when in conference mode.

								%

								%20) IEEEtran now provides \abovecaptionskip and \belowcaptionskip skip

								%    registers because article class provides them and some packages

								%    may error if they are missing. However, IEEEtran only uses

								%    \abovecaptionskip for actual caption spacing.

								%

								%21) Fixed bug that prevented users from redefining the section headings

								%    to use arabic digits. Thanks to Richardt H. Wilkinson for reporting

								%    this bug.

								%

								%22) Code cleaned up to be more efficient with the use of TeX registers;

								%    removed some old LaTeX 2.09 code; revised option processing to

								%    LaTeX2e standard; eliminated unwanted "phantom" spaces in some

								%    environments.

								%

								%23) Added new \IEEEeqnarray, \IEEEeqnarraybox, \IEEEeqnarrayboxm and

								%    \IEEEeqnarrayboxt environments to provide superior alternatives to the

								%    standard LaTeX \eqnarray, \array and \tabular. Additional new support

								%    commands include \IEEEeqnarraydecl, \IEEEeqnarrayboxdecl,

								%    \IEEEeqnarraymathstyle, \IEEEeqnarraytextstyle, \yesnumber. \IEEEnonumber,

								%    \IEEEyesnumber, \IEEEyessubnumber, \IEEEeqnarraynumspace, \IEEEeqnarraymulticol,

								%    \IEEEeqnarrayomit, \IEEEeqnarraydefcol, \IEEEeqnarraydefcolsep, \IEEEeqnarrayseprow,

								%    \IEEEeqnarrayseprowcut, \IEEEeqnarrayrulerow, \IEEEeqnarraydblrulerowcut,

								%    \IEEEeqnarraystrutmode, \IEEEeqnarraystrutsize, \IEEEeqnarraystrutsizeadd,

								%    \IEEEvisiblestrutstrue, \IEEEvisiblestrutsfalse and \IEEEstrut.

								%    These are documented in the user's guide.

								%

								%24) V1.6 changed back to using () around theorem names (which are also now in italics)

								%    as this is what IEEE is using now. Thanks to Christian Peel for reporting this.

								%    Also, when section numbers are used as the first part of theorem numbers, display

								%    them in arabic, not Roman.

								%

								%25) New \IEEEtriggeratref{X} command allows a page break to be triggered just

								%    before the given reference number "X". This is most useful when balancing

								%    the columns on the last page and a \newpage between references is desired.

								%    \IEEEtriggercmd{X} allows a different command to be executed at trigger.

								%

								%

								%*******

								% 7/2001 V1.5 (MDS) changes:

								%

								%

								% 1) Fixed \and within \author bug: (! Misplaced \crcr. \endtabular ->\crcr)

								%    Thanks to Rainer Dorsch for discovering and reporting that \and

								%    did not work.

								%

								% 2) Fixed the biography environment so that if a biography's text is shorter

								%    than the area allocated for the photo, a collision with the next

								%    biography does not occur. You can now put real graphics (using the

								%    graphicx package) into the biography photo box with a new optional

								%    argument of the biography command! For example:

								%

								%    \begin{biography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{./tux.eps}}]{Linux Penguin}

								%

								%    will use the specified graphic as the author's photo. The photo area is

								%    exactly 1in wide by 1.25in high - as is done in IEEE Transactions. Try

								%    to keep the same 4:5 aspect ratio if scanning/cropping your photos.

								%    Note the need for the extra set of enclosing braces around the

								%    \includegraphics. Without it, The LaTeX parser may get confused when it

								%    sees the \includegraphics's brackets within the biography's optional

								%    argument. Due to the length of the \includegraphics command, you may wish

								%    to define your own shorthand form of it. I have not done so with IEEEtran

								%    to prevent dependence on the graphicx package. If you do not use the

								%    optional argument, or leave it empty, a standard frame box with the

								%    words "Place Photo Here" will be used. If you want the space to remain

								%    completely empty, you can do:

								%

								%    \begin{biography}[\mbox{}]{The Invisible Man}

								%

								%    The interface to biography's optional argument is into a

								%    1in X 1.25in minipage in which the argument text is centered both

								%    horizontally and vertically:

								%

								%    \begin{minipage}[b][1.25in][c]{1in}%

								%    \centering

								%    #1%

								%    \end{minipage}

								%

								%    Within the biography environment, \unitlength is set to 1in.

								%    With this in mind, you can even design your own custom frameboxes.

								%    For instance:

								%

								%    \begin{biography}[\framebox(1,1.25){\parbox[][\height][c]{0.9in}{\centering PLACE\\ PHOTO\\ HERE}}]{Author Name}

								%

								%    will yield the same type of result as the default photo box.

								%

								%    Thanks to Herbert Voss for discovering the collision bug, suggesting the ability

								%    to handle graphics and providing some prototype code.

								%

								%

								%

								%*******

								% 3/2001 V1.4 (MDS) changes:

								%

								%

								% 1) New "draftcls" and "final" options have been added.

								%    Thanks to Dragan Cvetkovic for suggesting an option like draftcls.

								%

								% 2) Documentation changes to reflect the fact that this IEEEtran.cls

								%    is no longer beta test.

								%

								% 3) Slightly revised caption sizes. Figure and table captions are now

								%    in \footnotesize, not \small as before.

								%

								% 4) Allow user to control figure caption justification. IEEEtran.cls

								%    normally defaults to left justified as is done in Transactions.

								%    However, for conferences, you may wish to issue the command:

								%    \centerfigcaptionstrue

								%    in the preamble. Short (less than one line long) figure captions

								%    will then be centered. Multi-line figure captions will always be

								%    properly left justified. V1.6: This is already done for you when

								%    using the conference mode.

								%

								%

								%

								%*******

								% 1/2001 V1.3

								% Michael Shell (MDS) made extensive changes and additions:

								%

								%

								% BUGS FIXED (and many others too numerous to mention!):

								% 1) Fixed improper alignment with itemized, enumerated and

								%    description lists. Added new controls to these three

								%    environments so that it is easy to get the alignment IEEE

								%    uses. Furthermore, the itemize, enumerate and description lists

								%    no longer force a new paragraph to begin at the end the list

								%    (\par). (Sometimes lists are used within paragraphs.)

								%

								% 2) JVH's fixes now allow things like $\mathbf{N}(0,P(0))$

								%    to work properly without needing the extra braces:

								%    ${\mathbf{N}}(0,P(0))$. There is no longer any dependence

								%    on the "rawfonts" and "oldlfont" packages. Thanks Juergen!

								%

								% 3) Fixed underfull hbox errors and incorrect reference number

								%    alignment when the number of references in the bibliography

								%    exceeded 9 entries (which is almost every paper!).

								%

								% 4) Removed dependence on the LaTeX sizexx.clo files.

								%    Now, 9pt documents should work correctly even on systems that

								%    lack a size9.clo file. This is most often used in conjunction

								%    with the option "technote" for "correspondence" papers like those

								%    in IEEE Transactions on Information Theory. For virtually all

								%    other papers, 10pt is used and so it is the default.

								%    Some improper font sizes have been corrected. \footnotesize is

								%    now 8pt in 9pt docs, so footnotes in technotes should be the

								%    correct size now.

								%

								% 5) Added \interlinepenalty within the bibliography section to discourage

								%    LaTeX from breaking within a reference. IEEE almost never breaks within

								%    a reference and when they do it is usually in technotes

								%    (correspondence papers). You may get an underfull vbox warning in the

								%    bibliography indicating that the spacing just before the "REFERENCES"

								%    section is larger than normal, but the final result will be more like

								%    what IEEE will publish. See the comments in the BIBLIOGRAPHY section

								%    around line 2034 below if you want to change this behavior.

								%

								% 6) No longer "blows up" when you use \paragraph and have a table

								%    of contents.

								%

								% 7) Theorem environment changed, (but for V1.6, back to the old way, sigh).

								%

								% 8) Figure captions adjusted: IEEE left (not center) justifies

								%    figure captions (for journals) and does not indent figure caption text.

								%

								% 9) Adjusted some spacings in the table of contents(TOC))/list-of-figures/

								%    list-of-tables so that section/table numbers will not so easily

								%    collide with the titles. Section VIII was usually the worst offender.

								%    Still doesn't right justify the section numbers, but neither does

								%    article.cls (This must be why LaTeX likes the x.y.z section numbering

								%    scheme unlike I, II, III, etc. of IEEE. )

								%    It may be "normal" as it is (left justified). sigh.

								%

								%10) Now uses "index terms" now as a heading instead of "keywords".

								%    Furthermore, the "index terms" and "abstract" headings are in bold

								%    italic. This is how IEEE does things.

								%

								%11) \thebibliography and \biography now put entries into

								%    the table of contents for you.

								%

								% *******

								%

								%

								%

								%

								%

								% *******

								% 9/2000 (JVH) changes: (now designated as V1.2)

								%

								% made some corrections to get closer to LaTeX2e

								% 20000906 Juergen v.Hagen

								% vonhagen@ihefiji.etec.uni-karlsruhe.de

								%

								% Permission to redistribute granted as of December 2000.

								% *******

								%

								%

								%

								%

								%

								% *******

								%

								% 1996 (JWD) LaTeX2e version: (now designated as V1.1)

								%

								% In the most recent TeXhax digest, there was a request for a copy of

								% IEEEtrans.sty modified to work with LaTeX2e.  I have a version I

								% modified to make it IEEEtrans.cls, which I have sent to the person

								% making the request and am now sending to you to consider posting to

								% the archives.

								% --

								% Jon Dixon

								% dixonj@colorado.edu

								% http://spot.colorado.edu/~dixonj/

								%

								%*******

								%

								%

								%

								%

								%

								%*******

								%

								% 30-August-1993 original LaTeX 2.09 version (IEEEtran.sty),

								% (now designated as V1.0):

								%

								% by Gerry Murray and Silvano Balemi

								% Automatic Control Lab, ETH Zurich, Switzerland

								% balemi@aut.ee.ethz.ch

								%

								%*******

								%

								%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

								%

								%

								%

								%

								%

								\ProvidesClass{ieeeconf}[2004/1/15 revision V1.6b by Pradeep Misra]

								%\ProvidesClass{IEEEtran}[2002/11/18 revision V1.6b by Michael Shell]

								%\typeout{-- See the "IEEEtran_HOWTO" manual for usage information.}

								%\typeout{-- The source comments contain changelog notes.}

								\NeedsTeXFormat{LaTeX2e}


								% define new needed flags to indicate document options

								% and set a few "failsafe" defaults

								\newif\if@twocolumnmode      \global\@twocolumnmodetrue

								\newif\if@draftversion       \global\@draftversionfalse

								\newif\if@draftclsmode       \global\@draftclsmodefalse

								\newif\if@draftclsmodefoot   \global\@draftclsmodefootfalse

								\newif\if@confmode           \global\@confmodefalse

								\newif\if@peerreviewoption   \global\@peerreviewoptionfalse

								\newif\if@peerreviewcaoption \global\@peerreviewcaoptionfalse


								% we HAVE to turn off technote as there is no

								% "not a tech note" option

								\newif\if@technote      \global\@technotefalse


								% V1.6 we allow the user to control whether or not the

								% font interword spacings are tuned to be more like

								% that of IEEE. The default is to tune things.

								\newif\if@fonttunesettings   \global\@fonttunesettingstrue


								% V1.6b flag to show if using a4paper

								\newif\if@IEEEusingAfourpaper      \global\@IEEEusingAfourpaperfalse


								% IEEEtran class scratch pad registers

								% dimen

								\newdimen\@IEEEtrantmpdimenA

								\newdimen\@IEEEtrantmpdimenB

								% count

								\newcount\@IEEEtrantmpcountA

								\newcount\@IEEEtrantmpcountB

								% token list

								\newtoks\@IEEEtrantmptoksA


								% we use \@IEEEptsize so that we can ID the point size (even for 9pt docs)

								% as well as LaTeX's \@ptsize to retain some compatability with some

								% external packages

								\def\@IEEEptsize{10}

								\def\@ptsize{0}

								% LaTeX does not support 9pt, so we set \@ptsize to 0 - same as that of 10pt

								\DeclareOption{9pt}{\def\@IEEEptsize{9}\def\@ptsize{0}}

								\DeclareOption{10pt}{\def\@IEEEptsize{10}\def\@ptsize{0}}

								\DeclareOption{11pt}{\def\@IEEEptsize{11}\def\@ptsize{1}}

								\DeclareOption{12pt}{\def\@IEEEptsize{12}\def\@ptsize{2}}


								% \@IEEEmarginE is the side margin for equal margins

								% \@IEEEmarginW is the wider side margin when the margins are not equal

								% NOTE: BOTH of the above margins are as they appear

								% on the paper - they are NOT offset by 1 inch

								%\DeclareOption{letterpaper}{\setlength{\paperheight}{11in}%

								%                            \setlength{\paperwidth}{8.5in}%

								%                            \def\@IEEEmarginE{0.680in}%

								%                            \def\@IEEEmarginW{0.775in}%

								%                            \@IEEEusingAfourpaperfalse}

								%

								%

								%\DeclareOption{a4paper}{\setlength{\paperheight}{297mm}%

								%                        \setlength{\paperwidth}{210mm}%

								%                        \def\@IEEEmarginE{14.32mm}%

								%                        \def\@IEEEmarginW{17mm}

								%                        \@IEEEusingAfourpapertrue}

								%

								% [2004/1/15 revision V1.6b by Pradeep Misra]

								\DeclareOption{letterpaper}{\setlength{\paperheight}{11in}%

								                            \setlength{\paperwidth}{8.5in}%

								%			    \setlength{\topmargin}{0in}%

								                            \def\@IEEEmarginE{0.75in}%

								                            \def\@IEEEmarginW{0.75in}}


								\DeclareOption{a4paper}{\setlength{\paperheight}{297mm}%

								                        \setlength{\paperwidth}{210mm}%

											\setlength{\topmargin}{-0.69in}%

								                        \def\@IEEEmarginE{13.15mm}%

								                        \def\@IEEEmarginW{0.75in}}


								\DeclareOption{oneside}{\@twosidefalse \@mparswitchfalse}

								\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue}


								\DeclareOption{onecolumn}{\global\@twocolumnmodefalse}

								% the file twocolumn.sty is not read as it changes \textwidth.

								\DeclareOption{twocolumn}{\global\@twocolumnmodetrue}


								% If the user selects draft, then this class AND any packages

								% will go into draft mode.

								\DeclareOption{draft}{\global\@draftversiontrue \global\@draftclsmodetrue

								\global\@draftclsmodefoottrue}

								% draftcls is for a draft mode which will not affect any packages

								% used by the document.

								\DeclareOption{draftcls}{\global\@draftversionfalse \global\@draftclsmodetrue

								\global\@draftclsmodefoottrue}

								% draftclsnofoot is like draftcls, but without the footer.

								\DeclareOption{draftclsnofoot}{\global\@draftversionfalse \global\@draftclsmodetrue

								\global\@draftclsmodefootfalse}

								% we provide a final option just for completeness (article.cls has one)

								\DeclareOption{final}{\global\@draftversionfalse \global\@draftclsmodefalse

								\global\@draftclsmodefootfalse}


								\DeclareOption{journal}{\global\@peerreviewoptionfalse \global\@peerreviewcaoptionfalse

								\global\@confmodefalse \global\@technotefalse}


								\DeclareOption{conference}{\global\@peerreviewoptionfalse \global\@peerreviewcaoptionfalse

								\global\@confmodetrue \global\@technotefalse}


								\DeclareOption{technote}{\global\@peerreviewoptionfalse \global\@peerreviewcaoptionfalse

								\global\@confmodefalse \global\@technotetrue}


								\DeclareOption{peerreview}{\global\@peerreviewoptiontrue \global\@peerreviewcaoptionfalse

								\global\@confmodefalse \global\@technotefalse}


								\DeclareOption{peerreviewca}{\global\@peerreviewoptiontrue \global\@peerreviewcaoptiontrue

								\global\@confmodefalse \global\@technotefalse}


								\DeclareOption{nofonttune}{\global\@fonttunesettingsfalse}


								% IEEE uses Times font, so we'll default to times.

								% These three commands make up the entire times.sty package.

								\renewcommand{\sfdefault}{phv}

								\renewcommand{\rmdefault}{ptm}

								\renewcommand{\ttdefault}{pcr}

								% enable Times now - so that all class options can see the correct font families

								\normalfont\selectfont


								% default to US letter paper, 10pt, twocolumn, one sided, final, journal

								\ExecuteOptions{letterpaper,10pt,twocolumn,oneside,final,journal}

								% overrride these defaults per user requests

								\ProcessOptions


								% we can send console reminder messages to the user here

								\AtEndDocument{\if@confmode%

								\typeout{}%

								\typeout{** Conference Paper **}%

								\typeout{Before submitting the final camera ready copy, remember to:}%

								\typeout{}%

								\typeout{ 1. Manually equalize the lengths of two columns on the last page}%

								\typeout{ of your paper;}%

								\typeout{}%

								\typeout{ 2. Ensure that any PostScript and/or PDF output post-processing}%

								\typeout{ uses only Type 1 fonts and that every step in the generation}%

								\typeout{ process uses the US letter (8.5in X 11in) paper size.}%

								\typeout{}%

								\fi}


								% warn about the use of single column other than for draft mode

								\if@twocolumnmode\else%

								  \if@draftclsmode\else%

								   \typeout{** ATTENTION: Single column mode is not normally used with IEEE publications.}%

								  \fi%

								\fi


								% V1.6, if the user is using pdflatex, go ahead and set the output paper size.

								% Otherwise, we declare the papersize via a \special for dvips.

								% We keep the tests within braces because otherwise, if not using pdflatex,

								% \pdfpageheight and \pdfpagewidth will be set to \relax - possibly affecting

								% similar tests of other packages.

								{\@ifundefined{pdfpageheight}{% not using pdflatex, setup paper size for dvips

								\if@IEEEusingAfourpaper

								\special{papersize=210mm,297mm}%

								\else

								\special{papersize=8.5in,11in}%

								\fi}%

								{% using pdftex, set paper size for pdftex

								\global\pdfpageheight\paperheight\global\pdfpagewidth\paperwidth}}


								% The idea hinted here is for LaTeX to generate markleft{} and markright{}

								% automatically for you after you enter \author{}, \journal{},

								% \journaldate{}, journalvol{}, \journalnum{}, etc.

								% However, there may be some backward compatibility issues here as

								% well as some special applications for IEEEtran.cls and special issues

								% that may require the flexible \markleft{}, \markright{} and/or \markboth{}.

								% We'll leave this as an open future suggestion.

								%\newcommand{\journal}[1]{\def\@journal{#1}}

								%\def\@journal{}


								% pointsize values

								% used with ifx to determine the document's normal size

								\def\@IEEEptsizenine{9}

								\def\@IEEEptsizeten{10}

								\def\@IEEEptsizeeleven{11}

								\def\@IEEEptsizetwelve{12}


								% FONT DEFINITIONS (No sizexx.clo file needed)

								% V1.6 revised font sizes, displayskip values and

								%      revised normalsize baselineskip to reduce underfull vbox problems

								%      on the 58pc = 696pt = 9.5in text height we want

								%      normalsize     #lines/column  baselineskip (aka leading)

								%             9pt     63             11.0476pt (truncated down)

								%            10pt     58             12pt      (exact)

								%            11pt     52             13.3846pt (truncated down)

								%            12pt     50             13.92pt   (exact)

								%


								% we need to store the nominal baselineskip for the given font size

								% in case baselinestretch ever changes.

								\newskip\@IEEEnormalsizefontbaselineskip

								\@IEEEnormalsizefontbaselineskip\baselineskip


								\ifx\@IEEEptsize\@IEEEptsizenine

								\typeout{-- This is a 9 point document.}

								\def\normalsize{\@setfontsize{\normalsize}{9}{11.0476pt}}%

								\setlength{\@IEEEnormalsizefontbaselineskip}{11.0476pt}%

								\normalsize

								\abovedisplayskip 1.5ex plus3pt minus1pt%

								\belowdisplayskip \abovedisplayskip%

								\abovedisplayshortskip 0pt plus3pt%

								\belowdisplayshortskip 1.5ex plus3pt minus1pt

								\def\small{\@setfontsize{\small}{8.5}{10pt}}

								\def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}}

								\def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}}

								\def\tiny{\@setfontsize{\tiny}{5}{6pt}}

								% sublargesize is the same as large - 10pt

								\def\sublargesize{\@setfontsize{\sublargesize}{10}{12pt}}

								\def\large{\@setfontsize{\large}{10}{12pt}}

								\def\Large{\@setfontsize{\Large}{12}{14pt}}

								\def\LARGE{\@setfontsize{\LARGE}{14}{17pt}}

								\def\huge{\@setfontsize{\huge}{17}{20pt}}

								\def\Huge{\@setfontsize{\Huge}{20}{24pt}}

								\fi


								% Check if we have selected 10 points

								\ifx\@IEEEptsize\@IEEEptsizeten

								\typeout{-- This is a 10 point document.}

								\def\normalsize{\@setfontsize{\normalsize}{10}{12.00pt}}%

								\setlength{\@IEEEnormalsizefontbaselineskip}{12pt}%

								\normalsize

								\abovedisplayskip 1.5ex plus4pt minus2pt%

								\belowdisplayskip \abovedisplayskip%

								\abovedisplayshortskip 0pt plus4pt%

								\belowdisplayshortskip 1.5ex plus4pt minus2pt

								\def\small{\@setfontsize{\small}{9}{10pt}}

								\def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}}

								\def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}}

								\def\tiny{\@setfontsize{\tiny}{5}{6pt}}

								% sublargesize is a tad smaller than large - 11pt

								\def\sublargesize{\@setfontsize{\sublargesize}{11}{13.4pt}}

								\def\large{\@setfontsize{\large}{12}{14pt}}

								\def\Large{\@setfontsize{\Large}{14}{17pt}}

								\def\LARGE{\@setfontsize{\LARGE}{16}{20pt}}

								\def\huge{\@setfontsize{\huge}{20}{24pt}}

								\def\Huge{\@setfontsize{\Huge}{24}{28pt}}

								\fi


								% Check if we have selected 11 points

								\ifx\@IEEEptsize\@IEEEptsizeeleven

								\typeout{-- This is an 11 point document.}

								\def\normalsize{\@setfontsize{\normalsize}{11}{13.3846pt}}%

								\setlength{\@IEEEnormalsizefontbaselineskip}{13.3846pt}%

								\normalsize

								\abovedisplayskip 1.5ex plus5pt minus3pt%

								\belowdisplayskip \abovedisplayskip%

								\abovedisplayshortskip 0pt plus5pt%

								\belowdisplayshortskip 1.5ex plus5pt minus3pt

								\def\small{\@setfontsize{\small}{10}{12pt}}

								\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}

								\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}

								\def\tiny{\@setfontsize{\tiny}{6}{7pt}}

								% sublargesize is the same as large - 12pt

								\def\sublargesize{\@setfontsize{\sublargesize}{12}{14pt}}

								\def\large{\@setfontsize{\large}{12}{14pt}}

								\def\Large{\@setfontsize{\Large}{14}{17pt}}

								\def\LARGE{\@setfontsize{\LARGE}{17}{20pt}}

								\def\huge{\@setfontsize{\huge}{20}{24pt}}

								\def\Huge{\@setfontsize{\Huge}{24}{28pt}}

								\fi


								% Check if we have selected 12 points

								\ifx\@IEEEptsize\@IEEEptsizetwelve

								\typeout{-- This is a 12 point document.}

								\def\normalsize{\@setfontsize{\normalsize}{12}{13.92pt}}%

								\setlength{\@IEEEnormalsizefontbaselineskip}{13.92pt}%

								\normalsize

								\abovedisplayskip 1.5ex plus6pt minus4pt%

								\belowdisplayskip \abovedisplayskip%

								\abovedisplayshortskip 0pt plus6pt%

								\belowdisplayshortskip 1.5ex plus6pt minus4pt

								\def\small{\@setfontsize{\small}{10}{12pt}}

								\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}

								\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}

								\def\tiny{\@setfontsize{\tiny}{6}{7pt}}

								% sublargesize is the same as large - 14pt

								\def\sublargesize{\@setfontsize{\sublargesize}{14}{17pt}}

								\def\large{\@setfontsize{\large}{14}{17pt}}

								\def\Large{\@setfontsize{\Large}{17}{20pt}}

								\def\LARGE{\@setfontsize{\LARGE}{20}{24pt}}

								\def\huge{\@setfontsize{\huge}{22}{26pt}}

								\def\Huge{\@setfontsize{\Huge}{24}{28pt}}

								\fi


								% V1.6 The Computer Modern Fonts will issue a substitution warning for

								% 24pt titles (24.88pt is used instead) increase the substitution

								% tolerance to turn off this warning

								\def\fontsubfuzz{.9pt}

								% However, the default (and correct) Times font will scale exactly as needed.


								% warn the user in case they forget to use the 9pt option with

								% technote

								\if@technote%

								 \ifx\@IEEEptsize\@IEEEptsizenine\else%

								  \typeout{** ATTENTION: Technotes are normally 9pt documents.}%

								 \fi%

								\fi


								% set \baselinestretch

								\def\baselinestretch{1}

								\if@draftclsmode% draft mode uses larger than normal spacing

								\def\baselinestretch{1.5} % controls line spacing for draft version

								\fi                       % some people may like 1.7 or greater

								                          % so that there will be even more space

								                          % for hand written comments


								\normalsize % make \baselinestretch take affect


								% V1.6

								% store the normalsize baselineskip

								\newskip\normalsizebaselineskip

								\normalsizebaselineskip=\baselineskip\relax

								% store the nominal value of jot

								\newskip\normaljot

								\normaljot=0.25\normalsizebaselineskip\relax


								% set \jot

								\jot=\normaljot\relax


								% abstract and keywords are in \small, except

								% for 9pt docs in which they are in \footnotesize

								% Since 9pt docs use an 8pt footnotesize, \small

								% becomes a rather awkward 8.5pt

								\let\@IEEEabskeysecsize=\small

								\ifx\@IEEEptsize\@IEEEptsizenine

								 \let\@IEEEabskeysecsize=\footnotesize

								\fi


								% V1.6, we are now going to fine tune the interword spacing

								% The default interword glue for Times under TeX appears to use a

								% nominal interword spacing of 25% (relative to the font size, i.e., 1em)

								% a maximum of 40% and a minimum of 19%.

								% For example, 10pt text uses an interword glue of:

								%

								% 2.5pt plus 1.49998pt minus 0.59998pt

								%

								% However, IEEE allows for a more generous range which reduces the need

								% for hyphenation, especially for two column text. Furthermore, IEEE

								% tends to use a little bit more nominal space between the words.

								% IEEE's interword spacing percentages appear to be:

								% 35% nominal

								% 23% minimum

								% 50% maximum

								% (They may even be using a tad more for the largest fonts such as 24pt.)

								%

								% for bold text, IEEE increases the spacing a little more:

								% 37.5% nominal

								% 23% minimum

								% 55% maximum


								% here are the interword spacing ratios we'll use

								% for medium (normal weight)

								\def\@IEEEinterspaceratioM{0.35}

								\def\@IEEEinterspaceMINratioM{0.23}

								\def\@IEEEinterspaceMAXratioM{0.50}


								% for bold

								\def\@IEEEinterspaceratioB{0.375}

								\def\@IEEEinterspaceMINratioB{0.23}

								\def\@IEEEinterspaceMAXratioB{0.55}


								% command to revise the interword spacing for the current font under TeX:

								% \fontdimen2 = nominal interword space

								% \fontdimen3 = interword stretch

								% \fontdimen4 = interword shrink

								% since all changes to the \fontdimen are global, we can enclose these commands

								% in braces to confine any font attribute or length changes

								\def\@@@IEEEsetfontdimens#1#2#3{{%

								\setlength{\@IEEEtrantmpdimenB}{\f@size pt}% grab the font size in pt, could use 1em instead.

								\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%

								\fontdimen2\font=\@IEEEtrantmpdimenA\relax

								\addtolength{\@IEEEtrantmpdimenA}{-#2\@IEEEtrantmpdimenB}%

								\fontdimen3\font=-\@IEEEtrantmpdimenA\relax

								\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%

								\addtolength{\@IEEEtrantmpdimenA}{-#3\@IEEEtrantmpdimenB}%

								\fontdimen4\font=\@IEEEtrantmpdimenA\relax}}


								% revise the interword spacing for each font weight

								\def\@@IEEEsetfontdimens{{%

								\mdseries

								\@@@IEEEsetfontdimens{\@IEEEinterspaceratioM}{\@IEEEinterspaceMAXratioM}{\@IEEEinterspaceMINratioM}%

								\bfseries

								\@@@IEEEsetfontdimens{\@IEEEinterspaceratioB}{\@IEEEinterspaceMAXratioB}{\@IEEEinterspaceMINratioB}%

								}}


								% revise the interword spacing for each font shape

								% \slshape is not often used for IEEE work and is not altered here. The \scshape caps are

								% already a tad too large in the free LaTeX fonts (as compared to what IEEE uses) so we

								% won't alter these either.

								\def\@IEEEsetfontdimens{{%

								\normalfont

								\@@IEEEsetfontdimens

								\normalfont\itshape

								\@@IEEEsetfontdimens

								}}


								% if the nofonttune class option is not given, revise the interword spacing

								% for each font size (and shape and weight). Only the \rmfamily is done here

								% as \ttfamily uses a fixed spacing and \sffamily is not used as the main

								% text of IEEE papers.

								\def\@IEEEtunefonts{%

								\if@fonttunesettings

								{\selectfont\rmfamily

								\tiny\@IEEEsetfontdimens

								\scriptsize\@IEEEsetfontdimens

								\footnotesize\@IEEEsetfontdimens

								\small\@IEEEsetfontdimens

								\normalsize\@IEEEsetfontdimens

								\sublargesize\@IEEEsetfontdimens

								\large\@IEEEsetfontdimens

								\LARGE\@IEEEsetfontdimens

								\huge\@IEEEsetfontdimens

								\Huge\@IEEEsetfontdimens}\fi}


								% if needed, revise the interword spacing now - in case IEEEtran makes any default

								% length measurements, and make sure all the default fonts are loaded

								\@IEEEtunefonts


								% and again at the start of the document in case the user loaded different fonts

								\AtBeginDocument{\@IEEEtunefonts}


								% V1.6

								% LaTeX is a little to quick to use hyphenations

								% So, we increase the penalty for their use and raise

								% the badness level that triggers an underfull hbox

								% warning. The author may still have to tweak things,

								% but the appearance will be much better "right out

								% of the box" than that under V1.5 and prior.

								% TeX default is 50

								\hyphenpenalty=750

								% If we didn't adjust the interword spacing, 2200 might be better.

								% The TeX default is 1000

								\hbadness=1350

								% IEEE does not use extra spacing after punctuation

								\frenchspacing


								% we want to maintain textheight as an integer multiple of

								% \baselineskip.  Keep \topsep in with this game plan too.

								\topskip=\baselineskip

								% set sizes and margins

								% Book typesetting is a world where point and pica (12pt) reign supreme.

								% IEEE textwidth is 21 pica. They have a colsep of 1 pica.

								% V1.6 conference mode margins

								\if@confmode

								  % [2004/10/15 revision V1.6c by Pradeep Misra]

								 \topmargin        -0.25in

								 \textheight        9.5in % The standard for conferences

								  % However, we will adjust this a  tad so that an integer number

								  % of lines will always fit on each page

								  % The baselineskip (leading) for each document point size is used

								  % to determine these values

								  % rounded up an extra 0.1pt or so to prevent trouble with any rounding errors

								 \ifx\@IEEEptsize\@IEEEptsizenine\textheight=682.0pt\fi      %9.4722in  61 lines/page

								 \ifx\@IEEEptsize\@IEEEptsizeten\textheight=684.0pt\fi       %9.5in  57 lines/page

								 \ifx\@IEEEptsize\@IEEEptsizeeleven\textheight=673.2pt\fi   %9.2611in  51 lines/page

								 \ifx\@IEEEptsize\@IEEEptsizetwelve\textheight=676.8pt\fi   %9.2473in  47 lines/page

								\else

								 \topmargin        -49.0pt

								 \textheight        58pc % = 9.63in or 696pt

								\fi


								  % [2004/1/15 revision V1.6b by Pradeep Misra]

								%\textwidth         43pc   % 2 x 21pc + 1pc = 43pc

								%\columnsep          1pc


								\textwidth         7.0in   % 2 x 21pc + 1pc = 43pc

								\columnsep         0.2in


								% IEEE MARGIN INFO and new \overrideIEEEmargins command

								% V1.6 revised margins again

								% IEEE wants the side margins to be equal under both US letter

								% and A4 paper

								%

								% However, for those of you who need to bind copies of your work

								% (for review distribution, etc.) the \overrideIEEEmargins

								% command will shift the text a tad away from the binding

								% edge.

								%

								%


								% the default side margins are equal

								\oddsidemargin    \@IEEEmarginE

								\addtolength{\oddsidemargin}{-1in}% compensate for LaTeX's 1in offset

								\evensidemargin   \@IEEEmarginE

								\addtolength{\evensidemargin}{-1in}% compensate for LaTeX's 1in offset


								% execute \overrideIEEEmargins in the preamble to make the side margin

								% near the spine slightly wider so that the paper will be much more

								% agreeable to being bound.  \overrideIEEEmargins will have no effect

								% when in draft or draftcls mode.

								\def\overrideIEEEmargins{\if@draftclsmode\relax\else%

								 \typeout{** ATTENTION: Overriding IEEE standard margins (line \the\inputlineno).}%

								 \if@twoside

								  % for double sided, odd pages have the bound side on the left

								  % make this the wide margin

								  \oddsidemargin\@IEEEmarginW

								  % and even pages have the narrow margin on the left

								  % as they are bound on the right

								  % evensidemargin is to be the narrow margin

								  % calculate the narrow margin and set evensidemargin

								  \setlength{\evensidemargin}{\paperwidth}%

								  \addtolength{\evensidemargin}{-\@IEEEmarginW}%

								  \addtolength{\evensidemargin}{-\textwidth}%

								 \else

								  % for single sided the bound side is always on the left

								  % make this the wide margin

								  \oddsidemargin\@IEEEmarginW

								  \evensidemargin\@IEEEmarginW

								 \fi

								 \addtolength{\oddsidemargin}{-1.0in}%  compensate for LaTeX's 1in offset

								 \addtolength{\evensidemargin}{-1.0in}%

								\fi}


								\parindent        1.0em


								% conference papers do not have headers, other papers need

								% to reserve space for them

								\if@confmode

								\headsep          0in

								\headheight       0in

								\else

								\headsep          0.25in

								\headheight       12pt

								\fi


								% V1.6, if things get too close, go ahead and let them touch

								\lineskip            0pt

								\normallineskip      0pt

								\lineskiplimit       0pt

								\normallineskiplimit 0pt


								% The distance from the lower edge of the text body to the

								% footline

								\footskip 0.4in


								% normally zero, should be relative to font height.

								% put in a little rubber to help stop some bad breaks (underfull vboxes)

								\parskip 0ex plus 0.2ex minus 0.1ex


								% draft mode settings override that of all other modes

								% provides a nice 1" margin all around the paper and extra

								% space between the lines for editor's comments

								\if@draftclsmode

								\headsep          0.25in

								\headheight       12pt

								% want 1" from top of paper to text

								\setlength{\topmargin}{-\headsep}%

								\addtolength{\topmargin}{-\headheight}%


								% we want 1in side margins regardless of paper type

								\oddsidemargin      0in

								\evensidemargin     0in


								% set the text width - start with the entire page

								\setlength{\textwidth}{\paperwidth}%

								% subtract for the 1" top/bottom margins

								\addtolength{\textwidth}{-2.0in}%

								% give them a textheight that won't have underfull

								% vbox problems, but can't help them if they later change

								% baselinestretch from its default

								\setlength{\textheight}{\paperheight}%

								\addtolength{\textheight}{-2.0in}%

								% subtract of first line taken by \topskip

								\addtolength{\textheight}{-1\topskip}%

								% now digitize \textheight so that the length after

								% the first line is an integer multiple of  \baselineskip

								% to cut down on underfull vbox errors in draft mode

								\divide\textheight  by \baselineskip%

								\multiply\textheight  by \baselineskip%

								% add back the first line

								\addtolength{\textheight}{\topskip}%

								\fi


								% margin note stuff

								\marginparsep      10pt

								\marginparwidth    20pt

								\marginparpush     25pt


								% LIST SPACING CONTROLS


								% Controls the amount of EXTRA spacing

								% above and below \trivlist

								% Both \list and IED lists override this.

								% However, \trivlist will use this as will most

								% things built from \trivlist like the \center

								% environment.

								\topsep           0.5\baselineskip


								% Controls the additional spacing around lists preceded

								% or followed by blank lines. IEEE does not increase

								% spacing before or after paragraphs so it is set to zero.

								% \z@ is the same as zero, but faster.

								\partopsep          \z@


								% Controls the spacing between paragraphs in lists.

								% IEEE does not increase spacing before or after paragraphs

								% so this is also zero.

								% With IEEEtran.cls, global changes to

								% this value DO affect lists (but not IED lists).

								\parsep             \z@


								% Controls the extra spacing between list items.

								% IEEE does not put extra spacing between items.

								% With IEEEtran.cls, global changes to this value DO affect

								% lists (but not IED lists).

								\itemsep            \z@


								% \itemindent is the amount to indent the FIRST line of a list

								% item. It is auto set to zero within the \list environment. To alter

								% it, you have to do so when you call the \list.

								% However, IEEE uses this for the theorem environment

								% There is an alternative value for this near \leftmargini below

								\itemindent         -1em


								% \leftmargin, the spacing from the left margin of the main text to

								% the left of the main body of a list item is set by \list.

								% Hence this statement does nothing for lists.

								% But, quote and verse do use it for indention.


								\leftmargin         2em


								% we retain this stuff from the older IEEEtran.cls so that \list

								% will work the same way as before. However, itemize, enumerate and

								% description (IED) could care less about what these are as they

								% all are overridden.

								\leftmargini        2em

								%\itemindent         2em  % Alternative values: sometimes used.

								%\leftmargini        0em

								\leftmarginii       1em

								\leftmarginiii    1.5em

								\leftmarginiv     1.5em

								\leftmarginv      1.0em

								\leftmarginvi     1.0em

								\labelsep         0.5em

								\labelwidth         \z@


								% The old IEEEtran.cls behavior of \list is retained.

								% However, the new V1.3 IED list environments override all the

								% @list stuff (\@listX is called within \list for the

								% appropriate level just before the user's list_decl is called).

								% \topsep is now 2pt as IEEE puts a little extra space around

								% lists - used by those non-IED macros that depend on \list.

								% Note that \parsep and \itemsep are not redefined as in

								% the sizexx.clo \@listX (which article.cls uses) so global changes

								% of these values DO affect \list

								%

								\def\@listi{\leftmargin\leftmargini \topsep 2pt plus 1pt minus 1pt}

								\let\@listI\@listi

								\def\@listii{\leftmargin\leftmarginii\labelwidth\leftmarginii%

								    \advance\labelwidth-\labelsep \topsep 2pt}

								\def\@listiii{\leftmargin\leftmarginiii\labelwidth\leftmarginiii%

								    \advance\labelwidth-\labelsep \topsep 2pt}

								\def\@listiv{\leftmargin\leftmarginiv\labelwidth\leftmarginiv%

								    \advance\labelwidth-\labelsep \topsep 2pt}

								\def\@listv{\leftmargin\leftmarginv\labelwidth\leftmarginv%

								    \advance\labelwidth-\labelsep \topsep 2pt}

								\def\@listvi{\leftmargin\leftmarginvi\labelwidth\leftmarginvi%

								    \advance\labelwidth-\labelsep \topsep 2pt}


								% IEEE uses 5) not 5.

								\def\labelenumi{\theenumi)}     \def\theenumi{\arabic{enumi}}


								% IEEE uses a) not (a)

								\def\labelenumii{\theenumii)}  \def\theenumii{\alph{enumii}}


								% IEEE uses iii) not iii.

								\def\labelenumiii{\theenumiii)} \def\theenumiii{\roman{enumiii}}


								% IEEE uses A) not A.

								\def\labelenumiv{\theenumiv)}   \def\theenumiv{\Alph{enumiv}}


								% exactly the same as in article.cls

								\def\p@enumii{\theenumi}

								\def\p@enumiii{\theenumi(\theenumii)}

								\def\p@enumiv{\p@enumiii\theenumiii}


								% itemized list label styles

								\def\labelitemi{$\scriptstyle\bullet$}

								\def\labelitemii{\textbf{--}}

								\def\labelitemiii{$\ast$}

								\def\labelitemiv{$\cdot$}


								% IEEEtran.cls version numbers, provided as of V1.3

								% These values serve as a way a .tex file can

								% determine if the new features are provided.

								% The version number of this IEEEtrans.cls can be obtained from

								% these values. i.e., V1.4

								% KEEP THESE AS INTEGERS! i.e., NO {4a} or anything like that-

								% (no need to enumerate "a" minor changes here)

								\def\IEEEtransversionmajor{1}

								\def\IEEEtransversionminor{6}


								% **** V1.3 ENHANCEMENTS ****

								% Itemize, Enumerate and Description (IED) List Controls

								% ***************************

								%

								%

								% IEEE seems to use at least two different values by

								% which ITEMIZED list labels are indented to the right

								% For The Journal of Lightwave Technology (JLT) and The Journal

								% on Selected Areas in Communications (JSAC), they tend to use

								% an indention equal to \parindent. For Transactions on Communications

								% they tend to indent ITEMIZED lists a little more--- 1.3\parindent.

								% We'll provide both values here for you so that you can choose

								% which one you like in your document using a command such as:

								% setlength{\IEEEilabelindent}{\IEEEilabelindentB}

								\newdimen\IEEEilabelindentA

								\IEEEilabelindentA \parindent


								\newdimen\IEEEilabelindentB

								\IEEEilabelindentB 1.3\parindent

								% However, we'll default to using \parindent

								% which makes more sense to me

								\newdimen\IEEEilabelindent

								\IEEEilabelindent \IEEEilabelindentA


								% This controls the default amount the enumerated list labels

								% are indented to the right.

								% Normally, this is the same as the paragraph indention

								\newdimen\IEEEelabelindent

								\IEEEelabelindent \parindent


								% This controls the default amount the description list labels

								% are indented to the right.

								% Normally, this is the same as the paragraph indention

								\newdimen\IEEEdlabelindent

								\IEEEdlabelindent \parindent


								% This is the value actually used within the IED lists.

								% The IED environments automatically set its value to

								% one of the three values above, so global changes do

								% not have any effect

								\newdimen\labelindent

								\labelindent \parindent


								% The actual amount labels will be indented is

								% \labelindent multiplied by the factor below

								% corresponding to the level of nesting depth

								% This provides a means by which the user can

								% alter the effective \labelindent for deeper

								% levels

								% There may not be such a thing as correct "standard IEEE"

								% values. What IEEE actually does may depend on the specific

								% circumstances.

								% The first list level almost always has full indention.

								% The second levels I've seen have only 75% of the normal indentation

								% Three level or greater nestings are very rare. I am guessing

								% that they don't use any indentation.

								\def\IEEElabelindentfactori{1.0}   % almost always one

								\def\IEEElabelindentfactorii{0.75} % 0.0 or 1.0 may be used in some cases

								\def\IEEElabelindentfactoriii{0.0} % 0.75? 0.5? 0.0?

								\def\IEEElabelindentfactoriv{0.0}

								\def\IEEElabelindentfactorv{0.0}

								\def\IEEElabelindentfactorvi{0.0}


								% value actually used within IED lists, it is auto

								% set to one of the 6 values above

								% global changes here have no effect

								\def\labelindentfactor{1.0}


								% This controls the default spacing between the end of the IED

								% list labels and the list text, when normal text is used for

								% the labels.

								\newdimen\IEEEiednormlabelsep

								\IEEEiednormlabelsep 0.6em


								% This controls the default spacing between the end of the IED

								% list labels and the list text, when math symbols are used for

								% the labels (nomenclature lists). IEEE usually increases the

								% spacing in these cases

								\newdimen\IEEEiedmathlabelsep

								\IEEEiedmathlabelsep 1.2em


								% This controls the extra vertical separation put above and

								% below each IED list. IEEE usually puts a little extra spacing

								% around each list. However, this spacing is barely noticeable.

								\newskip\IEEEiedtopsep

								\IEEEiedtopsep 2pt plus 1pt minus 1pt


								% This command is executed within each IED list environment

								% at the beginning of the list. You can use this to set the

								% parameters for some/all your IED list(s) without disturbing

								% global parameters that affect things other than lists.

								% i.e., renewcommand{\iedlistdecl}{\setlength{\labelsep}{5em}}

								% will alter the \labelsep for the next list(s) until

								% \iedlistdecl is redefined.

								\def\iedlistdecl{\relax}


								% This command provides an easy way to set \leftmargin based

								% on the \labelwidth, \labelsep and the argument \labelindent

								% Usage: \calcleftmargin{width-to-indent-the-label}

								% output is in the \leftmargin variable, i.e., effectively:

								% \leftmargin = argument + \labelwidth + \labelsep

								% Note controlled spacing here, shield end of lines with %

								\def\calcleftmargin#1{\setlength{\leftmargin}{#1}%

								\addtolength{\leftmargin}{\labelwidth}%

								\addtolength{\leftmargin}{\labelsep}}


								% This command provides an easy way to set \labelwidth to the

								% width of the given text. It is the same as

								% \settowidth{\labelwidth}{label-text}

								% and useful as a shorter alternative.

								% Typically used to set \labelwidth to be the width

								% of the longest label in the list

								\def\setlabelwidth#1{\settowidth{\labelwidth}{#1}}


								% When this command is executed, IED lists will use the

								% IEEEiedmathlabelsep label separation rather than the normal

								% spacing. To have an effect, this command must be executed via

								% the \iedlistdecl or within the option of the IED list

								% environments.

								\def\usemathlabelsep{\setlength{\labelsep}{\IEEEiedmathlabelsep}}


								% A flag which controls whether the IED lists automatically

								% calculate \leftmargin from \labelindent, \labelwidth and \labelsep

								% Useful if you want to specify your own \leftmargin

								% This flag must be set (\nocalcleftmargintrue or \nocalcleftmarginfalse)

								% via the \iedlistdecl or within the option of the IED list

								% environments to have an effect.

								\newif\ifnocalcleftmargin

								\nocalcleftmarginfalse


								% A flag which controls whether \labelindent is multiplied by

								% the \labelindentfactor for each list level.

								% This flag must be set via the \iedlistdecl or within the option

								% of the IED list environments to have an effect.

								\newif\ifnolabelindentfactor

								\nolabelindentfactorfalse


								% internal variable to indicate type of IED label

								% justification

								% 0 - left; 1 - center; 2 - right

								\def\@iedjustify{0}


								% commands to allow the user to control IED

								% label justifications. Use these commands within

								% the IED environment option or in the \iedlistdecl

								% Note that changing the normal list justifications

								% is nonstandard and IEEE may not like it if you do so!

								% I include these commands as they may be helpful to

								% those who are using these enhanced list controls for

								% other non-IEEE related LaTeX work.

								% itemize and enumerate automatically default to right

								% justification, description defaults to left.

								\def\iedlabeljustifyl{\def\@iedjustify{0}}%left

								\def\iedlabeljustifyc{\def\@iedjustify{1}}%center

								\def\iedlabeljustifyr{\def\@iedjustify{2}}%right


								% commands to save to and restore from the list parameter copies

								% this allows us to set all the list parameters within

								% the list_decl and prevent \list (and its \@list)

								% from overriding any of our parameters

								% V1.6 use \edefs instead of dimen's to conserve dimen registers

								% Note controlled spacing here, shield end of lines with %

								\def\@IEEEsavelistparams{\edef\@IEEEiedtopsep{\the\topsep}%

								\edef\@IEEEiedlabelwidth{\the\labelwidth}%

								\edef\@IEEEiedlabelsep{\the\labelsep}%

								\edef\@IEEEiedleftmargin{\the\leftmargin}%

								\edef\@IEEEiedpartopsep{\the\partopsep}%

								\edef\@IEEEiedparsep{\the\parsep}%

								\edef\@IEEEieditemsep{\the\itemsep}%

								\edef\@IEEEiedrightmargin{\the\rightmargin}%

								\edef\@IEEEiedlistparindent{\the\listparindent}%

								\edef\@IEEEieditemindent{\the\itemindent}}


								% Note controlled spacing here

								\def\@IEEErestorelistparams{\topsep\@IEEEiedtopsep\relax%

								\labelwidth\@IEEEiedlabelwidth\relax%

								\labelsep\@IEEEiedlabelsep\relax%

								\leftmargin\@IEEEiedleftmargin\relax%

								\partopsep\@IEEEiedpartopsep\relax%

								\parsep\@IEEEiedparsep\relax%

								\itemsep\@IEEEieditemsep\relax%

								\rightmargin\@IEEEiedrightmargin\relax%

								\listparindent\@IEEEiedlistparindent\relax%

								\itemindent\@IEEEieditemindent\relax}


								% v1.6b provide original LaTeX IED list environments

								% note that latex.ltx defines \itemize and \enumerate, but not \description

								% which must be created by the base classes

								% save original LaTeX itemize and enumerate

								\let\LaTeXitemize\itemize

								\let\endLaTeXitemize\enditemize

								\let\LaTeXenumerate\enumerate

								\let\endLaTeXenumerate\endenumerate


								% provide original LaTeX description environment from article.cls

								\newenvironment{LaTeXdescription}

								               {\list{}{\labelwidth\z@ \itemindent-\leftmargin

								                        \let\makelabel\descriptionlabel}}

								               {\endlist}

								\newcommand*\descriptionlabel[1]{\hspace\labelsep

								                                 \normalfont\bfseries #1}


								% override LaTeX's default IED lists

								\def\itemize{\@IEEEitemize}

								\def\enditemize{\@endIEEEitemize}

								\def\enumerate{\@IEEEenumerate}

								\def\endenumerate{\@endIEEEenumerate}

								\def\description{\@IEEEdescription}

								\def\enddescription{\@endIEEEdescription}


								% provide the user with aliases - may help those using packages that

								% override itemize, enumerate, or description

								\def\IEEEitemize{\@IEEEitemize}

								\def\endIEEEitemize{\@endIEEEitemize}

								\def\IEEEenumerate{\@IEEEenumerate}

								\def\endIEEEenumerate{\@endIEEEenumerate}

								\def\IEEEdescription{\@IEEEdescription}

								\def\endIEEEdescription{\@endIEEEdescription}


								% V1.6 we want to keep the IEEEtran IED list definitions as our own internal

								% commands so they are protected against redefinition

								\def\@IEEEitemize{\@ifnextchar[{\@@IEEEitemize}{\@@IEEEitemize[\relax]}}

								\def\@IEEEenumerate{\@ifnextchar[{\@@IEEEenumerate}{\@@IEEEenumerate[\relax]}}

								\def\@IEEEdescription{\@ifnextchar[{\@@IEEEdescription}{\@@IEEEdescription[\relax]}}

								\def\@endIEEEitemize{\endlist}

								\def\@endIEEEenumerate{\endlist}

								\def\@endIEEEdescription{\endlist}


								% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS

								% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS

								% IEEEtran itemized list MDS 1/2001

								% Note controlled spacing here, shield end of lines with %

								\def\@@IEEEitemize[#1]{%

								                \ifnum\@itemdepth>3\relax\@toodeep\else%

								                \ifnum\@listdepth>5\relax\@toodeep\else%

								                \advance\@itemdepth\@ne%

								                \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%

								                % get the labelindentfactor for this level

								                \advance\@listdepth\@ne% we need to know what the level WILL be

								                \edef\labelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%

								                \advance\@listdepth-\@ne% undo our increment

								                \def\@iedjustify{2}% right justified labels are default

								                % set other defaults

								                \nocalcleftmarginfalse%

								                \nolabelindentfactorfalse%

								                \topsep\IEEEiedtopsep%

								                \labelindent\IEEEilabelindent%

								                \labelsep\IEEEiednormlabelsep%

								                \partopsep 0ex%

								                \parsep 0ex%

								                \itemsep 0ex%

								                \rightmargin 0em%

								                \listparindent 0em%

								                \itemindent 0em%

								                % calculate the label width

								                % the user can override this later if

								                % they specified a \labelwidth

								                \settowidth{\labelwidth}{\csname labelitem\romannumeral\the\@itemdepth\endcsname}%

								                \@IEEEsavelistparams% save our list parameters

								                \list{\csname\@itemitem\endcsname}{%

								                \@IEEErestorelistparams% override any list{} changes

								                                       % to our globals

								                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel

								                \iedlistdecl% let user alter parameters

								                #1\relax%

								                % If the user has requested not to use the

								                % labelindent factor, don't revise \labelindent

								                \ifnolabelindentfactor\relax%

								                \else\labelindent=\labelindentfactor\labelindent%

								                \fi%

								                % Unless the user has requested otherwise,

								                % calculate our left margin based

								                % on \labelindent, \labelwidth and

								                % \labelsep

								                \ifnocalcleftmargin\relax%

								                \else\calcleftmargin{\labelindent}%

								                \fi}\fi\fi}%


								% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS

								% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS

								% IEEEtran enumerate list MDS 1/2001

								% Note controlled spacing here, shield end of lines with %

								\def\@@IEEEenumerate[#1]{%

								                \ifnum\@enumdepth>3\relax\@toodeep\else%

								                \ifnum\@listdepth>5\relax\@toodeep\else%

								                \advance\@enumdepth\@ne%

								                \edef\@enumctr{enum\romannumeral\the\@enumdepth}%

								                % get the labelindentfactor for this level

								                \advance\@listdepth\@ne% we need to know what the level WILL be

								                \edef\labelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%

								                \advance\@listdepth-\@ne% undo our increment

								                \def\@iedjustify{2}% right justified labels are default

								                % set other defaults

								                \nocalcleftmarginfalse%

								                \nolabelindentfactorfalse%

								                \topsep\IEEEiedtopsep%

								                \labelindent\IEEEelabelindent%

								                \labelsep\IEEEiednormlabelsep%

								                \partopsep 0ex%

								                \parsep 0ex%

								                \itemsep 0ex%

								                \rightmargin 0em%

								                \listparindent 0em%

								                \itemindent 0em%

								                % calculate the label width

								                % We'll set it to the width suitable for all labels using

								                % normalfont 1) to 9)

								                % The user can override this later

								                \settowidth{\labelwidth}{9)}%

								                \@IEEEsavelistparams% save our list parameters

								                \list{\csname label\@enumctr\endcsname}{\usecounter{\@enumctr}%

								                \@IEEErestorelistparams% override any list{} changes

								                                       % to our globals

								                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel

								                \iedlistdecl% let user alter parameters

								                #1\relax%

								                % If the user has requested not to use the

								                % labelindent factor, don't revise \labelindent

								                \ifnolabelindentfactor\relax%

								                \else\labelindent=\labelindentfactor\labelindent%

								                \fi%

								                % Unless the user has requested otherwise,

								                % calculate our left margin based

								                % on \labelindent, \labelwidth and

								                % \labelsep

								                \ifnocalcleftmargin\relax%

								                \else\calcleftmargin{\labelindent}%

								                \fi}\fi\fi}%


								% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS

								% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS

								% IEEEtran description list MDS 1/2001

								% Note controlled spacing here, shield end of lines with %

								\def\@@IEEEdescription[#1]{%

								                \ifnum\@listdepth>5\relax\@toodeep\else%

								                % get the labelindentfactor for this level

								                \advance\@listdepth\@ne% we need to know what the level WILL be

								                \edef\labelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%

								                \advance\@listdepth-\@ne% undo our increment

								                \def\@iedjustify{0}% left justified labels are default

								                % set other defaults

								                \nocalcleftmarginfalse%

								                \nolabelindentfactorfalse%

								                \topsep\IEEEiedtopsep%

								                \labelindent\IEEEdlabelindent%

								                % assume normal labelsep

								                \labelsep\IEEEiednormlabelsep%

								                \partopsep 0ex%

								                \parsep 0ex%

								                \itemsep 0ex%

								                \rightmargin 0em%

								                \listparindent 0em%

								                \itemindent 0em%

								                % Bogus label width in case the user forgets

								                % to set it.

								                % TIP: If you want to see what a variable's width is you

								                % can use the TeX command \showthe\width-variable to

								                % display it on the screen during compilation

								                % (This might be helpful to know when you need to find out

								                % which label is the widest)

								                \settowidth{\labelwidth}{Hello}%

								                \@IEEEsavelistparams% save our list parameters

								                \list{}{\@IEEErestorelistparams% override any list{} changes

								                                               % to our globals

								                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel

								                \iedlistdecl% let user alter parameters

								                #1\relax%

								                % If the user has requested not to use the

								                % labelindent factor, don't revise \labelindent

								                \ifnolabelindentfactor\relax%

								                \else\labelindent=\labelindentfactor\labelindent%

								                \fi%

								                % Unless the user has requested otherwise,

								                % calculate our left margin based

								                % on \labelindent, \labelwidth and

								                % \labelsep

								                \ifnocalcleftmargin\relax%

								                \else\calcleftmargin{\labelindent}\relax%

								                \fi}\fi}


								% v1.6b we use one makelabel that does justification as needed.

								\def\@IEEEiedmakelabel#1{\relax\if\@iedjustify 0\relax

								\makebox[\labelwidth][l]{\normalfont #1}\else

								\if\@iedjustify 1\relax

								\makebox[\labelwidth][c]{\normalfont #1}\else

								\makebox[\labelwidth][r]{\normalfont #1}\fi\fi}


								% VERSE and QUOTE

								\def\verse{\let\\=\@centercr

								    \list{}{\itemsep\z@ \itemindent -1.5em \listparindent \itemindent

								    \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}

								\let\endverse\endlist

								\def\quotation{\list{}{\listparindent 1.5em \itemindent\listparindent

								    \rightmargin\leftmargin \parsep 0pt plus 1pt}\item[]}

								\let\endquotation=\endlist

								\def\quote{\list{}{\rightmargin\leftmargin}\item[]}

								\let\endquote=\endlist


								% \titlepage

								% provided only for backward compatibility. \maketitle is the correct

								% way to create the title page.

								\newif\if@restonecol

								\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn

								    \else \newpage \fi \thispagestyle{empty}\c@page\z@}

								\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}


								% standard values from article.cls

								\arraycolsep     5pt

								\arrayrulewidth .4pt

								\doublerulesep   2pt


								\tabcolsep       6pt

								\tabbingsep      0.5em


								%% FOOTNOTES

								%

								%\skip\footins 10pt plus 4pt minus 2pt

								% V1.6 respond to changes in font size

								% space added above the footnotes (if present)

								\skip\footins 0.9\baselineskip  plus 0.4\baselineskip  minus 0.2\baselineskip


								% V1.6, we need to make \footnotesep responsive to changes

								% in \baselineskip or strange spacings will result when in

								% draft mode. Here is a little LaTeX secret - \footnotesep

								% determines the height of an invisible strut that is placed

								% *above* the baseline of footnotes after the first. Since

								% LaTeX considers the space for characters to be 0.7/baselineskip

								% above the baseline and 0.3/baselineskip below it, we need to

								% use 0.7/baselineskip as a \footnotesep to maintain equal spacing

								% between all the lines of the footnotes. IEEE often uses a tad

								% more, so use 0.8\baselineskip. This slightly larger value also helps

								% the text to clear the footnote marks. Note that \thanks now uses

								% its own value of \footnotesep.

								{\footnotesize

								\global\footnotesep 0.8\baselineskip}


								\skip\@mpfootins = \skip\footins

								\fboxsep = 3pt

								\fboxrule = .4pt

								% V1.6 use 1em, the use LaTeX2e's \@makefnmark

								% Note that IEEE normally *left* aligns the footnote marks, so we don't need

								% box resizing tricks here.

								\long\def\@makefntext#1{\parindent 1em\indent\hbox{\@makefnmark}#1}% V1.6 use 1em


								\def\footnoterule{}


								% V1.6 do not allow LaTeX to break a footnote across multiple pages

								\interfootnotelinepenalty=10000


								% V1.6 discourage breaks within equations

								% Note that amsmath normally sets this to 10000,

								% but LaTeX2e normally uses 100.

								\interdisplaylinepenalty=2500


								\if@technote

								   \setcounter{secnumdepth}{3}

								\else

								   \setcounter{secnumdepth}{4}

								\fi


								\newcounter{section}

								\newcounter{subsection}[section]

								\newcounter{subsubsection}[subsection]

								\newcounter{paragraph}[subsubsection]


								% used only by IEEEtran's IEEEeqnarray as other packages may

								% have their own, different, implementations

								\newcounter{IEEEsubequation}[equation]


								% as shown when called by user from \ref, \label and in table of contents

								\def\thesection{\Roman{section}}                             % I

								\def\thesubsection{\thesection-\Alph{subsection}}            % I-A

								\def\thesubsubsection{\thesubsection.\arabic{subsubsection}} % I-A.1

								\def\theparagraph{\thesubsubsection.\alph{paragraph}}        % I-A.1.a

								\def\theequation{\arabic{equation}}                          % 1

								\def\theIEEEsubequation{\theequation\alph{IEEEsubequation}}  % 1a (used only by IEEEtran's IEEEeqnarray)


								% Main text forms (how shown in main text headings)

								% V1.6, using \thesection in \thesectiondis allows changes

								% in the former to automatically appear in the latter

								\def\thesectiondis{\thesection.}                   % I.

								\def\thesubsectiondis{\Alph{subsection}.}          % B.

								\def\thesubsubsectiondis{\arabic{subsubsection})}  % 3)

								\def\theparagraphdis{\alph{paragraph})}            % d)

								% just like LaTeX2e's \@eqnnum

								\def\theequationdis{{\normalfont \normalcolor (\theequation)}}% (1)

								% IEEEsubequation used only by IEEEtran's IEEEeqnarray

								\def\theIEEEsubequationdis{{\normalfont \normalcolor (\theIEEEsubequation)}}% (1a)

								% redirect LaTeX2e's equation number display and all that depend on

								% it, through IEEEtran's \theequationdis

								\def\@eqnnum{\theequationdis}


								% LIST OF FIGURES AND TABLES AND TABLE OF CONTENTS

								%

								\def\@pnumwidth{1.55em}

								\def\@tocrmarg{2.55em}

								\def\@dotsep{4.5}

								\setcounter{tocdepth}{3}


								% adjusted some spacings here so that section numbers will not easily

								% collide with the section titles.

								% VIII; VIII-A; and VIII-A.1 are usually the worst offenders.

								% MDS 1/2001

								\def\tableofcontents{\section*{Contents}\@starttoc{toc}}

								\def\l@section#1#2{\addpenalty{\@secpenalty}\addvspace{1.0em plus 1pt}%

								    \@tempdima 2.75em \begingroup \parindent \z@ \rightskip \@pnumwidth%

								    \parfillskip-\@pnumwidth {\bfseries\leavevmode #1}\hfil\hbox to\@pnumwidth{\hss #2}\par%

								    \endgroup}

								% argument format #1:level, #2:labelindent,#3:labelsep

								\def\l@subsection{\@dottedtocline{2}{2.75em}{3.75em}}

								\def\l@subsubsection{\@dottedtocline{3}{6.5em}{4.5em}}

								% must provide \l@ defs for ALL sublevels EVEN if tocdepth

								% is such as they will not appear in the table of contents

								% these defs are how TOC knows what level these things are!

								\def\l@paragraph{\@dottedtocline{4}{6.5em}{5.5em}}

								\def\l@subparagraph{\@dottedtocline{5}{6.5em}{6.5em}}

								\def\listoffigures{\section*{List of Figures}\@starttoc{lof}}

								\def\l@figure{\@dottedtocline{1}{0em}{2.75em}}

								\def\listoftables{\section*{List of Tables}\@starttoc{lot}}

								\let\l@table\l@figure


								%% Definitions for floats

								%%

								%% Normal Floats

								\floatsep 1\baselineskip plus  0.2\baselineskip minus  0.2\baselineskip

								\textfloatsep 1.7\baselineskip plus  0.2\baselineskip minus  0.4\baselineskip

								\@fptop 0pt plus 1fil

								\@fpsep 0.75\baselineskip plus 2fil

								\@fpbot 0pt plus 1fil

								\def\topfraction{1.0}

								\def\bottomfraction{.4}

								\def\floatpagefraction{0.8}

								\def\textfraction{.2}


								%% Double Column Floats

								\dblfloatsep 1\baselineskip plus  0.2\baselineskip minus  0.2\baselineskip


								\dbltextfloatsep 1.7\baselineskip plus  0.2\baselineskip minus  0.4\baselineskip

								% Note that it would be nice if the rubber here actually worked in LaTeX2e.

								% There is a long standing limitation in LaTeX, first discovered (to the best

								% of my knowledge) by Alan Jeffrey in 1992. LaTeX ignores the stretchable

								% portion of \dbltextfloatsep, and as a result, double column figures can and

								% do result in an non-integer number of lines in the main text columns with

								% underfull vbox errors as a consequence. A post to comp.text.tex

								% by Donald Arseneau confirms that this had not yet been fixed in 1998.

								% IEEEtran V1.6 will fix this problem for you in the titles, but it doesn't

								% protect you from other double floats. Happy vspace'ing.


								\@dblfptop 0pt plus 1fil

								\@dblfpsep 0.75\baselineskip plus 2fil

								\@dblfpbot 0pt plus 1fil

								\def\dbltopfraction{1.0}

								\def\dblfloatpagefraction{0.8}

								\setcounter{dbltopnumber}{4}


								\intextsep 1\baselineskip plus 0.2\baselineskip minus  0.2\baselineskip

								\setcounter{topnumber}{2}

								\setcounter{bottomnumber}{2}

								\setcounter{totalnumber}{4}


								%% redefine CAPTION

								% V1.4 add user control for short figure caption justification

								\newif\ifcenterfigcaptions


								% V1.6 set the default according to conference mode

								\if@confmode

								\centerfigcaptionstrue

								\else

								\centerfigcaptionsfalse

								\fi


								% article class provides these, we should too.

								\newlength\abovecaptionskip

								\newlength\belowcaptionskip

								% but only \abovecaptionskip is used above figure captions and *below* table

								% captions

								\setlength\abovecaptionskip{0.5\baselineskip}

								\setlength\belowcaptionskip{0pt}

								% V1.6 create hooks in case the caption spacing ever needs to be

								% overridden by a user

								\def\@IEEEfigurecaptionsepspace{\vskip\abovecaptionskip\relax}%

								\def\@IEEEtablecaptionsepspace{\vskip\abovecaptionskip\relax}%


								% 1.6b revise caption system so that \@makecaption uses two arguments

								% as with LaTeX2e. Otherwise, there will be problems when using hyperref.

								\def\@IEEEtablestring{table}


								\long\def\@makecaption#1#2{%

								% test if is a for a figure or table

								\ifx\@captype\@IEEEtablestring%

								% if a table, do table caption

								\begin{center}{\footnotesize #1}\\{\footnotesize\scshape #2}\end{center}%

								\@IEEEtablecaptionsepspace% V1.6 was a hard coded 8pt

								% if not a table, format it as a figure

								\else

								\@IEEEfigurecaptionsepspace% V1.6 was a hard coded 5pt

								% 3/2001 use footnotesize, not small; use two nonbreaking spaces, not one

								\setbox\@tempboxa\hbox{\footnotesize #1.~~ #2}%

								\ifdim \wd\@tempboxa >\hsize%

								% if caption is longer than a line, let it wrap around

								\setbox\@tempboxa\hbox{\footnotesize #1.~~ }%

								\parbox[t]{\hsize}{\footnotesize \noindent\unhbox\@tempboxa#2}%

								% if caption is shorter than a line,

								% allow user to control short figure caption justification (left or center)

								\else%

								\ifcenterfigcaptions \hbox to\hsize{\footnotesize\hfil\box\@tempboxa\hfil}%

								\else \hbox to\hsize{\footnotesize\box\@tempboxa\hfil}%

								\fi\fi\fi}


								\newcounter{figure}

								\def\thefigure{\@arabic\c@figure}

								\def\fps@figure{tbp}

								\def\ftype@figure{1}

								\def\ext@figure{lof}

								\def\fnum@figure{Fig.~\thefigure}

								\def\figure{\@float{figure}}

								\let\endfigure\end@float

								\@namedef{figure*}{\@dblfloat{figure}}

								\@namedef{endfigure*}{\end@dblfloat}

								\newcounter{table}

								\def\thetable{\@Roman\c@table}

								\def\fps@table{tbp}

								\def\ftype@table{2}

								\def\ext@table{lot}

								\def\fnum@table{TABLE~\thetable}

								% V1.6 IEEE uses 8pt text for tables

								% to default to footnotesize, we hack into LaTeX2e's \@floatboxreset and pray

								\def\table{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@float{table}}

								\let\endtable\end@float

								% v1.6b double column tables need to default to footnotesize as well.

								\@namedef{table*}{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@dblfloat{table}}

								\@namedef{endtable*}{\end@dblfloat}


								%%

								%% START OF IEEEeqnarry DEFINITIONS

								%%

								%% Inspired by the concepts, examples, and previous works of LaTeX

								%% coders and developers such as Donald Arseneau, Fred Bartlett,

								%% David Carlisle, Tony Liu, Frank Mittelbach, Piet van Oostrum,

								%% Roland Winkler and Mark Wooding.

								%% I don't make the claim that my work here is even near their calibre. ;)


								% hook to allow easy changeover to IEEEtran.cls/tools.sty error reporting

								\def\@IEEEclspkgerror{\ClassError{IEEEtran}}


								\newif\if@IEEEeqnarraystarform% flag to indicate if the environment was called as the star form

								\@IEEEeqnarraystarformfalse


								\newif\if@advanceIEEEeqncolcnt% tracks if the environment should advance the col counter

								% allows a way to make an \IEEEeqnarraybox that can be used within an \IEEEeqnarray

								% used by IEEEeqnarraymulticol so that it can work properly in both

								\@advanceIEEEeqncolcnttrue


								\newcount\@IEEEeqnnumcols % tracks how many IEEEeqnarray cols are defined

								\newcount\@IEEEeqncolcnt  % tracks how many IEEEeqnarray cols the user actually used


								% The default math style used by the columns

								\def\IEEEeqnarraymathstyle{\displaystyle}

								% The default text style used by the columns

								% default to using the current font

								\def\IEEEeqnarraytextstyle{\relax}


								% like the iedlistdecl but for \IEEEeqnarray

								\def\IEEEeqnarraydecl{\relax}

								\def\IEEEeqnarrayboxdecl{\relax}


								% \yesnumber is the opposite of \nonumber

								% a novel concept with the same def as the equationarray package

								% However, we give IEEE versions too since some LaTeX packages such as

								% the MDWtools mathenv.sty redefine \nonumber to something else.

								\providecommand{\yesnumber}{\global\@eqnswtrue}

								\def\IEEEyesnumber{\global\@eqnswtrue}

								\def\IEEEnonumber{\global\@eqnswfalse}


								\def\IEEEyessubnumber{\global\@IEEEissubequationtrue\global\@eqnswtrue%

								\if@IEEEeqnarrayISinner% only do something inside an IEEEeqnarray

								\if@IEEElastlinewassubequation\addtocounter{equation}{-1}\else\setcounter{IEEEsubequation}{1}\fi%

								\def\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\fi}


								% flag to indicate that an equation is a sub equation

								\newif\if@IEEEissubequation%

								\@IEEEissubequationfalse


								% allows users to "push away" equations that get too close to the equation numbers

								\def\IEEEeqnarraynumspace{\hphantom{\if@IEEEissubequation\theIEEEsubequationdis\else\theequationdis\fi}}


								% provides a way to span multiple columns within IEEEeqnarray environments

								% will consider \if@advanceIEEEeqncolcnt before globally advancing the

								% column counter - so as to work within \IEEEeqnarraybox

								% usage: \IEEEeqnarraymulticol{number cols. to span}{col type}{cell text}

								\long\def\IEEEeqnarraymulticol#1#2#3{\multispan{#1}%

								% check if column is defined

								\relax\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined%

								\csname @IEEEeqnarraycolPRE#2\endcsname#3\relax\relax\relax\relax\relax%

								\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST#2\endcsname%

								\else% if not, error and use default type

								\@IEEEclspkgerror{Invalid column type "#2" in \string\IEEEeqnarraymulticol.\MessageBreak

								Using a default centering column instead}%

								{You must define IEEEeqnarray column types before use.}%

								\csname @IEEEeqnarraycolPRE@IEEEdefault\endcsname#3\relax\relax\relax\relax\relax%

								\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST@IEEEdefault\endcsname%

								\fi%

								% advance column counter only if the IEEEeqnarray environment wants it

								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by #1\relax\fi}


								% like \omit, but maintains track of the column counter for \IEEEeqnarray

								\def\IEEEeqnarrayomit{\omit\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by 1\relax\fi}


								% provides a way to define a letter referenced column type

								% usage: \IEEEeqnarraydefcol{col. type letter/name}{pre insertion text}{post insertion text}

								\def\IEEEeqnarraydefcol#1#2#3{\expandafter\def\csname @IEEEeqnarraycolPRE#1\endcsname{#2}%

								\expandafter\def\csname @IEEEeqnarraycolPOST#1\endcsname{#3}%

								\expandafter\def\csname @IEEEeqnarraycolDEF#1\endcsname{1}}


								% provides a way to define a numerically referenced inter-column glue types

								% usage: \IEEEeqnarraydefcolsep{col. glue number}{glue definition}

								\def\IEEEeqnarraydefcolsep#1#2{\expandafter\def\csname @IEEEeqnarraycolSEP\romannumeral #1\endcsname{#2}%

								\expandafter\def\csname @IEEEeqnarraycolSEPDEF\romannumeral #1\endcsname{1}}


								\def\@IEEEeqnarraycolisdefined{1}% just a macro for 1, used for checking undefined column types


								% expands and appends the given argument to the \@IEEEtrantmptoksA token list

								% used to build up the \halign preamble

								\def\@IEEEappendtoksA#1{\edef\@@IEEEappendtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA #1}}%

								\@@IEEEappendtoksA}


								% also appends to \@IEEEtrantmptoksA, but does not expand the argument

								% uses \toks8 as a scratchpad register

								\def\@IEEEappendNOEXPANDtoksA#1{\toks8={#1}%

								\edef\@@IEEEappendNOEXPANDtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA\the\toks8}}%

								\@@IEEEappendNOEXPANDtoksA}


								% define some common column types for the user

								% math

								\IEEEeqnarraydefcol{l}{$\IEEEeqnarraymathstyle}{$\hfil}

								\IEEEeqnarraydefcol{c}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}

								\IEEEeqnarraydefcol{r}{\hfil$\IEEEeqnarraymathstyle}{$}

								\IEEEeqnarraydefcol{L}{$\IEEEeqnarraymathstyle{}}{{}$\hfil}

								\IEEEeqnarraydefcol{C}{\hfil$\IEEEeqnarraymathstyle{}}{{}$\hfil}

								\IEEEeqnarraydefcol{R}{\hfil$\IEEEeqnarraymathstyle{}}{{}$}

								% text

								\IEEEeqnarraydefcol{s}{\IEEEeqnarraytextstyle}{\hfil}

								\IEEEeqnarraydefcol{t}{\hfil\IEEEeqnarraytextstyle}{\hfil}

								\IEEEeqnarraydefcol{u}{\hfil\IEEEeqnarraytextstyle}{}


								% vertical rules

								\IEEEeqnarraydefcol{v}{}{\vrule width\arrayrulewidth}

								\IEEEeqnarraydefcol{vv}{\vrule width\arrayrulewidth\hfil}{\hfil\vrule width\arrayrulewidth}

								\IEEEeqnarraydefcol{V}{}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}

								\IEEEeqnarraydefcol{VV}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth\hfil}%

								{\hfil\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}


								% horizontal rules

								\IEEEeqnarraydefcol{h}{}{\leaders\hrule height\arrayrulewidth\hfil}

								\IEEEeqnarraydefcol{H}{}{\leaders\vbox{\hrule width\arrayrulewidth\vskip\doublerulesep\hrule width\arrayrulewidth}\hfil}


								% plain

								\IEEEeqnarraydefcol{x}{}{}

								\IEEEeqnarraydefcol{X}{$}{$}


								% the default column type to use in the event a column type is not defined

								\IEEEeqnarraydefcol{@IEEEdefault}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}


								% a zero tabskip (used for "-" col types)

								\def\@IEEEeqnarraycolSEPzero{0pt plus 0pt minus 0pt}

								% a centering tabskip (used for "+" col types)

								\def\@IEEEeqnarraycolSEPcenter{1000pt plus 0pt minus 1000pt}


								% top level default tabskip glues for the start, end, and inter-column

								% may be reset within environments not always at the top level, e.g., \IEEEeqnarraybox

								\edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPcenter}% default start glue

								\edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPcenter}% default end glue

								\edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue


								% creates a vertical rule that extends from the bottom to the top a a cell

								% Provided in case other packages redefine \vline some other way.

								% usage: \IEEEeqnarrayvrule[rule thickness]

								% If no argument is provided, \arrayrulewidth will be used for the rule thickness.

								\newcommand\IEEEeqnarrayvrule[1][\arrayrulewidth]{\vrule\@width#1\relax}


								% creates a blank separator row

								% usage: \IEEEeqnarrayseprow[separation length][font size commands]

								% default is \IEEEeqnarrayseprow[0.25\normalbaselineskip][\relax]

								% blank arguments inherit the default values

								% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers

								\def\IEEEeqnarrayseprow{\relax\@ifnextchar[{\@IEEEeqnarrayseprow}{\@IEEEeqnarrayseprow[0.25\normalbaselineskip]}}

								\def\@IEEEeqnarrayseprow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprow[#1]}{\@@IEEEeqnarrayseprow[#1][\relax]}}

								\def\@@IEEEeqnarrayseprow[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%

								\ifx\@IEEEeqnarrayseprowARGONE\@empty%

								% get the skip value, based on the font commands

								% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3

								% assign within a bogus box to confine the font changes

								{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%

								\else%

								{\setbox0=\hbox{#2\relax\global\skip5=#1}}%

								\fi%

								\@IEEEeqnarrayhoptolastcolumn\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}


								% creates a blank separator row, but omits all the column templates

								% usage: \IEEEeqnarrayseprowcut[separation length][font size commands]

								% default is \IEEEeqnarrayseprowcut[0.25\normalbaselineskip][\relax]

								% blank arguments inherit the default values

								% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers

								\def\IEEEeqnarrayseprowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols

								% advance column counter only if the IEEEeqnarray environment wants it

								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%

								\@ifnextchar[{\@IEEEeqnarrayseprowcut}{\@IEEEeqnarrayseprowcut[0.25\normalbaselineskip]}}

								\def\@IEEEeqnarrayseprowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprowcut[#1]}{\@@IEEEeqnarrayseprowcut[#1][\relax]}}

								\def\@@IEEEeqnarrayseprowcut[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%

								\ifx\@IEEEeqnarrayseprowARGONE\@empty%

								% get the skip value, based on the font commands

								% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3

								% assign within a bogus box to confine the font changes

								{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%

								\else%

								{\setbox0=\hbox{#2\relax\global\skip5=#1}}%

								\fi%

								\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}


								% draws a single rule across all the columns optional

								% argument determines the rule width, \arrayrulewidth is the default

								% updates column counter as needed and turns off struts

								% usage: \IEEEeqnarrayrulerow[rule line thickness]

								\def\IEEEeqnarrayrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols

								% advance column counter only if the IEEEeqnarray environment wants it

								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%

								\@ifnextchar[{\@IEEEeqnarrayrulerow}{\@IEEEeqnarrayrulerow[\arrayrulewidth]}}

								\def\@IEEEeqnarrayrulerow[#1]{\leaders\hrule height#1\hfil\relax% put in our rule

								% turn off any struts

								\IEEEeqnarraystrutsize{0pt}{0pt}[\relax]\relax}


								% draws a double rule by using a single rule row, a separator row, and then

								% another single rule row

								% first optional argument determines the rule thicknesses, \arrayrulewidth is the default

								% second optional argument determines the rule spacing, \doublerulesep is the default

								% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]

								\def\IEEEeqnarraydblrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols

								% advance column counter only if the IEEEeqnarray environment wants it

								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%

								\@ifnextchar[{\@IEEEeqnarraydblrulerow}{\@IEEEeqnarraydblrulerow[\arrayrulewidth]}}

								\def\@IEEEeqnarraydblrulerow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerow[#1]}%

								{\@@IEEEeqnarraydblrulerow[#1][\doublerulesep]}}

								\def\@@IEEEeqnarraydblrulerow[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%

								% we allow the user to say \IEEEeqnarraydblrulerow[][]

								\ifx\@IEEEeqnarraydblrulerowARG\@empty%

								\@IEEEeqnarrayrulerow[\arrayrulewidth]%

								\else%

								\@IEEEeqnarrayrulerow[#1]\relax%

								\fi%

								\def\@IEEEeqnarraydblrulerowARG{#2}%

								\ifx\@IEEEeqnarraydblrulerowARG\@empty%

								\\\IEEEeqnarrayseprow[\doublerulesep][\relax]%

								\else%

								\\\IEEEeqnarrayseprow[#2][\relax]%

								\fi%

								\\\multispan{\@IEEEeqnnumcols}%

								% advance column counter only if the IEEEeqnarray environment wants it

								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%

								\def\@IEEEeqnarraydblrulerowARG{#1}%

								\ifx\@IEEEeqnarraydblrulerowARG\@empty%

								\@IEEEeqnarrayrulerow[\arrayrulewidth]%

								\else%

								\@IEEEeqnarrayrulerow[#1]%

								\fi%

								}


								% draws a double rule by using a single rule row, a separator (cutting) row, and then

								% another single rule row

								% first optional argument determines the rule thicknesses, \arrayrulewidth is the default

								% second optional argument determines the rule spacing, \doublerulesep is the default

								% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]

								\def\IEEEeqnarraydblrulerowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols

								% advance column counter only if the IEEEeqnarray environment wants it

								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%

								\@ifnextchar[{\@IEEEeqnarraydblrulerowcut}{\@IEEEeqnarraydblrulerowcut[\arrayrulewidth]}}

								\def\@IEEEeqnarraydblrulerowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerowcut[#1]}%

								{\@@IEEEeqnarraydblrulerowcut[#1][\doublerulesep]}}

								\def\@@IEEEeqnarraydblrulerowcut[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%

								% we allow the user to say \IEEEeqnarraydblrulerow[][]

								\ifx\@IEEEeqnarraydblrulerowARG\@empty%

								\@IEEEeqnarrayrulerow[\arrayrulewidth]%

								\else%

								\@IEEEeqnarrayrulerow[#1]%

								\fi%

								\def\@IEEEeqnarraydblrulerowARG{#2}%

								\ifx\@IEEEeqnarraydblrulerowARG\@empty%

								\\\IEEEeqnarrayseprowcut[\doublerulesep][\relax]%

								\else%

								\\\IEEEeqnarrayseprowcut[#2][\relax]%

								\fi%

								\\\multispan{\@IEEEeqnnumcols}%

								% advance column counter only if the IEEEeqnarray environment wants it

								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%

								\def\@IEEEeqnarraydblrulerowARG{#1}%

								\ifx\@IEEEeqnarraydblrulerowARG\@empty%

								\@IEEEeqnarrayrulerow[\arrayrulewidth]%

								\else%

								\@IEEEeqnarrayrulerow[#1]%

								\fi%

								}


								% inserts a full row's worth of &'s

								% relies on \@IEEEeqnnumcols to provide the correct number of columns

								% uses \@IEEEtrantmptoksA, \count0 as scratch registers

								\def\@IEEEeqnarrayhoptolastcolumn{\@IEEEtrantmptoksA={}\count0=1\relax%

								\loop% add cols if the user did not use them all

								\ifnum\count0<\@IEEEeqnnumcols\relax%

								\@IEEEappendtoksA{&}%

								\advance\count0 by 1\relax% update the col count

								\repeat%

								\the\@IEEEtrantmptoksA%execute the &'s

								}


								\newif\if@IEEEeqnarrayISinner % flag to indicate if we are within the lines

								\@IEEEeqnarrayISinnerfalse    % of an IEEEeqnarray - after the IEEEeqnarraydecl


								\edef\@IEEEeqnarrayTHEstrutheight{0pt} % height and depth of IEEEeqnarray struts

								\edef\@IEEEeqnarrayTHEstrutdepth{0pt}


								\edef\@IEEEeqnarrayTHEmasterstrutheight{0pt} % default height and depth of

								\edef\@IEEEeqnarrayTHEmasterstrutdepth{0pt}  % struts within an IEEEeqnarray


								\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{0pt} % saved master strut height

								\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{0pt} % and depth


								\newif\if@IEEEeqnarrayusemasterstrut % flag to indicate that the master strut value

								\@IEEEeqnarrayusemasterstruttrue     % is to be used


								% saves the strut height and depth of the master strut

								\def\@IEEEeqnarraymasterstrutsave{\relax%

								\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%

								\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%

								% remove stretchability

								\dimen0\skip0\relax%

								\dimen2\skip2\relax%

								% save values

								\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{\the\dimen0}%

								\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{\the\dimen2}}


								% restores the strut height and depth of the master strut

								\def\@IEEEeqnarraymasterstrutrestore{\relax%

								\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutHSAVE\relax%

								\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutDSAVE\relax%

								% remove stretchability

								\dimen0\skip0\relax%

								\dimen2\skip2\relax%

								% restore values

								\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%

								\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}}


								% globally restores the strut height and depth to the

								% master values and sets the master strut flag to true

								\def\@IEEEeqnarraystrutreset{\relax%

								\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%

								\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%

								% remove stretchability

								\dimen0\skip0\relax%

								\dimen2\skip2\relax%

								% restore values

								\xdef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%

								\xdef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%

								\global\@IEEEeqnarrayusemasterstruttrue}


								% if the master strut is not to be used, make the current

								% values of \@IEEEeqnarrayTHEstrutheight, \@IEEEeqnarrayTHEstrutdepth

								% and the use master strut flag, global

								% this allows user strut commands issued in the last column to be carried

								% into the isolation/strut column

								\def\@IEEEeqnarrayglobalizestrutstatus{\relax%

								\if@IEEEeqnarrayusemasterstrut\else%

								\xdef\@IEEEeqnarrayTHEstrutheight{\@IEEEeqnarrayTHEstrutheight}%

								\xdef\@IEEEeqnarrayTHEstrutdepth{\@IEEEeqnarrayTHEstrutdepth}%

								\global\@IEEEeqnarrayusemasterstrutfalse%

								\fi}


								% usage: \IEEEeqnarraystrutsize{height}{depth}[font size commands]

								% If called outside the lines of an IEEEeqnarray, sets the height

								% and depth of both the master and local struts. If called inside

								% an IEEEeqnarray line, sets the height and depth of the local strut

								% only and sets the flag to indicate the use of the local strut

								% values. If the height or depth is left blank, 0.7\normalbaselineskip

								% and 0.3\normalbaselineskip will be used, respectively.

								% The optional argument can be used to evaluate the lengths under

								% a different font size and styles. If none is specified, the current

								% font is used.

								% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2

								\def\IEEEeqnarraystrutsize#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsize{#1}{#2}}{\@IEEEeqnarraystrutsize{#1}{#2}[\relax]}}

								\def\@IEEEeqnarraystrutsize#1#2[#3]{\def\@IEEEeqnarraystrutsizeARG{#1}%

								\ifx\@IEEEeqnarraystrutsizeARG\@empty%

								{\setbox0=\hbox{#3\relax\global\skip3=0.7\normalbaselineskip}}%

								\skip0=\skip3\relax%

								\else% arg one present

								{\setbox0=\hbox{#3\relax\global\skip3=#1\relax}}%

								\skip0=\skip3\relax%

								\fi% if null arg

								\def\@IEEEeqnarraystrutsizeARG{#2}%

								\ifx\@IEEEeqnarraystrutsizeARG\@empty%

								{\setbox0=\hbox{#3\relax\global\skip3=0.3\normalbaselineskip}}%

								\skip2=\skip3\relax%

								\else% arg two present

								{\setbox0=\hbox{#3\relax\global\skip3=#2\relax}}%

								\skip2=\skip3\relax%

								\fi% if null arg

								% remove stretchability, just to be safe

								\dimen0\skip0\relax%

								\dimen2\skip2\relax%

								% dimen0 = height, dimen2 = depth

								\if@IEEEeqnarrayISinner% inner does not touch master strut size

								\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%

								\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%

								\@IEEEeqnarrayusemasterstrutfalse% do not use master

								\else% outer, have to set master strut too

								\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%

								\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%

								\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%

								\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%

								\@IEEEeqnarrayusemasterstruttrue% use master strut

								\fi}


								% usage: \IEEEeqnarraystrutsizeadd{added height}{added depth}[font size commands]

								% If called outside the lines of an IEEEeqnarray, adds the given height

								% and depth to both the master and local struts.

								% If called inside an IEEEeqnarray line, adds the given height and depth

								% to the local strut only and sets the flag to indicate the use

								% of the local strut values.

								% In both cases, if a height or depth is left blank, 0pt is used instead.

								% The optional argument can be used to evaluate the lengths under

								% a different font size and styles. If none is specified, the current

								% font is used.

								% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2

								\def\IEEEeqnarraystrutsizeadd#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsizeadd{#1}{#2}}{\@IEEEeqnarraystrutsizeadd{#1}{#2}[\relax]}}

								\def\@IEEEeqnarraystrutsizeadd#1#2[#3]{\def\@IEEEeqnarraystrutsizearg{#1}%

								\ifx\@IEEEeqnarraystrutsizearg\@empty%

								\skip0=0pt\relax%

								\else% arg one present

								{\setbox0=\hbox{#3\relax\global\skip3=#1}}%

								\skip0=\skip3\relax%

								\fi% if null arg

								\def\@IEEEeqnarraystrutsizearg{#2}%

								\ifx\@IEEEeqnarraystrutsizearg\@empty%

								\skip2=0pt\relax%

								\else% arg two present

								{\setbox0=\hbox{#3\relax\global\skip3=#2}}%

								\skip2=\skip3\relax%

								\fi% if null arg

								% remove stretchability, just to be safe

								\dimen0\skip0\relax%

								\dimen2\skip2\relax%

								% dimen0 = height, dimen2 = depth

								\if@IEEEeqnarrayISinner% inner does not touch master strut size

								% get local strut size

								\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%

								\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%

								% add it to the user supplied values

								\advance\dimen0 by \skip0\relax%

								\advance\dimen2 by \skip2\relax%

								% update the local strut size

								\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%

								\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%

								\@IEEEeqnarrayusemasterstrutfalse% do not use master

								\else% outer, have to set master strut too

								% get master strut size

								\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%

								\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%

								% add it to the user supplied values

								\advance\dimen0 by \skip0\relax%

								\advance\dimen2 by \skip2\relax%

								% update the local and master strut sizes

								\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%

								\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%

								\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%

								\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%

								\@IEEEeqnarrayusemasterstruttrue% use master strut

								\fi}


								% allow user a way to see the struts

								\newif\ifIEEEvisiblestruts

								\IEEEvisiblestrutsfalse


								% inserts an invisible strut using the master or local strut values

								% uses scratch registers \skip0, \skip2, \dimen0, \dimen2

								\def\@IEEEeqnarrayinsertstrut{\relax%

								\if@IEEEeqnarrayusemasterstrut

								% get master strut size

								\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%

								\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%

								\else%

								% get local strut size

								\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%

								\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%

								\fi%

								% remove stretchability, probably not needed

								\dimen0\skip0\relax%

								\dimen2\skip2\relax%

								% dimen0 = height, dimen2 = depth

								% allow user to see struts if desired

								\ifIEEEvisiblestruts%

								\vrule width0.2pt height\dimen0 depth\dimen2\relax%

								\else%

								\vrule width0pt height\dimen0 depth\dimen2\relax\fi}


								% creates an invisible strut, useable even outside \IEEEeqnarray

								% if \IEEEvisiblestrutstrue, the strut will be visible and 0.2pt wide.

								% usage: \IEEEstrut[height][depth][font size commands]

								% default is \IEEEstrut[0.7\normalbaselineskip][0.3\normalbaselineskip][\relax]

								% blank arguments inherit the default values

								% uses \dimen0, \dimen2, \skip0, \skip2

								\def\IEEEstrut{\relax\@ifnextchar[{\@IEEEstrut}{\@IEEEstrut[0.7\normalbaselineskip]}}

								\def\@IEEEstrut[#1]{\relax\@ifnextchar[{\@@IEEEstrut[#1]}{\@@IEEEstrut[#1][0.3\normalbaselineskip]}}

								\def\@@IEEEstrut[#1][#2]{\relax\@ifnextchar[{\@@@IEEEstrut[#1][#2]}{\@@@IEEEstrut[#1][#2][\relax]}}

								\def\@@@IEEEstrut[#1][#2][#3]{\mbox{#3\relax%

								\def\@IEEEstrutARG{#1}%

								\ifx\@IEEEstrutARG\@empty%

								\skip0=0.7\normalbaselineskip\relax%

								\else%

								\skip0=#1\relax%

								\fi%

								\def\@IEEEstrutARG{#2}%

								\ifx\@IEEEstrutARG\@empty%

								\skip2=0.3\normalbaselineskip\relax%

								\else%

								\skip2=#2\relax%

								\fi%

								% remove stretchability, probably not needed

								\dimen0\skip0\relax%

								\dimen2\skip2\relax%

								\ifIEEEvisiblestruts%

								\vrule width0.2pt height\dimen0 depth\dimen2\relax%

								\else%

								\vrule width0.0pt height\dimen0 depth\dimen2\relax\fi}}


								% enables strut mode by setting a default strut size and then zeroing the

								% \baselineskip, \lineskip, \lineskiplimit and \jot

								\def\IEEEeqnarraystrutmode{\IEEEeqnarraystrutsize{0.7\normalbaselineskip}{0.3\normalbaselineskip}[\relax]%

								\baselineskip=0pt\lineskip=0pt\lineskiplimit=0pt\jot=0pt}


								\def\IEEEeqnarray{\@IEEEeqnarraystarformfalse\@IEEEeqnarray}

								\def\endIEEEeqnarray{\end@IEEEeqnarray}


								\@namedef{IEEEeqnarray*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarray}

								\@namedef{endIEEEeqnarray*}{\end@IEEEeqnarray}


								% \IEEEeqnarray is an enhanced \eqnarray.

								% The star form defaults to not putting equation numbers at the end of each row.

								% usage: \IEEEeqnarray[decl]{cols}

								\def\@IEEEeqnarray{\relax\@ifnextchar[{\@@IEEEeqnarray}{\@@IEEEeqnarray[\relax]}}

								\def\@@IEEEeqnarray[#1]#2{%

								   % default to showing the equation number or not based on whether or not

								   % the star form was involked

								   \if@IEEEeqnarraystarform\global\@eqnswfalse

								   \else% not the star form

								   \global\@eqnswtrue

								   \fi% if star form

								   \@IEEEissubequationfalse% default to no subequations

								   \@IEEElastlinewassubequationfalse% assume last line is not a sub equation

								   \@IEEEeqnarrayISinnerfalse% not yet within the lines of the halign

								   \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default

								   \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise

								   \IEEEvisiblestrutsfalse% diagnostic mode defaults to off

								   % no extra space unless the user specifically requests it

								   \lineskip=0pt\relax

								   \lineskiplimit=0pt\relax

								   \baselineskip=\normalbaselineskip\relax%

								   \jot=\normaljot\relax%

								   \mathsurround\z@\relax% no extra spacing around math

								   \@advanceIEEEeqncolcnttrue% advance the col counter for each col the user uses,

								                             % used in \IEEEeqnarraymulticol and in the preamble build

								   \stepcounter{equation}% advance equation counter before first line

								   \setcounter{IEEEsubequation}{0}% no subequation yet

								   \def\@currentlabel{\p@equation\theequation}% redefine the ref label

								   \IEEEeqnarraydecl\relax% allow a way for the user to make global overrides

								   #1\relax% allow user to override defaults

								   \let\\\@IEEEeqnarraycr% replace newline with one that can put in eqn. numbers

								   \global\@IEEEeqncolcnt\z@% col. count = 0 for first line

								   \@IEEEbuildpreamble #2\end\relax% build the preamble and put it into \@IEEEtrantmptoksA

								   % put in the column for the equation number

								   \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first

								   \toks0={##}%

								   % advance the \@IEEEeqncolcnt for the isolation col, this helps with error checking

								   \@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}%

								   % add the isolation column

								   \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}%

								   % advance the \@IEEEeqncolcnt for the equation number col, this helps with error checking

								   \@IEEEappendtoksA{&\global\advance\@IEEEeqncolcnt by 1\relax}%

								   % add the equation number col to the preamble

								   \@IEEEappendtoksA{\tabskip\z@skip\hb@xt@\z@\bgroup\hss\the\toks0\egroup}%

								   % note \@IEEEeqnnumcols does not count the equation col or isolation col

								   % set the starting tabskip glue as determined by the preamble build

								   \tabskip=\@IEEEBPstartglue\relax

								   % begin the display alignment

								   \@IEEEeqnarrayISinnertrue% commands are now within the lines

								   $$\everycr{}\halign to\displaywidth\bgroup

								   % "exspand" the preamble

								   \span\the\@IEEEtrantmptoksA\cr}


								% enter isolation/strut column (or the next column if the user did not use

								% every column), record the strut status, complete the columns, do the strut if needed,

								% restore counters to correct values and exit

								\def\end@IEEEeqnarray{\@IEEEeqnarrayglobalizestrutstatus&\@@IEEEeqnarraycr\egroup%

								\if@IEEElastlinewassubequation\global\advance\c@IEEEsubequation\m@ne\fi%

								\global\advance\c@equation\m@ne%

								$$\@ignoretrue}


								% need a way to remember if last line is a subequation

								\newif\if@IEEElastlinewassubequation%

								\@IEEElastlinewassubequationfalse


								% IEEEeqnarray uses a modifed \\ instead of the plain \cr to

								% end rows. This allows for things like \\*[vskip amount]

								% This "cr" macros are modified versions those for LaTeX2e's eqnarray

								% the {\ifnum0=`} braces must be kept away from the last column to avoid

								% altering spacing of its math, so we use & to advance to the next column

								% as there is an isolation/strut column after the user's columns

								\def\@IEEEeqnarraycr{\@IEEEeqnarrayglobalizestrutstatus&% save strut status and advance to next column

								   {\ifnum0=`}\fi

								   \@ifstar{%

								      \global\@eqpen\@M\@IEEEeqnarrayYCR

								   }{%

								      \global\@eqpen\interdisplaylinepenalty \@IEEEeqnarrayYCR

								   }%

								}


								\def\@IEEEeqnarrayYCR{\@testopt\@IEEEeqnarrayXCR\z@skip}


								\def\@IEEEeqnarrayXCR[#1]{%

								   \ifnum0=`{\fi}%

								   \@@IEEEeqnarraycr

								   \noalign{\penalty\@eqpen\vskip\jot\vskip #1\relax}}%


								\def\@@IEEEeqnarraycr{\@IEEEtrantmptoksA={}% clear token register

								    \advance\@IEEEeqncolcnt by -1\relax% adjust col count because of the isolation column

								    \ifnum\@IEEEeqncolcnt>\@IEEEeqnnumcols\relax

								    \@IEEEclspkgerror{Too many columns within the IEEEeqnarray\MessageBreak

								                          environment}%

								    {Use fewer \string &'s or put more columns in the IEEEeqnarry column\MessageBreak

								     specifications.}\relax%

								    \else

								    \loop% add cols if the user did not use them all

								    \ifnum\@IEEEeqncolcnt<\@IEEEeqnnumcols\relax

								    \@IEEEappendtoksA{&}%

								    \advance\@IEEEeqncolcnt by 1\relax% update the col count

								    \repeat

								    % this number of &'s will take us the the isolation column

								    \fi

								    % execute the &'s

								    \the\@IEEEtrantmptoksA%

								    % handle the strut/isolation column

								    \@IEEEeqnarrayinsertstrut% do the strut if needed

								    \@IEEEeqnarraystrutreset% reset the strut system for next line or IEEEeqnarray

								    &% and enter the equation number column

								    % is this line needs an equation number, display it and advance the

								    % (sub)equation counters, record what type this line was

								    \if@eqnsw%

								     \if@IEEEissubequation\theIEEEsubequationdis\addtocounter{equation}{1}\stepcounter{IEEEsubequation}%

								     \global\@IEEElastlinewassubequationtrue%

								     \else% display a standard equation number, initialize the IEEEsubequation counter

								     \theequationdis\stepcounter{equation}\setcounter{IEEEsubequation}{0}%

								     \global\@IEEElastlinewassubequationfalse\fi%

								    \fi%

								    % reset the eqnsw flag to indicate default preference of the display of equation numbers

								    \if@IEEEeqnarraystarform\global\@eqnswfalse\else\global\@eqnswtrue\fi

								    \global\@IEEEissubequationfalse% reset the subequation flag

								    % reset the number of columns the user actually used

								    \global\@IEEEeqncolcnt\z@\relax

								    % the real end of the line

								    \cr}


								% \IEEEeqnarraybox is like \IEEEeqnarray except the box form puts everything

								% inside a vtop, vbox, or vcenter box depending on the letter in the second

								% optional argument (t,b,c). Vbox is the default. Unlike \IEEEeqnarray,

								% equation numbers are not displayed and \IEEEeqnarraybox can be nested.

								% \IEEEeqnarrayboxm is for math mode (like \array) and does not put the vbox

								% within an hbox.

								% \IEEEeqnarrayboxt is for text mode (like \tabular) and puts the vbox within

								% a \hbox{$ $} construct.

								% \IEEEeqnarraybox will auto detect whether to use \IEEEeqnarrayboxm or

								% \IEEEeqnarrayboxt depending on the math mode.

								% The third optional argument specifies the width this box is to be set to -

								% natural width is the default.

								% The * forms do not add \jot line spacing

								% usage: \IEEEeqnarraybox[decl][pos][width]{cols}

								\def\IEEEeqnarrayboxm{\@IEEEeqnarraystarformfalse\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}

								\def\endIEEEeqnarrayboxm{\end@IEEEeqnarraybox}

								\@namedef{IEEEeqnarrayboxm*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}

								\@namedef{endIEEEeqnarrayboxm*}{\end@IEEEeqnarraybox}


								\def\IEEEeqnarrayboxt{\@IEEEeqnarraystarformfalse\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}

								\def\endIEEEeqnarrayboxt{\end@IEEEeqnarraybox}

								\@namedef{IEEEeqnarrayboxt*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}

								\@namedef{endIEEEeqnarrayboxt*}{\end@IEEEeqnarraybox}


								\def\IEEEeqnarraybox{\@IEEEeqnarraystarformfalse\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%

								\@IEEEeqnarraybox}

								\def\endIEEEeqnarraybox{\end@IEEEeqnarraybox}


								\@namedef{IEEEeqnarraybox*}{\@IEEEeqnarraystarformtrue\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%

								\@IEEEeqnarraybox}

								\@namedef{endIEEEeqnarraybox*}{\end@IEEEeqnarraybox}


								% flag to indicate if the \IEEEeqnarraybox needs to put things into an hbox{$ $}

								% for \vcenter in non-math mode

								\newif\if@IEEEeqnarrayboxHBOXSW%

								\@IEEEeqnarrayboxHBOXSWfalse


								\def\@IEEEeqnarraybox{\relax\@ifnextchar[{\@@IEEEeqnarraybox}{\@@IEEEeqnarraybox[\relax]}}

								\def\@@IEEEeqnarraybox[#1]{\relax\@ifnextchar[{\@@@IEEEeqnarraybox[#1]}{\@@@IEEEeqnarraybox[#1][b]}}

								\def\@@@IEEEeqnarraybox[#1][#2]{\relax\@ifnextchar[{\@@@@IEEEeqnarraybox[#1][#2]}{\@@@@IEEEeqnarraybox[#1][#2][\relax]}}


								% #1 = decl; #2 = t,b,c; #3 = width, #4 = col specs

								\def\@@@@IEEEeqnarraybox[#1][#2][#3]#4{\@IEEEeqnarrayISinnerfalse % not yet within the lines of the halign

								   \@IEEEeqnarraymasterstrutsave% save current master strut values

								   \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default

								   \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise

								   \IEEEvisiblestrutsfalse% diagnostic mode defaults to off

								   % no extra space unless the user specifically requests it

								   \lineskip=0pt\relax%

								   \lineskiplimit=0pt\relax%

								   \baselineskip=\normalbaselineskip\relax%

								   \jot=\normaljot\relax%

								   \mathsurround\z@\relax% no extra spacing around math

								   % the default end glues are zero for an \IEEEeqnarraybox

								   \edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPzero}% default start glue

								   \edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPzero}% default end glue

								   \edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue

								   \@advanceIEEEeqncolcntfalse% do not advance the col counter for each col the user uses,

								                              % used in \IEEEeqnarraymulticol and in the preamble build

								   \IEEEeqnarrayboxdecl\relax% allow a way for the user to make global overrides

								   #1\relax% allow user to override defaults

								   \let\\\@IEEEeqnarrayboxcr% replace newline with one that allows optional spacing

								   \@IEEEbuildpreamble #4\end\relax% build the preamble and put it into \@IEEEtrantmptoksA

								   % add an isolation column to the preamble to stop \\'s {} from getting into the last col

								   \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first

								   \toks0={##}%

								   % add the isolation column to the preamble

								   \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}%

								   % set the starting tabskip glue as determined by the preamble build

								   \tabskip=\@IEEEBPstartglue\relax

								   % begin the alignment

								   \everycr{}%

								   % use only the very first token to determine the positioning

								   % this stops some problems when the user uses more than one letter,

								   % but is probably not worth the effort

								   % \noindent is used as a delimiter

								   \def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%

								   \@IEEEgrabfirstoken#2\relax\relax\noindent

								   % \@IEEEgrabbedfirstoken has the first token, the rest are discarded

								   % if we need to put things into and hbox and go into math mode, do so now

								   \if@IEEEeqnarrayboxHBOXSW \leavevmode \hbox \bgroup $\fi%

								   % use the appropriate vbox type

								   \if\@IEEEgrabbedfirstoken t\relax\vtop\else\if\@IEEEgrabbedfirstoken c\relax%

								   \vcenter\else\vbox\fi\fi\bgroup%

								   \@IEEEeqnarrayISinnertrue% commands are now within the lines

								   \ifx#3\relax\halign\else\halign to #3\relax\fi%

								   \bgroup

								   % "exspand" the preamble

								   \span\the\@IEEEtrantmptoksA\cr}


								% carry strut status and enter the isolation/strut column,

								% exit from math mode if needed, and exit

								\def\end@IEEEeqnarraybox{\@IEEEeqnarrayglobalizestrutstatus% carry strut status

								&% enter isolation/strut column

								\@IEEEeqnarrayinsertstrut% do strut if needed

								\@IEEEeqnarraymasterstrutrestore% restore the previous master strut values

								% reset the strut system for next IEEEeqnarray

								% (sets local strut values back to previous master strut values)

								\@IEEEeqnarraystrutreset%

								% ensure last line, exit from halign, close vbox

								\crcr\egroup\egroup%

								% exit from math mode and close hbox if needed

								\if@IEEEeqnarrayboxHBOXSW $\egroup\fi}


								% IEEEeqnarraybox uses a modifed \\ instead of the plain \cr to

								% end rows. This allows for things like \\[vskip amount]

								% This "cr" macros are modified versions those for LaTeX2e's eqnarray

								% For IEEEeqnarraybox, \\* is the same as \\

								% the {\ifnum0=`} braces must be kept away from the last column to avoid

								% altering spacing of its math, so we use & to advance to the isolation/strut column

								% carry strut status into isolation/strut column

								\def\@IEEEeqnarrayboxcr{\@IEEEeqnarrayglobalizestrutstatus% carry strut status

								&% enter isolation/strut column

								\@IEEEeqnarrayinsertstrut% do strut if needed

								% reset the strut system for next line or IEEEeqnarray

								\@IEEEeqnarraystrutreset%

								{\ifnum0=`}\fi%

								\@ifstar{\@IEEEeqnarrayboxYCR}{\@IEEEeqnarrayboxYCR}}


								% test and setup the optional argument to \\[]

								\def\@IEEEeqnarrayboxYCR{\@testopt\@IEEEeqnarrayboxXCR\z@skip}


								% IEEEeqnarraybox does not automatically increase line spacing by \jot

								\def\@IEEEeqnarrayboxXCR[#1]{\ifnum0=`{\fi}%

								\cr\noalign{\if@IEEEeqnarraystarform\else\vskip\jot\fi\vskip#1\relax}}


								% starts the halign preamble build

								\def\@IEEEbuildpreamble{\@IEEEtrantmptoksA={}% clear token register

								\let\@IEEEBPcurtype=u%current column type is not yet known

								\let\@IEEEBPprevtype=s%the previous column type was the start

								\let\@IEEEBPnexttype=u%next column type is not yet known

								% ensure these are valid

								\def\@IEEEBPcurglue={0pt plus 0pt minus 0pt}%

								\def\@IEEEBPcurcolname{@IEEEdefault}% name of current column definition

								% currently acquired numerically referenced glue

								% use a name that is easier to remember

								\let\@IEEEBPcurnum=\@IEEEtrantmpcountA%

								\@IEEEBPcurnum=0%

								% tracks number of columns in the preamble

								\@IEEEeqnnumcols=0%

								% record the default end glues

								\edef\@IEEEBPstartglue{\@IEEEeqnarraycolSEPdefaultstart}%

								\edef\@IEEEBPendglue{\@IEEEeqnarraycolSEPdefaultend}%

								% now parse the user's column specifications

								\@@IEEEbuildpreamble}


								% parses and builds the halign preamble

								\def\@@IEEEbuildpreamble#1#2{\let\@@nextIEEEbuildpreamble=\@@IEEEbuildpreamble%

								% use only the very first token to check the end

								% \noindent is used as a delimiter as \end can be present here

								\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%

								\@IEEEgrabfirstoken#1\relax\relax\noindent

								\ifx\@IEEEgrabbedfirstoken\end\let\@@nextIEEEbuildpreamble=\@@IEEEfinishpreamble\else%

								% identify current and next token type

								\@IEEEgetcoltype{#1}{\@IEEEBPcurtype}{1}% current, error on invalid

								\@IEEEgetcoltype{#2}{\@IEEEBPnexttype}{0}% next, no error on invalid next

								% if curtype is a glue, get the glue def

								\if\@IEEEBPcurtype g\@IEEEgetcurglue{#1}{\@IEEEBPcurglue}\fi%

								% if curtype is a column, get the column def and set the current column name

								\if\@IEEEBPcurtype c\@IEEEgetcurcol{#1}\fi%

								% if curtype is a numeral, acquire the user defined glue

								\if\@IEEEBPcurtype n\@IEEEprocessNcol{#1}\fi%

								% process the acquired glue

								\if\@IEEEBPcurtype g\@IEEEprocessGcol\fi%

								% process the acquired col

								\if\@IEEEBPcurtype c\@IEEEprocessCcol\fi%

								% ready prevtype for next col spec.

								\let\@IEEEBPprevtype=\@IEEEBPcurtype%

								% be sure and put back the future token(s) as a group

								\fi\@@nextIEEEbuildpreamble{#2}}


								% executed just after preamble build is completed

								% warn about zero cols, and if prevtype type = u, put in end tabskip glue

								\def\@@IEEEfinishpreamble#1{\ifnum\@IEEEeqnnumcols<1\relax

								\@IEEEclspkgerror{No column specifiers declared for IEEEeqnarray}%

								{At least one column type must be declared for each IEEEeqnarray.}%

								\fi%num cols less than 1

								%if last type undefined, set default end tabskip glue

								\if\@IEEEBPprevtype u\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue}\fi}


								% Identify and return the column specifier's type code

								\def\@IEEEgetcoltype#1#2#3{%

								% use only the very first token to determine the type

								% \noindent is used as a delimiter as \end can be present here

								\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%

								\@IEEEgrabfirstoken#1\relax\relax\noindent

								% \@IEEEgrabfirstoken has the first token, the rest are discarded

								% n = number

								% g = glue (any other char in catagory 12)

								% c = letter

								% e = \end

								% u = undefined

								% third argument: 0 = no error message, 1 = error on invalid char

								\let#2=u\relax% assume invalid until know otherwise

								\ifx\@IEEEgrabbedfirstoken\end\let#2=e\else

								\ifcat\@IEEEgrabbedfirstoken\relax\else% screen out control sequences

								\if0\@IEEEgrabbedfirstoken\let#2=n\else

								\if1\@IEEEgrabbedfirstoken\let#2=n\else

								\if2\@IEEEgrabbedfirstoken\let#2=n\else

								\if3\@IEEEgrabbedfirstoken\let#2=n\else

								\if4\@IEEEgrabbedfirstoken\let#2=n\else

								\if5\@IEEEgrabbedfirstoken\let#2=n\else

								\if6\@IEEEgrabbedfirstoken\let#2=n\else

								\if7\@IEEEgrabbedfirstoken\let#2=n\else

								\if8\@IEEEgrabbedfirstoken\let#2=n\else

								\if9\@IEEEgrabbedfirstoken\let#2=n\else

								\ifcat,\@IEEEgrabbedfirstoken\let#2=g\relax

								\else\ifcat a\@IEEEgrabbedfirstoken\let#2=c\relax\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi

								\if#2u\relax

								\if0\noexpand#3\relax\else\@IEEEclspkgerror{Invalid character in column specifications}%

								{Only letters, numerals and certain other symbols are allowed \MessageBreak

								as IEEEeqnarray column specifiers.}\fi\fi}


								% identify the current letter referenced column

								% if invalid, use a default column

								\def\@IEEEgetcurcol#1{\expandafter\ifx\csname @IEEEeqnarraycolDEF#1\endcsname\@IEEEeqnarraycolisdefined%

								\def\@IEEEBPcurcolname{#1}\else% invalid column name

								\@IEEEclspkgerror{Invalid column type "#1" in column specifications.\MessageBreak

								Using a default centering column instead}%

								{You must define IEEEeqnarray column types before use.}%

								\def\@IEEEBPcurcolname{@IEEEdefault}\fi}


								% identify and return the predefined (punctuation) glue value

								\def\@IEEEgetcurglue#1#2{%

								% ! = \! (neg small)  -0.16667em (-3/18 em)

								% , = \, (small)       0.16667em ( 3/18 em)

								% : = \: (med)         0.22222em ( 4/18 em)

								% ; = \; (large)       0.27778em ( 5/18 em)

								% ' = \quad            1em

								% " = \qquad           2em

								% . = 0.5\arraycolsep

								% / = \arraycolsep

								% ? = 2\arraycolsep

								% * = 1fil

								% + = \@IEEEeqnarraycolSEPcenter

								% - = \@IEEEeqnarraycolSEPzero

								% Note that all em values are referenced to the math font (textfont2) fontdimen6

								% value for 1em.

								%

								% use only the very first token to determine the type

								% this prevents errant tokens from getting in the main text

								% \noindent is used as a delimiter here

								\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%

								\@IEEEgrabfirstoken#1\relax\relax\noindent

								% get the math font 1em value

								% LaTeX2e's NFSS2 does not preload the fonts, but \IEEEeqnarray needs

								% to gain access to the math (\textfont2) font's spacing parameters.

								% So we create a bogus box here that uses the math font to ensure

								% that \textfont2 is loaded and ready. If this is not done,

								% the \textfont2 stuff here may not work.

								% Thanks to Bernd Raichle for his 1997 post on this topic.

								{\setbox0=\hbox{$\displaystyle\relax$}}%

								% fontdimen6 has the width of 1em (a quad).

								\@IEEEtrantmpdimenA=\fontdimen6\textfont2\relax%

								% identify the glue value based on the first token

								% we discard anything after the first

								\if!\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=-0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else

								\if,\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else

								\if:\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.22222\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else

								\if;\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.27778\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else

								\if'\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=1\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else

								\if"\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=2\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else

								\if.\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.5\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else

								\if/\@IEEEgrabbedfirstoken\edef#2{\the\arraycolsep}\else

								\if?\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=2\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else

								\if *\@IEEEgrabbedfirstoken\edef#2{0pt plus 1fil minus 0pt}\else

								\if+\@IEEEgrabbedfirstoken\edef#2{\@IEEEeqnarraycolSEPcenter}\else

								\if-\@IEEEgrabbedfirstoken\edef#2{\@IEEEeqnarraycolSEPzero}\else

								\edef#2{\@IEEEeqnarraycolSEPzero}%

								\@IEEEclspkgerror{Invalid predefined inter-column glue type "#1" in\MessageBreak

								column specifications. Using a default value of\MessageBreak

								0pt instead}%

								{Only !,:;'"./?*+ and - are valid predefined glue types in the\MessageBreak

								IEEEeqnarray column specifications.}\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}


								% process a numerical digit from the column specification

								% and look up the corresponding user defined glue value

								% can transform current type from n to g or a as the user defined glue is acquired

								\def\@IEEEprocessNcol#1{\if\@IEEEBPprevtype g%

								\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak

								specifications. Ignoring consecutive glue specifiers\MessageBreak

								after the first}%

								{You cannot have two or more glue types next to each other\MessageBreak

								in the IEEEeqnarray column specifications.}%

								\let\@IEEEBPcurtype=a% abort this glue, future digits will be discarded

								\@IEEEBPcurnum=0\relax%

								\else% if we previously aborted a glue

								\if\@IEEEBPprevtype a\@IEEEBPcurnum=0\let\@IEEEBPcurtype=a%maintain digit abortion

								\else%acquire this number

								% save the previous type before the numerical digits started

								\if\@IEEEBPprevtype n\else\let\@IEEEBPprevsavedtype=\@IEEEBPprevtype\fi%

								\multiply\@IEEEBPcurnum by 10\relax%

								\advance\@IEEEBPcurnum by #1\relax% add in number, \relax is needed to stop TeX's number scan

								\if\@IEEEBPnexttype n\else%close acquisition

								\expandafter\ifx\csname @IEEEeqnarraycolSEPDEF\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname\@IEEEeqnarraycolisdefined%

								\edef\@IEEEBPcurglue{\csname @IEEEeqnarraycolSEP\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname}%

								\else%user glue not defined

								\@IEEEclspkgerror{Invalid user defined inter-column glue type "\number\@IEEEBPcurnum" in\MessageBreak

								column specifications. Using a default value of\MessageBreak

								0pt instead}%

								{You must define all IEEEeqnarray numerical inter-column glue types via\MessageBreak

								\string\IEEEeqnarraydefcolsep \space before they are used in column specifications.}%

								\edef\@IEEEBPcurglue{\@IEEEeqnarraycolSEPzero}%

								\fi% glue defined or not

								\let\@IEEEBPcurtype=g% change the type to reflect the acquired glue

								\let\@IEEEBPprevtype=\@IEEEBPprevsavedtype% restore the prev type before this number glue

								\@IEEEBPcurnum=0\relax%ready for next acquisition

								\fi%close acquisition, get glue

								\fi%discard or acquire number

								\fi%prevtype glue or not

								}


								% process an acquired glue

								% add any acquired column/glue pair to the preamble

								\def\@IEEEprocessGcol{\if\@IEEEBPprevtype a\let\@IEEEBPcurtype=a%maintain previous glue abortions

								\else

								% if this is the start glue, save it, but do nothing else

								% as this is not used in the preamble, but before

								\if\@IEEEBPprevtype s\edef\@IEEEBPstartglue{\@IEEEBPcurglue}%

								\else%not the start glue

								\if\@IEEEBPprevtype g%ignore if back to back glues

								\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak

								specifications. Ignoring consecutive glue specifiers\MessageBreak

								after the first}%

								{You cannot have two or more glue types next to each other\MessageBreak

								in the IEEEeqnarray column specifications.}%

								\let\@IEEEBPcurtype=a% abort this glue

								\else% not a back to back glue

								\if\@IEEEBPprevtype c\relax% if the previoustype was a col, add column/glue pair to preamble

								\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi

								\toks0={##}%

								% make preamble advance col counter if this environment needs this

								\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi

								% insert the column defintion into the preamble, being careful not to expand

								% the column definition

								\@IEEEappendtoksA{\tabskip=\@IEEEBPcurglue}%

								\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}%

								\@IEEEappendtoksA{\@IEEEBPcurcolname}%

								\@IEEEappendNOEXPANDtoksA{\endcsname}%

								\@IEEEappendtoksA{\the\toks0}%

								\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax%

								\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}%

								\@IEEEappendtoksA{\@IEEEBPcurcolname}%

								\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax%

								\relax\relax\relax\relax\relax\endgroup}%

								\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble

								\else% error: non-start glue with no pending column

								\@IEEEclspkgerror{Inter-column glue specifier without a prior column\MessageBreak

								type in the column specifications. Ignoring this glue\MessageBreak

								specifier}%

								{Except for the first and last positions, glue can be placed only\MessageBreak

								between column types.}%

								\let\@IEEEBPcurtype=a% abort this glue

								\fi% previous was a column

								\fi% back-to-back glues

								\fi% is start column glue

								\fi% prev type not a

								}


								% process an acquired letter referenced column and, if necessary, add it to the preamble

								\def\@IEEEprocessCcol{\if\@IEEEBPnexttype g\else

								\if\@IEEEBPnexttype n\else

								% we have a column followed by something other than a glue (or numeral glue)

								% so we must add this column to the preamble now

								\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi%col separator for those after the first

								\if\@IEEEBPnexttype e\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue\relax}\else%put in end glue

								\@IEEEappendtoksA{\tabskip=\@IEEEeqnarraycolSEPdefaultmid\relax}\fi% or default mid glue

								\toks0={##}%

								% make preamble advance col counter if this environment needs this

								\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi

								% insert the column definition into the preamble, being careful not to expand

								% the column definition

								\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}%

								\@IEEEappendtoksA{\@IEEEBPcurcolname}%

								\@IEEEappendNOEXPANDtoksA{\endcsname}%

								\@IEEEappendtoksA{\the\toks0}%

								\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax%

								\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}%

								\@IEEEappendtoksA{\@IEEEBPcurcolname}%

								\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax%

								\relax\relax\relax\relax\relax\endgroup}%

								\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble

								\fi%next type not numeral

								\fi%next type not glue

								}


								%%

								%% END OF IEEEeqnarry DEFINITIONS

								%%


								% set up the running headings, this complex because of all the different

								% modes IEEEtran supports

								\if@twoside

								 \if@technote

								   \def\ps@headings{%

								       \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}

								       \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}

								       \if@draftclsmode

								            \if@draftclsmodefoot

								               \def\@oddfoot{\scriptsize\@date\hfil DRAFT}

								               \def\@evenfoot{\scriptsize DRAFT\hfil\@date}

								            \else

								               \def\@oddfoot{}\def\@evenfoot{}%

								            \fi

								       \else

								            \def\@oddfoot{}\def\@evenfoot{}

								       \fi}

								 \else % not a technote

								   \def\ps@headings{%

								       \if@confmode

								        \def\@oddhead{}

								        \def\@evenhead{}

								       \else

								        \def\@oddhead{\hbox{}\scriptsize\rightmark \hfil \thepage}

								        \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}

								       \fi

								       \if@draftclsmode

								            \def\@oddhead{\hbox{}\scriptsize\rightmark \hfil \thepage}

								            \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}

								            \if@draftclsmodefoot

								               \def\@oddfoot{\scriptsize\@date\hfil DRAFT}

								               \def\@evenfoot{\scriptsize DRAFT\hfil\@date}

								            \else

								               \def\@oddfoot{}\def\@evenfoot{}%

								            \fi

								       \else

								            \def\@oddfoot{}\def\@evenfoot{}%

								       \fi}

								 \fi

								\else % single side

								\def\ps@headings{%

								    \if@confmode

								     \def\@oddhead{}

								     \def\@evenhead{}

								    \else

								     \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}

								     \def\@evenhead{}

								    \fi

								    \if@draftclsmode

								          \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}

								          \def\@evenhead{}

								          \if@draftclsmodefoot

								             \def\@oddfoot{\scriptsize \@date \hfil DRAFT}

								          \else

								             \def\@oddfoot{}

								          \fi

								    \else

								         \def\@oddfoot{}

								    \fi

								    \def\@evenfoot{}}

								\fi


								% title page style

								\def\ps@titlepagestyle{\def\@oddfoot{}\def\@evenfoot{}%

								\if@confmode

								   \def\@oddhead{}%

								   \def\@evenhead{}%

								\else

								   \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}%

								   \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}%

								\fi

								\if@draftclsmode

								   \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}%

								   \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}%

								   \if@draftclsmodefoot

								      \def\@oddfoot{\scriptsize \@date\hfil DRAFT}%

								      \def\@evenfoot{\scriptsize DRAFT\hfil \@date}%

								   \fi

								\else

								   % all non-draft mode footers

								   \if@IEEEusingpubid

								      % for title pages that are using a pubid

								      % do not repeat pubid if using peer review option

								      \if@peerreviewoption

								      \else

								         \footskip 0pt%

								         \def\@oddfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@pubid}\hss}%

								         \def\@evenfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@pubid}\hss}%

								      \fi

								   \fi

								\fi}


								% peer review cover page style

								\def\ps@peerreviewcoverpagestyle{%

								\def\@oddhead{}\def\@evenhead{}%

								\def\@oddfoot{}\def\@evenfoot{}%

								\if@draftclsmode

								   \if@draftclsmodefoot

								      \def\@oddfoot{\scriptsize \@date\hfil DRAFT}%

								      \def\@evenfoot{\scriptsize DRAFT\hfil \@date}%

								   \fi

								\else

								   % non-draft mode footers

								   \if@IEEEusingpubid

								      \footskip 0pt%

								      \def\@oddfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@pubid}\hss}%

								      \def\@evenfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@pubid}\hss}%

								   \fi

								\fi}


								% start with empty headings

								\def\rightmark{}\def\leftmark{}


								%% Defines the command for putting the header. \footernote{TEXT} is the same

								%% as \markboth{TEXT}{TEXT}.

								%% Note that all the text is forced into uppercase, if you have some text

								%% that needs to be in lower case, for instance et. al., then either manually

								%% set \leftmark and \rightmark or use \MakeLowercase{et. al.} within the

								%% arguments to \markboth.

								\def\markboth#1#2{\def\leftmark{\MakeUppercase{#1}}\def\rightmark{\MakeUppercase{#2}}}

								\def\footernote#1{\markboth{#1}{#1}}


								\def\today{\ifcase\month\or

								    January\or February\or March\or April\or May\or June\or

								    July\or August\or September\or October\or November\or December\fi

								    \space\number\day, \number\year}


								%% CITATION AND BIBLIOGRAPHY COMMANDS

								%%

								%% V1.6 no longer supports the older, nonstandard \shortcite and \citename setup stuff

								%

								%

								% Modify Latex2e \@citex to separate citations with "], ["

								\def\@citex[#1]#2{%

								  \let\@citea\@empty

								  \@cite{\@for\@citeb:=#2\do

								    {\@citea\def\@citea{], [}%

								     \edef\@citeb{\expandafter\@firstofone\@citeb\@empty}%

								     \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi

								     \@ifundefined{b@\@citeb}{\mbox{\reset@font\bfseries ?}%

								       \G@refundefinedtrue

								       \@latex@warning

								         {Citation `\@citeb' on page \thepage \space undefined}}%

								       {\hbox{\csname b@\@citeb\endcsname}}}}{#1}}


								% V1.6 we create hooks for the optional use of Donald Arseneau's

								% cite.sty package. cite.sty is "smart" and will notice that the

								% following format controls are already defined and will not

								% redefine them. The result will be the proper sorting of the

								% citation numbers and auto detection of 3 or more entry "ranges" -

								% all in IEEE style:  [1], [2], [5]--[7], [12]

								% This also allows for an optional note, i.e., \cite[mynote]{..}.

								% If the \cite with note has more than one reference, the note will

								% be applied to the last of the listed references. It is generally

								% desired that if a note is given, only one reference is listed in

								% that \cite.

								% Thanks to Mr. Arseneau for providing the required format arguments

								% to produce the IEEE style.

								\def\citepunct{], [}

								\def\citedash{]--[}


								% V1.6b providing this command makes hyperref think the natbib package is

								% in use so that it will not interfere with cite.sty. However, as a result,

								% citation numbers will not be hyperlinked.

								\def\NAT@parse{\typeout{IEEEtran error: Attempt to use fake Natbib command

								which is provided to fool Hyperref.}}

								% it easy enough to override via:

								% \let\NAT@parse\undefined


								% V1.6 class files should always provide these

								\def\newblock{\hskip .11em\@plus.33em\@minus.07em}

								\let\@openbib@code\@empty


								% Provide support for the control entries of IEEEtran.bst V1.00 and later.

								\def\bstctlcite#1{\@bsphack

								  \@for\@citeb:=#1\do{%

								    \edef\@citeb{\expandafter\@firstofone\@citeb}%

								    \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi}%

								  \@esphack}


								% V1.6 provide a way for a user to execute a command just before

								% a given reference number - used to insert a \newpage to balance

								% the columns on the last page

								\edef\@IEEEtriggerrefnum{0}   % the default of zero means that

								                              % the command is not executed

								\def\@IEEEtriggercmd{\newpage}


								% allow the user to alter the triggered command

								\long\def\IEEEtriggercmd#1{\long\def\@IEEEtriggercmd{#1}}


								% allow user a way to specify the reference number just before the

								% command is executed

								\def\IEEEtriggeratref#1{\@IEEEtrantmpcountA=#1%

								\edef\@IEEEtriggerrefnum{\the\@IEEEtrantmpcountA}}%


								% trigger command at the given reference

								\def\@IEEEbibitemprefix{\@IEEEtrantmpcountA=\@IEEEtriggerrefnum\relax%

								\advance\@IEEEtrantmpcountA by -1\relax%

								\ifnum\c@enumiv=\@IEEEtrantmpcountA\relax\@IEEEtriggercmd\relax\fi}


								\def\@biblabel#1{[#1]}


								\def\thebibliography#1{\section*{References}%

								    \addcontentsline{toc}{section}{References}%

								    % V1.6 add some rubber space here and provide a command trigger

								    \footnotesize \vskip 0.3\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip%

								    \list{\@biblabel{\@arabic\c@enumiv}}%

								    {\settowidth\labelwidth{\@biblabel{#1}}%

								    \leftmargin\labelwidth

								    \advance\leftmargin\labelsep\relax

								    \itemsep 0pt plus .5pt\relax%

								    \usecounter{enumiv}%

								    \let\p@enumiv\@empty

								    \renewcommand\theenumiv{\@arabic\c@enumiv}}%

								    \let\@IEEElatexbibitem\bibitem%

								    \def\bibitem{\@IEEEbibitemprefix\@IEEElatexbibitem}%

								\def\newblock{\hskip .11em plus .33em minus .07em}%

								% originally:

								%   \sloppy\clubpenalty4000\widowpenalty4000%

								% by adding the \interlinepenalty here, we make it more

								% difficult, but not impossible, for LaTeX to break within a reference.

								% IEEE almost never breaks a reference (but they do it more often with

								% technotes). You may get an underfull vbox warning around the bibliography,

								% but the final result will be much more like what IEEE will publish.

								% MDS 11/2000

								\if@technote\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty100%

								\else\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty500\fi%

								    \sfcode`\.=1000\relax}

								\let\endthebibliography=\endlist


								% TITLE PAGE COMMANDS

								%

								%

								% \IEEEmembership is used to produce the sublargesize italic font used to indicate author

								% IEEE membership.

								\def\IEEEmembership#1{{\sublargesize\normalfont\textit{#1}}}


								% \authorrefmark{} produces a footnote type symbol to indicate author affiliation.

								% When given an argument of 1 to 9, \authorrefmark{} follows the standard LaTeX footnote

								% symbol sequence convention. However, for arguments 10 and above, \authorrefmark{}

								% reverts to using lower case roman numerals, so it cannot overflow. Do note that you

								% cannot use \footnotemark[] in place of \authorrefmark{} within \author as the footnote

								% symbols will have been turned off to prevent \thanks from creating footnote marks.

								% \authorrefmark{} produces a symbol that appears to LaTeX as having zero vertical

								% height - this allows for a more compact line packing, but the user must ensure that

								% the interline spacing is large enough to prevent \authorrefmark{} from colliding

								% with the text above.

								\def\authorrefmark#1{\raisebox{0pt}[0pt][0pt]{\textsuperscript{\footnotesize\ensuremath{\ifcase#1\or *\or \dagger\or \ddagger\or%

								    \mathsection\or \mathparagraph\or \|\or **\or \dagger\dagger%

								    \or \ddagger\ddagger \else\textsuperscript{\expandafter\romannumeral#1}\fi}}}}


								% FONT CONTROLS AND SPACINGS FOR CONFERENCE MODE AUTHOR NAME AND AFFILIATION BLOCKS

								%

								% The default font styles for the author name and affiliation blocks (confmode)

								\def\@IEEEauthorblockNstyle{\normalfont\sublargesize}

								\def\@IEEEauthorblockAstyle{\normalfont\normalsize}

								% The default if the user does not use an author block

								\def\@IEEEauthordefaulttextstyle{\normalfont\sublargesize}


								% spacing from title (or special paper notice) to author name blocks (confmode)

								% can be negative

								\def\@IEEEauthorblockconfadjspace{-0.25em}


								% spacing between name and affiliation blocks (confmode)

								% This can be negative.

								% IEEE doesn't want any added spacing here, but I will leave these

								% controls in place in case they ever change their mind.

								% Personally, I like 0.75ex.

								%\def\@IEEEauthorblockNtopspace{0.75ex}

								%\def\@IEEEauthorblockAtopspace{0.75ex}

								\def\@IEEEauthorblockNtopspace{0.0ex}

								\def\@IEEEauthorblockAtopspace{0.0ex}

								% baseline spacing within name and affiliation blocks (confmode)

								% must be positive, spacings below certain values will make

								% the position of line of text sensitive to the contents of the

								% line above it i.e., whether or not the prior line has descenders,

								% subscripts, etc. For this reason it is a good idea to keep

								% these above 2.6ex

								\def\@IEEEauthorblockNinterlinespace{2.6ex}

								\def\@IEEEauthorblockAinterlinespace{2.75ex}


								% This tracks the required strut size.

								% See the \@IEEEauthorhalign command for the actual default value used.

								\def\@IEEEauthorblockXinterlinespace{2.7ex}


								% variables to retain font size and style across groups

								% values given here have no effect as they will be overwritten later

								\gdef\@IEEESAVESTATEfontsize{10}

								\gdef\@IEEESAVESTATEfontbaselineskip{12}

								\gdef\@IEEESAVESTATEfontencoding{OT1}

								\gdef\@IEEESAVESTATEfontfamily{ptm}

								\gdef\@IEEESAVESTATEfontseries{m}

								\gdef\@IEEESAVESTATEfontshape{n}


								% saves the current font attributes

								\def\@IEEEcurfontSAVE{\global\let\@IEEESAVESTATEfontsize\f@size%

								\global\let\@IEEESAVESTATEfontbaselineskip\f@baselineskip%

								\global\let\@IEEESAVESTATEfontencoding\f@encoding%

								\global\let\@IEEESAVESTATEfontfamily\f@family%

								\global\let\@IEEESAVESTATEfontseries\f@series%

								\global\let\@IEEESAVESTATEfontshape\f@shape}


								% restores the saved font attributes

								\def\@IEEEcurfontRESTORE{\fontsize{\@IEEESAVESTATEfontsize}{\@IEEESAVESTATEfontbaselineskip}%

								\fontencoding{\@IEEESAVESTATEfontencoding}%

								\fontfamily{\@IEEESAVESTATEfontfamily}%

								\fontseries{\@IEEESAVESTATEfontseries}%

								\fontshape{\@IEEESAVESTATEfontshape}%

								\selectfont}


								% variable to indicate if the current block is the first block in the column

								\newif\if@IEEEprevauthorblockincol   \@IEEEprevauthorblockincolfalse


								% the command places a strut with height and depth = \@IEEEauthorblockXinterlinespace

								% we use this technique to have complete manual control over the spacing of the lines

								% within the halign environment.

								% We set the below baseline portion at 30%, the above

								% baseline portion at 70% of the total length.

								% Responds to changes in the document's \baselinestretch

								\def\@IEEEauthorstrutrule{\@IEEEtrantmpdimenA\@IEEEauthorblockXinterlinespace%

								\@IEEEtrantmpdimenA=\baselinestretch\@IEEEtrantmpdimenA%

								\rule[-0.3\@IEEEtrantmpdimenA]{0pt}{\@IEEEtrantmpdimenA}}


								% blocks to hold the authors' names and affilations.

								% Makes formatting easy for conferences

								%

								% use real definitions in conference mode

								% name block

								\def\authorblockN#1{\relax\@IEEEauthorblockNstyle% set the default text style

								\gdef\@IEEEauthorblockXinterlinespace{0pt}% disable strut for spacer row

								% the \expandafter hides the \cr in conditional tex, see the array.sty docs

								% for details, probably not needed here as the \cr is in a macro

								% do a spacer row if needed

								\if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockNtopspaceline\fi

								\global\@IEEEprevauthorblockincoltrue% we now have a block in this column

								%restore the correct strut value

								\gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockNinterlinespace}%

								% input the author names

								#1%

								% end the row if the user did not already

								\crcr}

								% spacer row for names

								\def\@IEEEauthorblockNtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockNtopspace}}

								%

								% affiliation block

								\def\authorblockA#1{\relax\@IEEEauthorblockAstyle% set the default text style

								\gdef\@IEEEauthorblockXinterlinespace{0pt}%disable strut for spacer row

								% the \expandafter hides the \cr in conditional tex, see the array.sty docs

								% for details, probably not needed here as the \cr is in a macro

								% do a spacer row if needed

								\if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockAtopspaceline\fi

								\global\@IEEEprevauthorblockincoltrue% we now have a block in this column

								%restore the correct strut value

								\gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockAinterlinespace}%

								% input the author affiliations

								#1%

								% end the row if the user did not already

								\crcr}

								% spacer row for affiliations

								\def\@IEEEauthorblockAtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockAtopspace}}


								% allow papers to compile even if author blocks are used in modes other

								% than conference or peerreviewca. For such cases, we provide dummy blocks.

								\if@confmode

								\else

								   \if@peerreviewcaoption\else

								      % not conference or peerreviewca mode

								      \def\authorblockN#1{#1}%

								      \def\authorblockA#1{#1}%

								   \fi

								\fi


								% we provide our own halign so as not to have to depend on tabular

								\def\@IEEEauthorhalign{\@IEEEauthordefaulttextstyle% default text style

								   \lineskip=0pt\relax% disable line spacing

								   \lineskiplimit=0pt\relax%

								   \baselineskip=0pt\relax%

								   \@IEEEcurfontSAVE% save the current font

								   \mathsurround\z@\relax% no extra spacing around math

								   \let\\\@IEEEauthorhaligncr% replace newline with halign friendly one

								   \tabskip=0pt\relax% no column spacing

								   \everycr{}% ensure no problems here

								   \@IEEEprevauthorblockincolfalse% no author blocks yet

								   \def\@IEEEauthorblockXinterlinespace{2.7ex}% default interline space

								   \vtop\bgroup%vtop box

								   \halign\bgroup&\relax\hfil\@IEEEcurfontRESTORE\relax ##\relax

								   \hfil\@IEEEcurfontSAVE\@IEEEauthorstrutrule\cr}


								% ensure last line, exit from halign, close vbox

								\def\end@IEEEauthorhalign{\crcr\egroup\egroup}


								% handle bogus star form

								\def\@IEEEauthorhaligncr{{\ifnum0=`}\fi\@ifstar{\@@IEEEauthorhaligncr}{\@@IEEEauthorhaligncr}}


								% test and setup the optional argument to \\[]

								\def\@@IEEEauthorhaligncr{\@testopt\@@@IEEEauthorhaligncr\z@skip}


								% end the line and do the optional spacer

								\def\@@@IEEEauthorhaligncr[#1]{\ifnum0=`{\fi}\cr\noalign{\vskip#1\relax}}


								% flag to prevent multiple \and warning messages

								\newif\if@IEEEWARNand

								\@IEEEWARNandtrue


								% if in conference or peerreviewca modes, we support the use of \and as \author is a

								% tabular environment, otherwise we warn the user that \and is invalid

								% outside of conference or peerreviewca modes.

								\def\and{\relax} % provide a bogus \and that we will then override


								\renewcommand{\and}[1][\relax]{\if@IEEEWARNand\typeout{** WARNING: \noexpand\and is valid only

								                               when in conference or peerreviewca}\typeout{modes (line \the\inputlineno).}\fi\global\@IEEEWARNandfalse}


								\if@confmode%

								\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%

								\fi

								\if@peerreviewcaoption

								\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%

								\fi


								% page clearing command

								% based on LaTeX2e's \cleardoublepage, but allows different page styles

								% for the inserted blank pages

								\def\@IEEEcleardoublepage#1{\clearpage\if@twoside\ifodd\c@page\else

								\hbox{}\thispagestyle{#1}\newpage\if@twocolumn\hbox{}\thispagestyle{#1}\newpage\fi\fi\fi}


								% user command to invoke the title page

								\def\maketitle{\par%

								  \begingroup%

								  \normalfont%

								  \def\thefootnote{}%  the \thanks{} mark type is empty

								  \def\footnotemark{}% and kill space from \thanks within author

								  \footnotesize%       equal spacing between thanks lines

								  \footnotesep 0.7\baselineskip%see global setting of \footnotesep for more info

								  \normalsize%

								  \if@peerreviewoption

								     \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%

								     \thispagestyle{peerreviewcoverpagestyle}\@thanks%

								  \else

								     \if@twocolumn%

								        \if@technote%

								           \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%

								        \else

								           \twocolumn[\@maketitle\@IEEEdynamictitlevspace\@IEEEaftertitletext]%

								        \fi

								     \else

								        \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%

								     \fi

								     \thispagestyle{titlepagestyle}\@thanks%

								  \fi

								  % pullup page for pubid if used.

								  \if@IEEEusingpubid

								     \enlargethispage{-\@pubidpullup}%

								  \fi

								  \endgroup

								  \setcounter{footnote}{0}\let\maketitle\relax\let\@maketitle\relax

								  \gdef\@thanks{}

								  % v1.6b do not clear these as we will need the title again for peer review papers

								  % \gdef\@author{}\gdef\@title{}%

								  \let\thanks\relax}


								% formats the Title, authors names, affiliations and special paper notice

								% THIS IS A CONTROLLED SPACING COMMAND! Do not allow blank lines or unintentional

								% spaces to enter the definition - use % at the end of each line

								% Changed Title font to \LARGE from \Huge

								\def\@maketitle{\newpage

								\begin{center}%

								\if@technote%

								   {\bfseries\large\@title\par}\vskip 1.3em{\lineskip .5em\@author\@specialpapernotice\par}%

								\else% not a technote

								   \vskip0.25in{\LARGE\@title\par}\vskip1.0em\par%

								   % V1.6 handle \author differently if in conference mode

								   \if@confmode%

								      {\@specialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%

								      \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par}%

								   \else% peerreviewca, peerreview or journal

								      \if@peerreviewcaoption

								         % peerreviewca handles author names just like conference mode

								         {\@specialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%

								         \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par}%

								      \else % journal or peerreview

								         {\lineskip.5em\sublargesize\@author\@specialpapernotice\par}%

								      \fi

								   \fi

								\fi\end{center}}


								% V1.6b define the \IEEEpeerreviewmaketitle as needed

								\if@peerreviewoption

								\def\IEEEpeerreviewmaketitle{\@IEEEcleardoublepage{empty}%

								\if@twocolumnmode

								\twocolumn[\@IEEEpeerreviewmaketitle\@IEEEdynamictitlevspace]

								\else

								\newpage\@IEEEpeerreviewmaketitle\@IEEEstatictitlevskip

								\fi

								\thispagestyle{titlepagestyle}}

								\else

								% \IEEEpeerreviewmaketitle does nothing if peer review option has not been selected

								\def\IEEEpeerreviewmaketitle{\relax}

								\fi


								% peerreview formats the repeated title like the title in journal papers.

								\def\@IEEEpeerreviewmaketitle{\begin{center}%

								\normalfont\normalsize\vskip0.2em{\Huge\@title\par}\vskip1.0em\par

								\end{center}}


								% V1.6

								% this is a static rubber spacer between the title/authors and the main text

								% used for single column text, or when the title appears in the first column

								% of two column text (technotes).

								\def\@IEEEstatictitlevskip{{\normalfont\normalsize

								% adjust spacing to next text

								% v1.6b handle peer review papers

								\if@peerreviewoption

								% for peer review papers, the same value is used for both title pages

								% regardless of the other paper modes

								   \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip

								\else

								   \if@confmode% conference

								      \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip%

								   \else%

								      \if@technote% technote

								         \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip%

								      \else% journal uses more space

								         \vskip 2.5\baselineskip plus 0.75\baselineskip minus 0.375\baselineskip%

								      \fi

								   \fi

								\fi}}


								% V1.6

								% This is a dynamically determined rigid spacer between the title/authors

								% and the main text. This is used only for single column titles over two

								% column text (most common)

								% This is bit tricky because we have to ensure that the textheight of the

								% main text is an integer multiple of \baselineskip

								% otherwise underfull vbox problems may develop in the second column of the

								% text on the titlepage

								% The possible use of \pubid must also be taken into account.

								\def\@IEEEdynamictitlevspace{{%

								    % we run within a group so that all the macros can be forgotten when we are done

								    \def\thanks##1{\relax}%don't allow \thanks to run when we evaluate the vbox height

								    \normalfont\normalsize% we declare more descriptive variable names

								    \let\@maintextheight=\@IEEEtrantmpdimenA%height of the main text columns

								    \let\@INTmaintextheight=\@IEEEtrantmpdimenB%height of the main text columns with integer # lines

								    % set the nominal and minimum values for the title spacer

								    % the dynamic algorithm will not allow the spacer size to

								    % become less than \@MINtitlevspace - instead it will be

								    % lengthened

								    % default to journal values

								    \def\@NORMtitlevspace{2.5\baselineskip}%

								    \def\@MINtitlevspace{2\baselineskip}%

								    % conferences and technotes need tighter spacing

								    \if@confmode%conference

								     \def\@NORMtitlevspace{1\baselineskip}%

								     \def\@MINtitlevspace{0.75\baselineskip}%

								    \fi

								    \if@technote%technote

								      \def\@NORMtitlevspace{1\baselineskip}%

								      \def\@MINtitlevspace{0.75\baselineskip}%

								    \fi%

								    % get the height that the title will take up

								    \if@peerreviewoption

								       \settoheight{\@maintextheight}{\vbox{\hsize\textwidth \@IEEEpeerreviewmaketitle}}%

								    \else

								       \settoheight{\@maintextheight}{\vbox{\hsize\textwidth \@maketitle}}%

								    \fi

								    \@maintextheight=-\@maintextheight% title takes away from maintext, so reverse sign

								    % add the height of the page textheight

								    \advance\@maintextheight by \textheight%

								    % correct for title pages using pubid

								    \if@peerreviewoption\else

								       % peerreview papers use the pubid on the cover page only.

								       % And the cover page uses a static spacer.

								       \if@IEEEusingpubid\advance\@maintextheight by -\@pubidpullup\fi

								    \fi%

								    % subtract off the nominal value of the title bottom spacer

								    \advance\@maintextheight by -\@NORMtitlevspace%

								    % \topskip takes away some too

								    \advance\@maintextheight by -\topskip%

								    % calculate the column height of the main text for lines

								    % now we calculate the main text height as if holding

								    % an integer number of \normalsize lines after the first

								    % and discard any excess fractional remainder

								    % we subtracted the first line, because the first line

								    % is placed \topskip into the maintext, not \baselineskip like the

								    % rest of the lines.

								    \@INTmaintextheight=\@maintextheight%

								    \divide\@INTmaintextheight  by \baselineskip%

								    \multiply\@INTmaintextheight  by \baselineskip%

								    % now we calculate how much the title spacer height will

								    % have to be reduced from nominal (\@REDUCEmaintextheight is always

								    % a positive value) so that the maintext area will contain an integer

								    % number of normal size lines

								    % we change variable names here (to avoid confusion) as we no longer

								    % need \@INTmaintextheight and can reuse its dimen register

								    \let\@REDUCEmaintextheight=\@INTmaintextheight%

								    \advance\@REDUCEmaintextheight by -\@maintextheight%

								    \advance\@REDUCEmaintextheight by \baselineskip%

								    % this is the calculated height of the spacer

								    % we change variable names here (to avoid confusion) as we no longer

								    % need \@maintextheight and can reuse its dimen register

								    \let\@COMPENSATElen=\@maintextheight%

								    \@COMPENSATElen=\@NORMtitlevspace% set the nominal value

								    % we go with the reduced length if it is smaller than an increase

								    \ifdim\@REDUCEmaintextheight < 0.5\baselineskip\relax%

								     \advance\@COMPENSATElen by -\@REDUCEmaintextheight%

								     % if the resulting spacer is too small back out and go with an increase instead

								     \ifdim\@COMPENSATElen<\@MINtitlevspace\relax%

								      \advance\@COMPENSATElen by \baselineskip%

								     \fi%

								    \else%

								     % go with an increase because it is closer to the nominal than a decrease

								     \advance\@COMPENSATElen by -\@REDUCEmaintextheight%

								     \advance\@COMPENSATElen by \baselineskip%

								    \fi%

								    % set the calculated rigid spacer

								    \vspace{\@COMPENSATElen}}}


								% V1.6

								% we allow the user access to the last part of the title area

								% useful in emergencies such as when a different spacing is needed

								% This text is NOT compensated for in the dynamic sizer.

								\let\@IEEEaftertitletext=\relax

								\def\IEEEaftertitletext#1{\def\@IEEEaftertitletext{#1}}


								% V1.6 have abstract and keywords strip leading spaces, pars and newlines

								% so that spacing is more tightly controlled.

								\def\abstract{\normalfont%

								    \if@twocolumn%

								      \@IEEEabskeysecsize\bfseries\textit{Abstract}---\,%

								    \else%

								      \begin{center}\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{Abstract}\end{center}\quotation\@IEEEabskeysecsize%

								    \fi\@IEEEgobbleleadPARNLSP}

								% V1.6 IEEE wants only 1 pica from end of abstract to introduction heading when in

								% conference mode (the heading already has this much above it)

								\def\endabstract{\relax\if@confmode\vspace{0ex}\else\vspace{1.34ex}\fi\par\if@twocolumn\else\endquotation\fi%

								    \normalfont\normalsize}


								\def\keywords{\normalfont%

								    % IEEE uses the term (in bold italics) "Index Terms" now.

								    \if@twocolumn%

								      \@IEEEabskeysecsize\bfseries\textit{Index Terms}---\,\relax%

								    \else%

								      \begin{center}\@IEEEabskeysecsize\bfseries Index Terms\end{center}\quotation\@IEEEabskeysecsize%

								    \fi\@IEEEgobbleleadPARNLSP}

								\def\endkeywords{\relax\if@technote\vspace{1.34ex}\else\vspace{0.67ex}\fi%

								    \par\if@twocolumn\else\endquotation\fi%

								    \normalsize\normalfont}


								% gobbles all leading \, \\ and \par, upon finding first token that

								% is not a \ , \\ or a \par, it ceases and returns that token

								%

								% used to strip leading \, \\ and \par from the input

								% so that such things in the beginning of an environment will not

								% affect the formatting of the text

								\long\def\@IEEEgobbleleadPARNLSP#1{\let\@IEEEswallowthistoken=0%

								\let\@IEEEgobbleleadPARNLSPtoken#1%

								\let\@IEEEgobbleleadPARtoken=\par%

								\let\@IEEEgobbleleadNLtoken=\\%

								\let\@IEEEgobbleleadSPtoken=\ %

								\def\@IEEEgobbleleadSPMACRO{\ }%

								\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadPARtoken%

								\let\@IEEEswallowthistoken=1%

								\fi%

								\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadNLtoken%

								\let\@IEEEswallowthistoken=1%

								\fi%

								\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPtoken%

								\let\@IEEEswallowthistoken=1%

								\fi%

								% a control space will come in as a macro

								% when it is the last one on a line

								\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPMACRO%

								\let\@IEEEswallowthistoken=1%

								\fi%

								% if we have to swallow this token, do so and taste the next one

								% else spit it out and stop gobbling

								\ifx\@IEEEswallowthistoken 1\let\@IEEEnextgobbleleadPARNLSP=\@IEEEgobbleleadPARNLSP\else%

								\let\@IEEEnextgobbleleadPARNLSP=#1\fi%

								\@IEEEnextgobbleleadPARNLSP}%


								% TITLING OF SECTIONS

								\def\@IEEEsectpunct{:\ \,}  % Punctuation after run-in section heading  (headings which are

								                            % part of the paragraphs), need little bit more than a space


								\def\@seccntformat#1{\csname the#1dis\endcsname\hskip 0.5em\relax}


								\def\@sect#1#2#3#4#5#6[#7]#8{%

								  \ifnum #2>\c@secnumdepth%

								     \def\@svsec{}%

								  \else%

								     \refstepcounter{#1}

								     % load section label and spacer into \@svsec

								     \protected@edef\@svsec{\@seccntformat{#1}\relax}%

								  \fi%

								  \@tempskipa #5\relax%

								  \ifdim \@tempskipa>\z@% tempskipa determines whether is treated as a high

								     \begingroup #6\relax% or low level heading

								      \noindent % subsections are NOT indented

								       % print top level headings. \@svsec is label, #8 is heading title

								       %\@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}

								       % IEEE does not block indent the section title text, it flows like normal

								       \relax{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}%

								     \endgroup%

								     % got rid of sectionmark stuff

								     % \csname #1mark\endcsname{#7}

								     \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else%

								               \protect\numberline{\csname the#1\endcsname}\fi#7}%

								  \else % printout low level headings

								     % svsechd seems to swallow the trailing space, protect it with \mbox{}

								     % got rid of sectionmark stuff

								     \def\@svsechd{#6\hskip #3\@svsec #8\@IEEEsectpunct\mbox{}%\csname #1mark\endcsname{#7}

								     \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else%

								               \protect\numberline{\csname the#1\endcsname}\fi#7}}

								  \fi%skip down

								  \@xsect{#5}}


								% section* handler

								\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax%

								  \ifdim \@tempskipa>\z@%

								     %\begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup

								     % IEEE does not block indent the section title text, it flows like normal

								     \begingroup \noindent #4\relax{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup%

								  % svsechd swallows the trailing space, protect it with \mbox{}

								  \else \def\@svsechd{#4\hskip #1\relax #5\@IEEEsectpunct\mbox{}}\fi%

								  \@xsect{#3}}


								%% SECTION heading spacing and font

								%%

								% arguments are: #1 - sectiontype name

								% (for \@sect)   #2 - section level

								%                #3 - section heading indent

								%                #4 - top separation (absolute value used, neg indicates not to indent main text)

								%                     If negative, make stretch parts negative too!

								%                #5 - (absolute value used) positive: bottom separation after heading,

								%                      negative: amount to indent main text after heading

								%                Both #4 and #5 negative means to indent main text and use negative top separation

								%                #6 - font control

								% You've got to have \normalfont\normalsize in the font specs below to prevent

								% trouble when you do something like:

								% \section{Note}{\ttfamily TT-TEXT} is known to ...

								% IEEE sometimes REALLY stretches the area before a section

								% heading by up to about 0.5in. However, it may not be a good

								% idea to let LaTeX have quite this much rubber.

								\if@confmode%

								% IEEE wants section heading spacing to decrease for conference mode

								\def\section{\@startsection{section}{1}{\z@}{1.5ex plus 1.5ex minus 0.5ex}%

								{0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}%

								\def\subsection{\@startsection{subsection}{2}{\z@}{1.5ex plus 1.5ex minus 0.5ex}%

								{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%

								\else % for journals

								\def\section{\@startsection{section}{1}{\z@}{3.0ex plus 1.5ex minus 1.5ex}% V1.6 3.0ex from 3.5ex

								{0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}%

								\def\subsection{\@startsection{subsection}{2}{\z@}{3.5ex plus 1.5ex minus 1.5ex}%

								{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%

								\fi

								% decided to put in a little rubber above the section, might help somebody

								\def\subsubsection{\@startsection{subsubsection}{3}{\parindent}{0ex plus 0.1ex minus 0.1ex}%

								{0ex}{\normalfont\normalsize\itshape}}%

								\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{0ex plus 0.1ex minus 0.1ex}%

								{0ex}{\normalfont\normalsize\itshape}}%


								%% ENVIRONMENTS

								% "box" symbols at end of proofs

								\def\QEDclosed{\mbox{\rule[0pt]{1.3ex}{1.3ex}}} % for a filled box

								% V1.6 some journals use an open box instead that will just fit around a closed one

								\def\QEDopen{{\setlength{\fboxsep}{0pt}\setlength{\fboxrule}{0.2pt}\fbox{\rule[0pt]{0pt}{1.3ex}\rule[0pt]{1.3ex}{0pt}}}}

								\def\QED{\QEDclosed} % default to closed


								\def\proof{\noindent\hspace{2em}{\itshape Proof: }}

								\def\endproof{\hspace*{\fill}~\QED\par\endtrivlist\unskip}

								%\itemindent is set to \z@ by list, so define new temporary variable

								\newdimen\@IEEEtmpitemindent

								\def\@begintheorem#1#2{\@IEEEtmpitemindent\itemindent\topsep 0pt\rmfamily\trivlist%

								    \item[\hskip \labelsep{\indent\itshape #1\ #2:}]\itemindent\@IEEEtmpitemindent}

								\def\@opargbegintheorem#1#2#3{\@IEEEtmpitemindent\itemindent\topsep 0pt\rmfamily \trivlist%

								% V1.6 IEEE is back to using () around theorem names which are also in italics

								% Thanks to Christian Peel for reporting this.

								    \item[\hskip\labelsep{\indent\itshape #1\ #2\ (#3):}]\itemindent\@IEEEtmpitemindent}

								\def\@endtheorem{\endtrivlist\unskip}


								% V1.6

								% display command for the section the theorem is in - so that \thesection

								% is not used as this will be in Roman numerals when we want arabic.

								% LaTeX2e uses \def\@thmcounter#1{\noexpand\arabic{#1}} for the theorem number

								% (second part) display and \def\@thmcountersep{.} as a separator.

								\def\@IEEEthmcounterin#1{\arabic{#1}}

								% redefine the #1#2[#3] form of newtheorem to use a hook to \@IEEEthmcounterin

								\def\@xnthm#1#2[#3]{%

								  \expandafter\@ifdefinable\csname #1\endcsname

								    {\@definecounter{#1}\@newctr{#1}[#3]%

								     \expandafter\xdef\csname the#1\endcsname{%

								     \noexpand\@IEEEthmcounterin{#3}\@thmcountersep\@thmcounter{#1}}%

								     \global\@namedef{#1}{\@thm{#1}{#2}}%

								     \global\@namedef{end#1}{\@endtheorem}}}


								%% SET UP THE DEFAULT PAGESTYLE

								\ps@headings

								\pagenumbering{arabic}


								% normally the page counter starts at 1

								\setcounter{page}{1}

								% however, for peerreview the cover sheet is page 0 or page -1

								% (for duplex printing)

								\if@peerreviewoption

								   \if@twoside

								      \setcounter{page}{-1}

								   \else

								      \setcounter{page}{0}

								   \fi

								\fi


								% standard book class behavior - let bottom line float up and down as

								% needed when single sided

								\if@twoside\else\raggedbottom\fi

								% if two column - turn on twocolumn, allow word spacings to stretch more and

								% enforce a rigid position for the last lines

								\if@twocolumnmode

								% the peer review option delays invoking twocolumn

								   \if@peerreviewoption\else

								      \twocolumn

								   \fi

								\sloppy

								\flushbottom

								\fi


								% \APPENDIX and \APPENDICES definitions


								% This is the \@ifmtarg command from the LaTeX ifmtarg package

								% by Peter Wilson (CUA) and Donald Arseneau

								% \@ifmtarg is used to determine if an argument to a command

								% is present or not.

								% For instance:

								% \@ifmtarg{#1}{\typeout{empty}}{\typeout{has something}}

								% \@ifmtarg is used with our redefined \section command if

								% \appendices is invoked.

								% The command \section will behave slightly differently depending

								% on whether the user specifies a title:

								% \section{My appendix title}

								% or not:

								% \section{}

								% This way, we can eliminate the blank lines where the title

								% would be, and the unneeded : after Appendix in the table of

								% contents

								\begingroup

								\catcode`\Q=3

								\long\gdef\@ifmtarg#1{\@xifmtarg#1QQ\@secondoftwo\@firstoftwo\@nil}

								\long\gdef\@xifmtarg#1#2Q#3#4#5\@nil{#4}

								\endgroup

								% end of \@ifmtarg defs


								% save the "original" meaning of \section so we can redefine

								% \section after a call to \appendix or \appendices

								\let\@IEEEappendixsavesection\section


								% neat trick to grab and process the argument from \section{argument}

								% we process differently if the user invoked \section{} with no

								% argument (title)

								% note we reroute the call to the old \section*

								\def\@IEEEprocessthesectionargument#1{%

								\@ifmtarg{#1}{%

								\@IEEEappendixsavesection*{Appendix \thesectiondis}%

								\addcontentsline{toc}{section}{Appendix \thesection}}{%

								\@IEEEappendixsavesection*{Appendix \thesectiondis \\* #1}%

								\addcontentsline{toc}{section}{Appendix \thesection: #1}}}


								% we use this if the user calls \section{} after

								% \appendix-- which has no meaning. So, we ignore the

								% command and its argument. Then, warn the user.

								\def\@IEEEdestroythesectionargument#1{\typeout{** WARNING: Ignoring useless

								\protect\section\space in Appendix (line \the\inputlineno).}}


								% remember \thesection forms will be displayed in \ref calls

								% and in the Table of Contents.

								% The \sectiondis form is used in the actual heading itself


								% appendix command for one single appendix

								% normally has no heading. However, if you want a

								% heading, you can do so via the optional argument:

								% \appendix[Optional Heading]

								\def\appendix{\relax}

								\renewcommand{\appendix}[1][]{\par%

								    % v1.6 keep hyperref's identifiers unique

								    \def\theHsection{Appendix.A}%

								    % v1.6 adjust hyperref's string name for the section

								    \xdef\Hy@chapapp{appendix}%

								    \setcounter{section}{0}%

								    \setcounter{subsection}{0}%

								    \setcounter{subsubsection}{0}%

								    \setcounter{paragraph}{0}%

								    \def\thesection{}%

								    \def\thesectiondis{}%

								    \def\thesubsection{\Alph{subsection}}%

								    \refstepcounter{section}% update the \ref counter

								    \@ifmtarg{#1}{\@IEEEappendixsavesection*{Appendix}%

								                  \addcontentsline{toc}{section}{Appendix}}{%

								             \@IEEEappendixsavesection*{Appendix \\* #1}%

								             \addcontentsline{toc}{section}{Appendix: #1}}%

								    % redefine \section command for appendix

								    % leave \section* as is

								    \def\section{\@ifstar{\@IEEEappendixsavesection*}{%

								                    \@IEEEdestroythesectionargument}}% throw out the argument

								                                                     % of the normal form

								}


								% provides the user a way to choose between

								% Appendix A

								%    and

								% Appendix I

								% notation

								% defaults to Roman.

								\newif\ifuseRomanappendices

								\useRomanappendicestrue


								% appendices command for multiple appendices

								% user then calls \section with an argument (possibly empty) to

								% declare the individual appendices

								\def\appendices{\par%

								    % v1.6 keep hyperref's identifiers unique

								    \def\theHsection{Appendix.\Alph{section}}%

								    % v1.6 adjust hyperref's string name for the section

								    \xdef\Hy@chapapp{appendix}%

								    \setcounter{section}{-1}% we want \refstepcounter to use section 0

								    \setcounter{subsection}{0}%

								    \setcounter{subsubsection}{0}%

								    \setcounter{paragraph}{0}%

								    \ifuseRomanappendices%

								    \def\thesection{\Roman{section}}%

								    \def\thesectiondis{\Roman{section}}%

								    \else%

								    \def\thesection{\Alph{section}}%

								    \def\thesectiondis{\Alph{section}}%

								    \fi%

								    \refstepcounter{section}% update the \ref counter

								    \setcounter{section}{0}% NEXT \section will be the FIRST appendix

								    % redefine \section command for appendices

								    % leave \section* as is

								    \def\section{\@ifstar{\@IEEEappendixsavesection*}{% process the *-form

								                    \refstepcounter{section}% or is a new section so,

								                    \@IEEEprocessthesectionargument}}% process the argument

								                                                 % of the normal form

								}


								% \PARstart

								% Definition for the big two line drop cap letter at the beginning of the

								% first paragraph of journal papers. The first argument is the first letter

								% of the first word, the second argument is the remaining letters of the

								% first word which will be rendered in upper case.

								% In V1.6 this has been completely rewritten to:

								%

								% 1. no longer have problems when the user begins an environment

								%    within the paragraph that uses \PARstart.

								% 2. auto-detect and use the current font family

								% 3. revise handling of the space at the end of the first word so that

								%    interword glue will now work as normal.

								% 4. produce correctly aligned edges for the (two) indented lines.

								%

								% We generalize things via control macros - playing with these is fun too.

								%

								% the number of lines that are indented to clear it

								\def\@IEEEPARstartDROPLINES{2}

								% minimum number of lines left on a page to allow a \@PARstart

								% Does not take into consideration rubber shrink, so it tends to

								% be overly cautious

								\def\@IEEEPARstartMINPAGELINES{2}

								% the depth the letter is lowered below the baseline

								% the height (and size) of the letter is determined by the sum

								% of this value and the height of a capital "T" in the current

								% font. It is a good idea to set this value in terms of the baselineskip

								% so that it can respond to changes therein.

								\def\@IEEEPARstartDROPDEPTH{1.1\baselineskip}

								% This is the separation distance from the drop letter to the main text.

								% Lengths that depend on the font (i.e., ex, em, etc.) will be referenced

								% to the font that is active when PARstart is called.

								\def\@IEEEPARstartSEP{0.15em}


								% definition of \PARstart

								% THIS IS A CONTROLLED SPACING AREA, DO NOT ALLOW SPACES WITHIN THESE LINES

								%

								% The token \@IEEEPARstartfont will be globally defined after the first use

								% of \PARstart and will be a font command which creates the big letter

								% The first argument is the first letter of the first word and the second

								% argument is the rest of the first word(s).

								\def\PARstart#1#2{\par{%

								% if this page does not have enough space, break it and lets start

								% on a new one

								\@IEEEtranneedspace{\@IEEEPARstartMINPAGELINES\baselineskip}{\relax}%

								% calculate the desired height of the big letter

								% it extends from the top of a capital "T" in the current font

								% down to \@IEEEPARstartDROPDEPTH below the current baseline

								\settoheight{\@IEEEtrantmpdimenA}{T}%

								\addtolength{\@IEEEtrantmpdimenA}{\@IEEEPARstartDROPDEPTH}%

								% extract the name of the current font in bold

								% and place it in \@IEEEPARstartFONTNAME

								\def\@IEEEPARstartGETFIRSTWORD##1 ##2\relax{##1}%

								{\bfseries%

								\edef\@IEEEPARstartFONTNAMESPACE{\fontname\font\space}%

								\xdef\@IEEEPARstartFONTNAME{\expandafter\@IEEEPARstartGETFIRSTWORD\@IEEEPARstartFONTNAMESPACE\relax}}%

								% define a font based on this name with a point size equal to the desired

								% height of the drop letter

								\font\@IEEEPARstartsubfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenA\relax%

								% save this value as a counter (integer) value (sp points)

								\@IEEEtrantmpcountA=\@IEEEtrantmpdimenA%

								% now get the height of the actual letter produced by this font size

								\settoheight{\@IEEEtrantmpdimenB}{\@IEEEPARstartsubfont\MakeUppercase{#1}}%

								% If something bogus happens like the first argument is empty or the

								% current font is strange, do not allow a zero height.

								\ifdim\@IEEEtrantmpdimenB=0pt\relax%

								\typeout{** WARNING: PARstart drop letter has zero height! (line \the\inputlineno)}%

								\typeout{ Forcing the drop letter font size to 10pt.}%

								\@IEEEtrantmpdimenB=10pt%

								\fi%

								% and store it as a counter

								\@IEEEtrantmpcountB=\@IEEEtrantmpdimenB%

								% Since a font size doesn't exactly correspond to the height of the capital

								% letters in that font, the actual height of the letter, \@IEEEtrantmpcountB,

								% will be less than that desired, \@IEEEtrantmpcountA

								% we need to raise the font size, \@IEEEtrantmpdimenA

								% by \@IEEEtrantmpcountA / \@IEEEtrantmpcountB

								% But, TeX doesn't have floating point division, so we have to use integer

								% division. Hence the use of the counters.

								% We need to reduce the denominator so that the loss of the remainder will

								% have minimal affect on the accuracy of the result

								\divide\@IEEEtrantmpcountB by 200%

								\divide\@IEEEtrantmpcountA by \@IEEEtrantmpcountB%

								% Then reequalize things when we use TeX's ability to multiply by

								% floating point values

								\@IEEEtrantmpdimenB=0.005\@IEEEtrantmpdimenA%

								\multiply\@IEEEtrantmpdimenB by \@IEEEtrantmpcountA%

								% \@IEEEPARstartfont is globaly set to the calculated font of the big letter

								% We need to carry this out of the local calculation area to to create the

								% big letter.

								\global\font\@IEEEPARstartfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenB%

								% Now set \@IEEEtrantmpdimenA to the width of the big letter

								% We need to carry this out of the local calculation area to set the

								% hanging indent

								\settowidth{\global\@IEEEtrantmpdimenA}{\@IEEEPARstartfont\MakeUppercase{#1}}}%

								% end of the isolated calculation environment

								% add in the extra clearance we want

								\advance\@IEEEtrantmpdimenA by \@IEEEPARstartSEP%

								% \@IEEEtrantmpdimenA has the width of the big letter plus the

								% separation space and \@IEEEPARstartfont is the font we need to use

								% Now, we make the letter and issue the hanging indent command

								% The letter is placed in a box of zero width and height so that other

								% text won't be displaced by it.

								\noindent\hangindent\@IEEEtrantmpdimenA\hangafter=-\@IEEEPARstartDROPLINES%

								\makebox[0pt][l]{\hspace{-\@IEEEtrantmpdimenA}\raisebox{-\@IEEEPARstartDROPDEPTH}[0pt][0pt]{\@IEEEPARstartfont\MakeUppercase{#1}}}\MakeUppercase{#2}}


								% V1.6 \CMPARstart is no longer needed as \PARstart now uses whatever

								% the current font family is.

								% \CMPARstart is provided here for backward compatability.

								\let\CMPARstart=\PARstart


								% determines if the space remaining on a given page is equal to or greater

								% than the specified space of argument one

								% if not, execute argument two (only if the remaining space is greater than zero)

								% and issue a \newpage

								%

								% example: \@IEEEtranneedspace{2in}{\vfill}

								%

								% Does not take into consideration rubber shrinkage, so it tends to

								% be overly cautious

								% Based on an example posted by Donald Arseneau

								% Note this macro uses \@IEEEtrantmpdimenB internally for calculations,

								% so DO NOT PASS \@IEEEtrantmpdimenB to this routine

								% if you need a dimen register, import with \@IEEEtrantmpdimenA instead

								\def\@IEEEtranneedspace#1#2{\penalty-100\begingroup%shield temp variable

								\@IEEEtrantmpdimenB\pagegoal\advance\@IEEEtrantmpdimenB-\pagetotal% space left

								\ifdim #1>\@IEEEtrantmpdimenB\relax% not enough space left

								\ifdim\@IEEEtrantmpdimenB>\z@\relax #2\fi%

								\newpage%

								\fi\endgroup}


								% BIOGRAPHY ENVIRONMENT

								% Allows user to enter BIOGRAPHY leaving place for picture (adapts to font size)

								% As of V1.5, a new optional argument allows you to have a real graphic!

								% V1.5 and later also fixes the "colliding biographies" which could happen when a

								% biography's text was shorter than the space for the photo.

								% MDS 7/2001

								% V1.6 prevent multiple biographies from making multiple TOC entries

								\newif\if@biographyTOCentrynotmade

								\global\@biographyTOCentrynotmadetrue


								% biography counter so hyperref can jump directly to the biographies

								% and not just the previous section

								\newcounter{biography}

								\setcounter{biography}{0}


								% photo area size

								\def\@IEEEBIOphotowidth{1.0in}    % width of the biography photo area

								\def\@IEEEBIOphotodepth{1.25in}   % depth (height) of the biography photo area

								% area cleared for photo

								\def\@IEEEBIOhangwidth{1.14in}    % width cleared for the biography photo area

								\def\@IEEEBIOhangdepth{1.25in}    % depth cleared for the biography photo area

								                                  % actual depth will be a multiple of

								                                  % \baselineskip, rounded up

								\def\@IEEEBIOskipN{4\baselineskip}% nominal value of the vskip above the biography


								\newenvironment{biography}[2][]{\normalfont\footnotesize%

								\unitlength 1in\parskip=0pt\par\parindent 1em\interlinepenalty500%

								% we need enough space to support the hanging indent

								% the nominal value of the spacer

								% and one extra line for good measure

								\@IEEEtrantmpdimenA=\@IEEEBIOhangdepth%

								\advance\@IEEEtrantmpdimenA by \@IEEEBIOskipN%

								\advance\@IEEEtrantmpdimenA by 1\baselineskip%

								% if this page does not have enough space, break it and lets start

								% with a new one

								\@IEEEtranneedspace{\@IEEEtrantmpdimenA}{\relax}%

								% nominal spacer can strech, not shrink use 1fil so user can out stretch with \vfill

								\vskip \@IEEEBIOskipN plus 1fil minus 0\baselineskip%

								% the default box for where the photo goes

								\def\@IEEEtempbiographybox{{\setlength{\fboxsep}{0pt}\framebox{\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}\centering PLACE\\ PHOTO\\ HERE \end{minipage}}}}%

								%

								% detect if the optional argument was supplied, this requires the

								% \@ifmtarg command as defined in the appendix section above

								% and if so, override the default box with what they want

								\@ifmtarg{#1}{\relax}{\def\@IEEEtempbiographybox{\mbox{\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}%

								\centering%

								#1%

								\end{minipage}}}}% end if optional argument supplied

								% Make an entry into the table of contents only if we have not done so before

								\if@biographyTOCentrynotmade%

								% link labels to the biography counter so hyperref will jump

								% to the biography, not the previous section

								\setcounter{biography}{-1}%

								\refstepcounter{biography}%

								\addcontentsline{toc}{section}{Biographies}%

								\global\@biographyTOCentrynotmadefalse%

								\fi%

								% one more biography

								\refstepcounter{biography}%

								% Make an entry for this name into the table of contents

								\addcontentsline{toc}{subsection}{#2}%

								% V1.6 properly handle if a new paragraph should occur while the

								% hanging indent is still active. Do this by redefining \par so

								% that it will not start a new paragraph. (But it will appear to the

								% user as if it did.) Also, strip any leading pars, newlines, or spaces.

								\let\@IEEEBIOORGparCMD=\par% save the original \par command

								\edef\par{\hfil\break\indent}% the new \par will not be a "real" \par

								\settoheight{\@IEEEtrantmpdimenA}{\@IEEEtempbiographybox}% get height of biography box

								\@IEEEtrantmpdimenB=\@IEEEBIOhangdepth%

								\@IEEEtrantmpcountA=\@IEEEtrantmpdimenB% countA has the hang depth

								\divide\@IEEEtrantmpcountA by \baselineskip%  calculates lines needed to produce the hang depth

								\advance\@IEEEtrantmpcountA by 1% ensure we overestimate

								% set the hanging indent

								\hangindent\@IEEEBIOhangwidth%

								\hangafter-\@IEEEtrantmpcountA%

								% reference the top of the photo area to the top of a capital T

								\settoheight{\@IEEEtrantmpdimenB}{\mbox{T}}%

								% set the photo box, give it zero width and height so as not to disturb anything

								\noindent\makebox[0pt][l]{\hspace{-\@IEEEBIOhangwidth}\raisebox{\@IEEEtrantmpdimenB}[0pt][0pt]{\raisebox{-\@IEEEBIOphotodepth}[0pt][0pt]{\@IEEEtempbiographybox}}}%

								% now place the author name and begin the bio text

								\noindent\textbf{#2\ }\@IEEEgobbleleadPARNLSP}{\relax\let\par=\@IEEEBIOORGparCMD\par%

								% 7/2001 V1.5 detect when the biography text is shorter than the photo area

								% and pad the unused area - preventing a collision from the next biography entry

								% MDS

								\ifnum \prevgraf <\@IEEEtrantmpcountA\relax% detect when the biography text is shorter than the photo

								    \advance\@IEEEtrantmpcountA by -\prevgraf% calculate how many lines we need to pad

								    \advance\@IEEEtrantmpcountA by -1\relax% we compensate for the fact that we indented an extra line

								    \@IEEEtrantmpdimenA=\baselineskip% calculate the length of the padding

								    \multiply\@IEEEtrantmpdimenA by \@IEEEtrantmpcountA%

								    \noindent\rule{0pt}{\@IEEEtrantmpdimenA}% insert an invisible support strut

								\fi%

								\par\normalfont}


								% V1.6

								% added biography without a photo environment

								\newenvironment{biographynophoto}[1]{%

								% Make an entry into the table of contents only if we have not done so before

								\if@biographyTOCentrynotmade%

								% link labels to the biography counter so hyperref will jump

								% to the biography, not the previous section

								\setcounter{biography}{-1}%

								\refstepcounter{biography}%

								\addcontentsline{toc}{section}{Biographies}%

								\global\@biographyTOCentrynotmadefalse%

								\fi%

								% one more biography

								\refstepcounter{biography}%

								% Make an entry for this name into the table of contents

								\addcontentsline{toc}{subsection}{#1}%

								\normalfont\footnotesize\interlinepenalty500%

								\vskip 4\baselineskip plus 1fil minus 0\baselineskip%

								\parskip=0pt\par%

								\noindent\textbf{#1\ }\@IEEEgobbleleadPARNLSP}{\relax\par\normalfont}


								% provide the user with some old font commands

								% got this from article.cls

								\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}

								\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}

								\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}

								\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}

								\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}

								\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}

								\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}

								\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal}

								\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal}


								% SPECIAL PAPER NOTICE COMMANDS

								%

								% holds the special notice text

								\def\@specialpapernotice{\relax}


								% for special papers, like invited papers, the user can do:

								% \specialpapernotice{(Invited Paper)} before \maketitle

								\def\specialpapernotice#1{\if@confmode%

								\def\@specialpapernotice{{\sublargesize\textit{#1}\vspace*{1em}}}%

								\else%

								\def\@specialpapernotice{{\\*[1.5ex]\sublargesize\textit{#1}}\vspace*{-2ex}}%

								\fi}


								% PUBLISHER ID COMMANDS

								% to insert a publisher's ID footer

								% V1.6 \pubid has been changed so that the change in page size and style

								% occurs in \maketitle. \pubid must now be issued prior to \maketitle

								% use \pubidadjcol as before - in the second column of the title page

								% These changes allow \maketitle to take the reduced page height into

								% consideration when dynamically setting the space between the author

								% names and the maintext.

								%

								% the amount the main text is pulled up to make room for the

								% publisher's ID footer

								% IEEE uses about 1.3\baselineskip for journals,

								% dynamic title spacing will clean up the fraction

								\def\@pubidpullup{1.3\baselineskip}

								\if@technote

								% for technotes it must be an integer of baselineskip as there can be no

								% dynamic title spacing for two column mode technotes (the title is in the

								% in first column) and we should maintain an integer number of lines in the

								% second column

								% There are some examples (such as older issues of "Transactions on

								% Information Theory") in which IEEE really pulls the text off the ID for

								% technotes - about 0.55in (or 4\baselineskip). We'll use 2\baselineskip

								% and call it even.

								\def\@pubidpullup{2\baselineskip}

								\fi


								% holds the ID text

								\def\@pubid{\relax}


								% flag so \maketitle can tell if \pubid was called

								\newif\if@IEEEusingpubid

								\global\@IEEEusingpubidfalse

								% issue this command in the page to have the ID at the bottom

								% V1.6 use before \maketitle

								\def\pubid#1{\def\@pubid{#1} \global\@IEEEusingpubidtrue}


								% command which will pull up (shorten) the column it is executed in

								% to make room for the publisher ID. Place in the second column of

								% the title page when using \pubid

								% Is smart enough not to do anything when in single column text or

								% if the user hasn't called \pubid

								% currently needed in for the second column of a page with the

								% publisher ID. If not needed in future releases, please provide this

								% command and define it as \relax for backward compatibility

								% v1.6b do not allow command to operate if the peer review option has been

								% selected because \pubidadjcol will not be on the cover page.

								\def\pubidadjcol{\if@peerreviewoption\else\if@twocolumn\if@IEEEusingpubid\enlargethispage{-\@pubidpullup}\fi\fi\fi}


								% Special thanks to Peter Wilson, Daniel Luecking, and the other

								% gurus at comp.text.tex, for helping me to understand how best to

								% implement the pubid command in LaTeX.


								%% Lockout some commands under various conditions


								% general purpose bit bucket

								\newsavebox{\@IEEEtranrubishbin}


								% flags to prevent multiple warning messages

								\newif\if@IEEEWARNthanks

								\newif\if@IEEEWARNPARstart

								\newif\if@IEEEWARNCMPARstart

								\newif\if@IEEEWARNkeywords

								\newif\if@IEEEWARNbiography

								\newif\if@IEEEWARNbiographynophoto

								\newif\if@IEEEWARNpubid

								\newif\if@IEEEWARNpubidadjcol

								\newif\if@IEEEWARNIEEEmembership

								\newif\if@IEEEWARNIEEEaftertitletext

								\@IEEEWARNthankstrue

								\@IEEEWARNPARstarttrue

								\@IEEEWARNCMPARstarttrue

								\@IEEEWARNkeywordstrue

								\@IEEEWARNbiographytrue

								\@IEEEWARNbiographynophototrue

								\@IEEEWARNpubidtrue

								\@IEEEWARNpubidadjcoltrue

								\@IEEEWARNIEEEmembershiptrue

								\@IEEEWARNIEEEaftertitletexttrue


								%% Lockout some commands when in various modes, but allow them to be restored if needed

								%%

								% save commands which might be locked out

								% so that the user can later restore them if needed

								\let\@IEEESAVECMDthanks\thanks

								\let\@IEEESAVECMDPARstart\PARstart

								\let\@IEEESAVECMDCMPARstart\CMPARstart

								\let\@IEEESAVECMDkeywords\keywords

								\let\@IEEESAVECMDendkeywords\endkeywords

								\let\@IEEESAVECMDbiography\biography

								\let\@IEEESAVECMDendbiography\endbiography

								\let\@IEEESAVECMDbiographynophoto\biographynophoto

								\let\@IEEESAVECMDendbiographynophoto\endbiographynophoto

								\let\@IEEESAVECMDpubid\pubid

								\let\@IEEESAVECMDpubidadjcol\pubidadjcol

								\let\@IEEESAVECMDIEEEmembership\IEEEmembership

								\let\@IEEESAVECMDIEEEaftertitletext\IEEEaftertitletext


								% disable \PARstart when in draft mode

								% This may have originally been done because the pre-V1.6 drop letter

								% algorithm had problems with a non-unity baselinestretch

								% At any rate, it seems too formal to have a drop letter in a draft

								% paper.

								\if@draftclsmode

								\def\PARstart#1#2{#1#2\if@IEEEWARNPARstart\typeout{** ATTENTION: \noexpand\PARstart is disabled in draft mode (line \the\inputlineno).}\fi\global\@IEEEWARNPARstartfalse}

								\def\CMPARstart#1#2{#1#2\if@IEEEWARNPARstart\typeout{** ATTENTION: \noexpand\CMPARstart is disabled in draft mode (line \the\inputlineno).}\fi\global\@IEEEWARNCMPARstartfalse}

								\fi

								% and for technotes

								\if@technote

								\def\PARstart#1#2{#1#2\if@IEEEWARNPARstart\typeout{** WARNING: \noexpand\PARstart is locked out for technotes (line \the\inputlineno).}\fi\global\@IEEEWARNPARstartfalse}

								\def\CMPARstart#1#2{#1#2\if@IEEEWARNPARstart\typeout{** WARNING: \noexpand\CMPARstart is locked out for technotes (line \the\inputlineno).}\fi\global\@IEEEWARNCMPARstartfalse}

								\fi


								% lockout unneeded commands when in conference mode

								\if@confmode

								% when locked out, \thanks, \keywords, \biography, \biographynophoto, \pubid,

								% \IEEEmembership and \IEEEaftertitletext will all swallow their given text.

								% \PARstart and \CMPARstart will output a normal character instead

								% warn the user about these commands only once to prevent the console screen

								% from filling up with redundant messages

								\def\thanks#1{\if@IEEEWARNthanks\typeout{** WARNING: \noexpand\thanks is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNthanksfalse}

								\def\PARstart#1#2{#1#2\if@IEEEWARNPARstart\typeout{** WARNING: \noexpand\PARstart is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNPARstartfalse}

								\def\CMPARstart#1#2{#1#2\if@IEEEWARNPARstart\typeout{** WARNING: \noexpand\CMPARstart is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNCMPARstartfalse}


								\renewenvironment{keywords}[1]{\if@IEEEWARNkeywords\typeout{** WARNING: \noexpand\keywords is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNkeywordsfalse%

								\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}


								% LaTeX treats environments and commands with optional arguments differently.

								% the actual ("internal") command is stored as \\commandname

								% (accessed via \csname\string\commandname\endcsname )

								% the "external" command \commandname is a macro with code to determine

								% whether or not the optional argument is presented and to provide the

								% default if it is absent. So, in order to save and restore such a command

								% we would have to save and restore \\commandname as well. But, if LaTeX

								% ever changes the way it names the internal names, the trick would break.

								% Instead let us just define a new environment so that the internal

								% name can be left undisturbed.

								\newenvironment{@IEEEbogusbiography}[2][]{\if@IEEEWARNbiography\typeout{** WARNING: \noexpand\biography is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNbiographyfalse%

								\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}

								% and make biography point to our bogus biography

								\let\biography=\@IEEEbogusbiography

								\let\endbiography=\end@IEEEbogusbiography


								\renewenvironment{biographynophoto}[1]{\if@IEEEWARNbiographynophoto\typeout{** WARNING: \noexpand\biographynophoto is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNbiographynophotofalse%

								\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}


								\def\pubid#1{\if@IEEEWARNpubid\typeout{** WARNING: \noexpand\pubid is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNpubidfalse}

								\def\pubidadjcol{\if@IEEEWARNpubidadjcol\typeout{** WARNING: \noexpand\pubidadjcol is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNpubidadjcolfalse}

								\def\IEEEmembership#1{\if@IEEEWARNIEEEmembership\typeout{** WARNING: \noexpand\IEEEmembership is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEmembershipfalse}

								\def\IEEEaftertitletext#1{\if@IEEEWARNIEEEaftertitletext\typeout{** WARNING: \noexpand\IEEEaftertitletext is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEaftertitletextfalse}

								\fi


								% provide a way to restore the commands that are locked out

								\def\IEEEoverridecommandlockouts{%

								\typeout{** ATTENTION: Overriding command lockouts (line \the\inputlineno).}%

								\let\thanks\@IEEESAVECMDthanks%

								\let\PARstart\@IEEESAVECMDPARstart%

								\let\CMPARstart\@IEEESAVECMDCMPARstart%

								\let\keywords\@IEEESAVECMDkeywords%

								\let\endkeywords\@IEEESAVECMDendkeywords%

								\let\biography\@IEEESAVECMDbiography%

								\let\endbiography\@IEEESAVECMDendbiography%

								\let\biographynophoto\@IEEESAVECMDbiographynophoto%

								\let\endbiographynophoto\@IEEESAVECMDendbiographynophoto%

								\let\pubid\@IEEESAVECMDpubid%

								\let\pubidadjcol\@IEEESAVECMDpubidadjcol%

								\let\IEEEmembership\@IEEESAVECMDIEEEmembership%

								\let\IEEEaftertitletext\@IEEESAVECMDIEEEaftertitletext}


								\endinput


								%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End of IEEEtran.cls  %%%%%%%%%%%%%%%%%%%%%%%%%%%%

								% That's all folks!