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+
+<!--
+ File mmlextra.ent produced by the XSL script characters.xsl
+ from input data in unicode.xml.
+
+ 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 4.0.
+
+-->
+
+<!ENTITY % plane1D "&#38;#38;#x1D">
+
+<!ENTITY af "&#x02061;" ><!--character showing function application in presentation tagging -->
+<!ENTITY aopf "%plane1D;552;" ><!-- -->
+<!ENTITY asympeq "&#x0224D;" ><!--Old ISOAMSR asymp (for HTML compatibility) -->
+<!ENTITY bopf "%plane1D;553;" ><!-- -->
+<!ENTITY copf "%plane1D;554;" ><!-- -->
+<!ENTITY Cross "&#x02A2F;" ><!--cross or vector product -->
+<!ENTITY DD "&#x02145;" ><!--D for use in differentials, e.g., within integrals -->
+<!ENTITY dd "&#x02146;" ><!--d for use in differentials, e.g., within integrals -->
+<!ENTITY dopf "%plane1D;555;" ><!-- -->
+<!ENTITY DownArrowBar "&#x02913;" ><!--down arrow to bar -->
+<!ENTITY DownBreve " &#x00311;" ><!--breve, inverted (non-spacing) -->
+<!ENTITY DownLeftRightVector "&#x02950;" ><!--left-down-right-down harpoon -->
+<!ENTITY DownLeftTeeVector "&#x0295E;" ><!--left-down harpoon from bar -->
+<!ENTITY DownLeftVectorBar "&#x02956;" ><!--left-down harpoon to bar -->
+<!ENTITY DownRightTeeVector "&#x0295F;" ><!--right-down harpoon from bar -->
+<!ENTITY DownRightVectorBar "&#x02957;" ><!--right-down harpoon to bar -->
+<!ENTITY ee "&#x02147;" ><!--e use for the exponential base of the natural logarithms -->
+<!ENTITY EmptySmallSquare "&#x025FB;" ><!--empty small square -->
+<!ENTITY EmptyVerySmallSquare "&#x025AB;" ><!--empty small square -->
+<!ENTITY eopf "%plane1D;556;" ><!-- -->
+<!ENTITY Equal "&#x02A75;" ><!--two consecutive equal signs -->
+<!ENTITY FilledSmallSquare "&#x025FC;" ><!--filled small square -->
+<!ENTITY FilledVerySmallSquare "&#x025AA;" ><!--filled very small square -->
+<!ENTITY fopf "%plane1D;557;" ><!-- -->
+<!ENTITY gopf "%plane1D;558;" ><!-- -->
+<!ENTITY GreaterGreater "&#x02AA2;" ><!--alias for GT -->
+<!ENTITY Hat "&#x0005E;" ><!--circumflex accent -->
+<!ENTITY hopf "%plane1D;559;" ><!-- -->
+<!ENTITY HorizontalLine "&#x02500;" ><!--short horizontal line -->
+<!ENTITY ic "&#x02063;" ><!--short form of &InvisibleComma; -->
+<!ENTITY ii "&#x02148;" ><!--i for use as a square root of -1 -->
+<!ENTITY iopf "%plane1D;55A;" ><!-- -->
+<!ENTITY it "&#x02062;" ><!--marks multiplication when it is understood without a mark -->
+<!ENTITY jopf "%plane1D;55B;" ><!-- -->
+<!ENTITY kopf "%plane1D;55C;" ><!-- -->
+<!ENTITY larrb "&#x021E4;" ><!--leftwards arrow to bar -->
+<!ENTITY LeftDownTeeVector "&#x02961;" ><!--down-left harpoon from bar -->
+<!ENTITY LeftDownVectorBar "&#x02959;" ><!--down-left harpoon to bar -->
+<!ENTITY LeftRightVector "&#x0294E;" ><!--left-up-right-up harpoon -->
+<!ENTITY LeftTeeVector "&#x0295A;" ><!--left-up harpoon from bar -->
+<!ENTITY LeftTriangleBar "&#x029CF;" ><!--left triangle, vertical bar -->
+<!ENTITY LeftUpDownVector "&#x02951;" ><!--up-left-down-left harpoon -->
+<!ENTITY LeftUpTeeVector "&#x02960;" ><!--up-left harpoon from bar -->
+<!ENTITY LeftUpVectorBar "&#x02958;" ><!--up-left harpoon to bar -->
+<!ENTITY LeftVectorBar "&#x02952;" ><!--left-up harpoon to bar -->
+<!ENTITY LessLess "&#x02AA1;" ><!--alias for Lt -->
+<!ENTITY lopf "%plane1D;55D;" ><!-- -->
+<!ENTITY mapstodown "&#x021A7;" ><!--downwards arrow from bar -->
+<!ENTITY mapstoleft "&#x021A4;" ><!--leftwards arrow from bar -->
+<!ENTITY mapstoup "&#x021A5;" ><!--upwards arrow from bar -->
+<!ENTITY MediumSpace "&#x0205F;" ><!--space of width 4/18 em -->
+<!ENTITY mopf "%plane1D;55E;" ><!-- -->
+<!ENTITY nbump "&#x0224E;&#x00338;" ><!--not bumpy equals -->
+<!ENTITY nbumpe "&#x0224F;&#x00338;" ><!--not bumpy single equals -->
+<!ENTITY nesim "&#x02242;&#x00338;" ><!--not equal or similar -->
+<!ENTITY NewLine "&#x0000A;" ><!--force a line break; line feed -->
+<!ENTITY NoBreak "&#x02060;" ><!--never break line here -->
+<!ENTITY nopf "%plane1D;55F;" ><!-- -->
+<!ENTITY NotCupCap "&#x0226D;" ><!--alias for &nasymp; -->
+<!ENTITY NotHumpEqual "&#x0224F;&#x00338;" ><!--alias for &nbumpe; -->
+<!ENTITY NotLeftTriangleBar "&#x029CF;&#x00338;" ><!--not left triangle, vertical bar -->
+<!ENTITY NotNestedGreaterGreater "&#x02AA2;&#x00338;" ><!--not double greater-than sign -->
+<!ENTITY NotNestedLessLess "&#x02AA1;&#x00338;" ><!--not double less-than sign -->
+<!ENTITY NotRightTriangleBar "&#x029D0;&#x00338;" ><!--not vertical bar, right triangle -->
+<!ENTITY NotSquareSubset "&#x0228F;&#x00338;" ><!--square not subset -->
+<!ENTITY NotSquareSuperset "&#x02290;&#x00338;" ><!--negated set-like partial order operator -->
+<!ENTITY NotSucceedsTilde "&#x0227F;&#x00338;" ><!--not succeeds or similar -->
+<!ENTITY oopf "%plane1D;560;" ><!-- -->
+<!ENTITY OverBar "&#x000AF;" ><!--over bar -->
+<!ENTITY OverBrace "&#x0FE37;" ><!--over brace -->
+<!ENTITY OverBracket "&#x023B4;" ><!--over bracket -->
+<!ENTITY OverParenthesis "&#x0FE35;" ><!--over parenthesis -->
+<!ENTITY planckh "&#x0210E;" ><!--the ring (skew field) of quaternions -->
+<!ENTITY popf "%plane1D;561;" ><!-- -->
+<!ENTITY Product "&#x0220F;" ><!--alias for &prod; -->
+<!ENTITY qopf "%plane1D;562;" ><!-- -->
+<!ENTITY rarrb "&#x021E5;" ><!--leftwards arrow to bar -->
+<!ENTITY RightDownTeeVector "&#x0295D;" ><!--down-right harpoon from bar -->
+<!ENTITY RightDownVectorBar "&#x02955;" ><!--down-right harpoon to bar -->
+<!ENTITY RightTeeVector "&#x0295B;" ><!--right-up harpoon from bar -->
+<!ENTITY RightTriangleBar "&#x029D0;" ><!--vertical bar, right triangle -->
+<!ENTITY RightUpDownVector "&#x0294F;" ><!--up-right-down-right harpoon -->
+<!ENTITY RightUpTeeVector "&#x0295C;" ><!--up-right harpoon from bar -->
+<!ENTITY RightUpVectorBar "&#x02954;" ><!--up-right harpoon to bar -->
+<!ENTITY RightVectorBar "&#x02953;" ><!--up-right harpoon to bar -->
+<!ENTITY ropf "%plane1D;563;" ><!-- -->
+<!ENTITY RoundImplies "&#x02970;" ><!--round implies -->
+<!ENTITY RuleDelayed "&#x029F4;" ><!--rule-delayed (colon right arrow) -->
+<!ENTITY sopf "%plane1D;564;" ><!-- -->
+<!ENTITY Tab "&#x00009;" ><!--tabulator stop; horizontal tabulation -->
+<!ENTITY ThickSpace "&#x02009;&#x0200A;&#x0200A;" ><!--space of width 5/18 em -->
+<!ENTITY topf "%plane1D;565;" ><!-- -->
+<!ENTITY UnderBar " &#x00332;" ><!--combining low line -->
+<!ENTITY UnderBrace "&#x0FE38;" ><!--under brace -->
+<!ENTITY UnderBracket "&#x023B5;" ><!--under bracket -->
+<!ENTITY UnderParenthesis "&#x0FE36;" ><!--under parenthesis -->
+<!ENTITY uopf "%plane1D;566;" ><!-- -->
+<!ENTITY UpArrowBar "&#x02912;" ><!--up arrow to bar -->
+<!ENTITY Upsilon "&#x003A5;" ><!--ISOGRK1 Ugr, HTML4 Upsilon -->
+<!ENTITY VerticalLine "&#x0007C;" ><!--alias ISONUM verbar -->
+<!ENTITY VerticalSeparator "&#x02758;" ><!--vertical separating operator -->
+<!ENTITY vopf "%plane1D;567;" ><!-- -->
+<!ENTITY wopf "%plane1D;568;" ><!-- -->
+<!ENTITY xopf "%plane1D;569;" ><!-- -->
+<!ENTITY yopf "%plane1D;56A;" ><!-- -->
+<!ENTITY ZeroWidthSpace "&#x0200B;" ><!--zero width space -->
+<!ENTITY zopf "%plane1D;56B;" ><!-- -->