
<!--
     File mmlextra.ent produced by the XSL script entities.xsl
     from input data in unicode.xml.

     Copyright 1998 - 2010 W3C.

     Use and distribution of this code are permitted under the terms of the
     W3C Software Notice and License.
     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231.html

     Please report any errors to David Carlisle
     via the public W3C list www-math@w3.org.

     The numeric character values assigned to each entity
     (should) match the Unicode assignments in Unicode 5.x.

-->


<!-- 

       Public identifier: -//W3C//ENTITIES Additional MathML Symbols//EN//XML
       System identifier: http://www.w3.org/2003/entities/2007/mmlextra.ent

     The public identifier should always be used verbatim.
     The system identifier may be changed to suit local requirements.

     Typical invocation:

       <!ENTITY % mmlextra PUBLIC
         "-//W3C//ENTITIES Additional MathML Symbols//EN//XML"
         "http://www.w3.org/2003/entities/2007/mmlextra.ent"
       >
       %mmlextra;

-->

<!ENTITY af               "&#x02061;" ><!--FUNCTION APPLICATION -->
<!ENTITY aopf             "&#x1D552;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL A -->
<!ENTITY asympeq          "&#x0224D;" ><!--EQUIVALENT TO -->
<!ENTITY bopf             "&#x1D553;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL B -->
<!ENTITY copf             "&#x1D554;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL C -->
<!ENTITY Cross            "&#x02A2F;" ><!--VECTOR OR CROSS PRODUCT -->
<!ENTITY dd               "&#x02146;" ><!--DOUBLE-STRUCK ITALIC SMALL D -->
<!ENTITY DD               "&#x02145;" ><!--DOUBLE-STRUCK ITALIC CAPITAL D -->
<!ENTITY dopf             "&#x1D555;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL D -->
<!ENTITY DownArrowBar     "&#x02913;" ><!--DOWNWARDS ARROW TO BAR -->
<!ENTITY DownBreve        " &#x00311;" ><!--COMBINING INVERTED BREVE -->
<!ENTITY DownLeftRightVector "&#x02950;" ><!--LEFT BARB DOWN RIGHT BARB DOWN HARPOON -->
<!ENTITY DownLeftTeeVector "&#x0295E;" ><!--LEFTWARDS HARPOON WITH BARB DOWN FROM BAR -->
<!ENTITY DownLeftVectorBar "&#x02956;" ><!--LEFTWARDS HARPOON WITH BARB DOWN TO BAR -->
<!ENTITY DownRightTeeVector "&#x0295F;" ><!--RIGHTWARDS HARPOON WITH BARB DOWN FROM BAR -->
<!ENTITY DownRightVectorBar "&#x02957;" ><!--RIGHTWARDS HARPOON WITH BARB DOWN TO BAR -->
<!ENTITY ee               "&#x02147;" ><!--DOUBLE-STRUCK ITALIC SMALL E -->
<!ENTITY EmptySmallSquare "&#x025FB;" ><!--WHITE MEDIUM SQUARE -->
<!ENTITY EmptyVerySmallSquare "&#x025AB;" ><!--WHITE SMALL SQUARE -->
<!ENTITY eopf             "&#x1D556;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL E -->
<!ENTITY Equal            "&#x02A75;" ><!--TWO CONSECUTIVE EQUALS SIGNS -->
<!ENTITY FilledSmallSquare "&#x025FC;" ><!--BLACK MEDIUM SQUARE -->
<!ENTITY FilledVerySmallSquare "&#x025AA;" ><!--BLACK SMALL SQUARE -->
<!ENTITY fopf             "&#x1D557;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL F -->
<!ENTITY gopf             "&#x1D558;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL G -->
<!ENTITY GreaterGreater   "&#x02AA2;" ><!--DOUBLE NESTED GREATER-THAN -->
<!ENTITY Hat              "&#x0005E;" ><!--CIRCUMFLEX ACCENT -->
<!ENTITY hopf             "&#x1D559;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL H -->
<!ENTITY HorizontalLine   "&#x02500;" ><!--BOX DRAWINGS LIGHT HORIZONTAL -->
<!ENTITY ic               "&#x02063;" ><!--INVISIBLE SEPARATOR -->
<!ENTITY ii               "&#x02148;" ><!--DOUBLE-STRUCK ITALIC SMALL I -->
<!ENTITY iopf             "&#x1D55A;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL I -->
<!ENTITY it               "&#x02062;" ><!--INVISIBLE TIMES -->
<!ENTITY jopf             "&#x1D55B;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL J -->
<!ENTITY kopf             "&#x1D55C;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL K -->
<!ENTITY larrb            "&#x021E4;" ><!--LEFTWARDS ARROW TO BAR -->
<!ENTITY LeftDownTeeVector "&#x02961;" ><!--DOWNWARDS HARPOON WITH BARB LEFT FROM BAR -->
<!ENTITY LeftDownVectorBar "&#x02959;" ><!--DOWNWARDS HARPOON WITH BARB LEFT TO BAR -->
<!ENTITY LeftRightVector  "&#x0294E;" ><!--LEFT BARB UP RIGHT BARB UP HARPOON -->
<!ENTITY LeftTeeVector    "&#x0295A;" ><!--LEFTWARDS HARPOON WITH BARB UP FROM BAR -->
<!ENTITY LeftTriangleBar  "&#x029CF;" ><!--LEFT TRIANGLE BESIDE VERTICAL BAR -->
<!ENTITY LeftUpDownVector "&#x02951;" ><!--UP BARB LEFT DOWN BARB LEFT HARPOON -->
<!ENTITY LeftUpTeeVector  "&#x02960;" ><!--UPWARDS HARPOON WITH BARB LEFT FROM BAR -->
<!ENTITY LeftUpVectorBar  "&#x02958;" ><!--UPWARDS HARPOON WITH BARB LEFT TO BAR -->
<!ENTITY LeftVectorBar    "&#x02952;" ><!--LEFTWARDS HARPOON WITH BARB UP TO BAR -->
<!ENTITY LessLess         "&#x02AA1;" ><!--DOUBLE NESTED LESS-THAN -->
<!ENTITY lopf             "&#x1D55D;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL L -->
<!ENTITY mapstodown       "&#x021A7;" ><!--DOWNWARDS ARROW FROM BAR -->
<!ENTITY mapstoleft       "&#x021A4;" ><!--LEFTWARDS ARROW FROM BAR -->
<!ENTITY mapstoup         "&#x021A5;" ><!--UPWARDS ARROW FROM BAR -->
<!ENTITY MediumSpace      "&#x0205F;" ><!--MEDIUM MATHEMATICAL SPACE -->
<!ENTITY mopf             "&#x1D55E;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL M -->
<!ENTITY nbump            "&#x0224E;&#x00338;" ><!--GEOMETRICALLY EQUIVALENT TO with slash -->
<!ENTITY nbumpe           "&#x0224F;&#x00338;" ><!--DIFFERENCE BETWEEN with slash -->
<!ENTITY nesim            "&#x02242;&#x00338;" ><!--MINUS TILDE with slash -->
<!ENTITY NewLine          "&#x0000A;" ><!--LINE FEED (LF) -->
<!ENTITY NoBreak          "&#x02060;" ><!--WORD JOINER -->
<!ENTITY nopf             "&#x1D55F;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL N -->
<!ENTITY NotCupCap        "&#x0226D;" ><!--NOT EQUIVALENT TO -->
<!ENTITY NotHumpEqual     "&#x0224F;&#x00338;" ><!--DIFFERENCE BETWEEN with slash -->
<!ENTITY NotLeftTriangleBar "&#x029CF;&#x00338;" ><!--LEFT TRIANGLE BESIDE VERTICAL BAR with slash -->
<!ENTITY NotNestedGreaterGreater "&#x02AA2;&#x00338;" ><!--DOUBLE NESTED GREATER-THAN with slash -->
<!ENTITY NotNestedLessLess "&#x02AA1;&#x00338;" ><!--DOUBLE NESTED LESS-THAN with slash -->
<!ENTITY NotRightTriangleBar "&#x029D0;&#x00338;" ><!--VERTICAL BAR BESIDE RIGHT TRIANGLE with slash -->
<!ENTITY NotSquareSubset  "&#x0228F;&#x00338;" ><!--SQUARE IMAGE OF with slash -->
<!ENTITY NotSquareSuperset "&#x02290;&#x00338;" ><!--SQUARE ORIGINAL OF with slash -->
<!ENTITY NotSucceedsTilde "&#x0227F;&#x00338;" ><!--SUCCEEDS OR EQUIVALENT TO with slash -->
<!ENTITY oopf             "&#x1D560;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL O -->
<!ENTITY OverBar          "&#x0203E;" ><!--OVERLINE -->
<!ENTITY OverBrace        "&#x023DE;" ><!--TOP CURLY BRACKET -->
<!ENTITY OverBracket      "&#x023B4;" ><!--TOP SQUARE BRACKET -->
<!ENTITY OverParenthesis  "&#x023DC;" ><!--TOP PARENTHESIS -->
<!ENTITY planckh          "&#x0210E;" ><!--PLANCK CONSTANT -->
<!ENTITY popf             "&#x1D561;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL P -->
<!ENTITY Product          "&#x0220F;" ><!--N-ARY PRODUCT -->
<!ENTITY qopf             "&#x1D562;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL Q -->
<!ENTITY rarrb            "&#x021E5;" ><!--RIGHTWARDS ARROW TO BAR -->
<!ENTITY RightDownTeeVector "&#x0295D;" ><!--DOWNWARDS HARPOON WITH BARB RIGHT FROM BAR -->
<!ENTITY RightDownVectorBar "&#x02955;" ><!--DOWNWARDS HARPOON WITH BARB RIGHT TO BAR -->
<!ENTITY RightTeeVector   "&#x0295B;" ><!--RIGHTWARDS HARPOON WITH BARB UP FROM BAR -->
<!ENTITY RightTriangleBar "&#x029D0;" ><!--VERTICAL BAR BESIDE RIGHT TRIANGLE -->
<!ENTITY RightUpDownVector "&#x0294F;" ><!--UP BARB RIGHT DOWN BARB RIGHT HARPOON -->
<!ENTITY RightUpTeeVector "&#x0295C;" ><!--UPWARDS HARPOON WITH BARB RIGHT FROM BAR -->
<!ENTITY RightUpVectorBar "&#x02954;" ><!--UPWARDS HARPOON WITH BARB RIGHT TO BAR -->
<!ENTITY RightVectorBar   "&#x02953;" ><!--RIGHTWARDS HARPOON WITH BARB UP TO BAR -->
<!ENTITY ropf             "&#x1D563;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL R -->
<!ENTITY RoundImplies     "&#x02970;" ><!--RIGHT DOUBLE ARROW WITH ROUNDED HEAD -->
<!ENTITY RuleDelayed      "&#x029F4;" ><!--RULE-DELAYED -->
<!ENTITY sopf             "&#x1D564;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL S -->
<!ENTITY Tab              "&#x00009;" ><!--CHARACTER TABULATION -->
<!ENTITY ThickSpace       "&#x0205F;&#x0200A;" ><!--space of width 5/18 em -->
<!ENTITY topf             "&#x1D565;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL T -->
<!ENTITY UnderBar         "&#x0005F;" ><!--LOW LINE -->
<!ENTITY UnderBrace       "&#x023DF;" ><!--BOTTOM CURLY BRACKET -->
<!ENTITY UnderBracket     "&#x023B5;" ><!--BOTTOM SQUARE BRACKET -->
<!ENTITY UnderParenthesis "&#x023DD;" ><!--BOTTOM PARENTHESIS -->
<!ENTITY uopf             "&#x1D566;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL U -->
<!ENTITY UpArrowBar       "&#x02912;" ><!--UPWARDS ARROW TO BAR -->
<!ENTITY Upsilon          "&#x003A5;" ><!--GREEK CAPITAL LETTER UPSILON -->
<!ENTITY VerticalLine     "&#x0007C;" ><!--VERTICAL LINE -->
<!ENTITY VerticalSeparator "&#x02758;" ><!--LIGHT VERTICAL BAR -->
<!ENTITY vopf             "&#x1D567;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL V -->
<!ENTITY wopf             "&#x1D568;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL W -->
<!ENTITY xopf             "&#x1D569;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL X -->
<!ENTITY yopf             "&#x1D56A;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL Y -->
<!ENTITY ZeroWidthSpace   "&#x0200B;" ><!--ZERO WIDTH SPACE -->
<!ENTITY zopf             "&#x1D56B;" ><!--MATHEMATICAL DOUBLE-STRUCK SMALL Z -->
