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  1. !function(){function LMcreateElementXHTML(t){return isIE?document.createElement(t):document.createElementNS("http://www.w3.org/1999/xhtml",t)}function LMnoMathMLNote(){var nd=LMcreateElementXHTML("h3");nd.setAttribute("align","center"),nd.appendChild(LMcreateElementXHTML("p")),nd.appendChild(document.createTextNode("To view the "));var an=LMcreateElementXHTML("a");return an.appendChild(document.createTextNode("LaTeXMathML")),an.setAttribute("href","http://www.maths.nott.ac.uk/personal/drw/lm.html"),nd.appendChild(an),nd.appendChild(document.createTextNode(" notation use Internet Explorer 6+")),an=LMcreateElementXHTML("a"),an.appendChild(document.createTextNode("MathPlayer")),an.setAttribute("href","http://www.dessci.com/en/products/mathplayer/download.htm"),nd.appendChild(an),nd.appendChild(document.createTextNode(" or Netscape/Mozilla/Firefox")),nd.appendChild(LMcreateElementXHTML("p")),nd}function LMisMathMLavailable(){if("Netscape"==navigator.appName.slice(0,8))return navigator.appVersion.slice(0,1)>="5"?null:LMnoMathMLNote();if("Microsoft"!=navigator.appName.slice(0,9))return LMnoMathMLNote();try{new ActiveXObject("MathPlayer.Factory.1");return null}catch(e){return LMnoMathMLNote()}}function compareNames(s1,s2){return s1.input>s2.input?1:-1}function LMinitSymbols(){for(LMsymbols.sort(compareNames),i=0;i<LMsymbols.length;i++)LMnames[i]=LMsymbols[i].input}function LMcreateElementMathML(t){return isIE?document.createElement("m:"+t):document.createElementNS(LMmathml,t)}function LMcreateMmlNode(t,frag){if(isIE)var node=document.createElement("m:"+t);else var node=document.createElementNS(LMmathml,t);return node.appendChild(frag),node}function LMremoveCharsAndBlanks(str,n){var st;st=str.slice(n);for(var i=0;i<st.length&&st.charCodeAt(i)<=32;i+=1);return st.slice(i)}function LMposition(arr,str,n){if(0==n){var h,m;for(n=-1,h=arr.length;h>n+1;)m=n+h>>1,arr[m]<str?n=m:h=m;return h}for(var i=n;i<arr.length&&arr[i]<str;i++);return i}function LMgetSymbol(str){for(var mk,st,tagst,k=0,j=0,match="",more=!0,i=1;i<=str.length&&more;i++)st=str.slice(0,i),j=k,k=LMposition(LMnames,st,j),k<LMnames.length&&str.slice(0,LMnames[k].length)==LMnames[k]&&(match=LMnames[k],mk=k,i=match.length),more=k<LMnames.length&&str.slice(0,LMnames[k].length)>=LMnames[k];return LMpreviousSymbol=LMcurrentSymbol,""!=match?(LMcurrentSymbol=LMsymbols[mk].ttype,LMsymbols[mk]):(LMcurrentSymbol=CONST,k=1,st=str.slice(0,1),tagst=st>="0"&&"9">=st?"mn":("A">st||st>"Z")&&("a">st||st>"z")?"mo":"mi",{input:st,tag:tagst,output:st,ttype:CONST})}function LMparseSexpr(str){var symbol,node,result,result2,i,st,newFrag=document.createDocumentFragment();if(str=LMremoveCharsAndBlanks(str,0),symbol=LMgetSymbol(str),null==symbol||symbol.ttype==RIGHTBRACKET)return[null,str,null];if(symbol.ttype==DEFINITION&&(str=symbol.output+LMremoveCharsAndBlanks(str,symbol.input.length),symbol=LMgetSymbol(str),null==symbol||symbol.ttype==RIGHTBRACKET))return[null,str,null];switch(str=LMremoveCharsAndBlanks(str,symbol.input.length),symbol.ttype){case SPACE:return node=LMcreateElementMathML(symbol.tag),node.setAttribute(symbol.atname,symbol.atval),[node,str,symbol.tag];case UNDEROVER:return isIE&&"\\big"==symbol.input.substr(0,4)&&(str="\\"+symbol.input.substr(4)+str,symbol=LMgetSymbol(str),symbol.ttype=UNDEROVER,str=LMremoveCharsAndBlanks(str,symbol.input.length)),[LMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),str,symbol.tag];case CONST:var output=symbol.output;if(isIE)if("'"==symbol.input)output="′";else if("''"==symbol.input)output="″";else if("'''"==symbol.input)output="″′";else if("''''"==symbol.input)output="″″";else if("\\square"==symbol.input)output="□";else if("\\frac"==symbol.input.substr(0,5)){var denom=symbol.input.substr(6,1);if("5"==denom||"6"==denom)return str=symbol.input.replace(/\\frac/,"\\frac ")+str,[node,str,symbol.tag]}return node=LMcreateMmlNode(symbol.tag,document.createTextNode(output)),[node,str,symbol.tag];case LONG:return node=LMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),node.setAttribute("minsize","1.5"),node.setAttribute("maxsize","1.5"),node=LMcreateMmlNode("mover",node),node.appendChild(LMcreateElementMathML("mspace")),[node,str,symbol.tag];case STRETCHY:return isIE&&"\\backslash"==symbol.input&&(symbol.output="\\"),node=LMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),"|"!=symbol.input&&"\\vert"!=symbol.input&&"\\|"!=symbol.input&&"\\Vert"!=symbol.input||(node.setAttribute("lspace","0em"),node.setAttribute("rspace","0em")),node.setAttribute("maxsize",symbol.atval),null!=symbol.rtag?[node,str,symbol.rtag]:[node,str,symbol.tag];case BIG:var atval=symbol.atval;if(isIE&&(atval=symbol.ieval),symbol=LMgetSymbol(str),null==symbol)return[null,str,null];if(str=LMremoveCharsAndBlanks(str,symbol.input.length),node=LMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),isIE){var space=LMcreateElementMathML("mspace");space.setAttribute("height",atval+"ex"),node=LMcreateMmlNode("mrow",node),node.appendChild(space)}else node.setAttribute("minsize",atval),node.setAttribute("maxsize",atval);return[node,str,symbol.tag];case LEFTBRACKET:return"\\left"==symbol.input&&(symbol=LMgetSymbol(str),null!=symbol&&("."==symbol.input&&(symbol.invisible=!0),str=LMremoveCharsAndBlanks(str,symbol.input.length))),result=LMparseExpr(str,!0,!1),null==symbol||"boolean"==typeof symbol.invisible&&symbol.invisible?node=LMcreateMmlNode("mrow",result[0]):(node=LMcreateMmlNode("mo",document.createTextNode(symbol.output)),node=LMcreateMmlNode("mrow",node),node.appendChild(result[0])),[node,result[1],result[2]];case MATRIX:if("\\begin{array}"==symbol.input){var mask="";if(symbol=LMgetSymbol(str),str=LMremoveCharsAndBlanks(str,0),null==symbol)mask="l";else if(str=LMremoveCharsAndBlanks(str,symbol.input.length),"{"!=symbol.input)mask="l";else do symbol=LMgetSymbol(str),null!=symbol&&(str=LMremoveCharsAndBlanks(str,symbol.input.length),"}"!=symbol.input&&(mask+=symbol.input));while(null!=symbol&&""!=symbol.input&&"}"!=symbol.input);if(result=LMparseExpr("{"+str,!0,!0),node=LMcreateMmlNode("mtable",result[0]),mask=mask.replace(/l/g,"left "),mask=mask.replace(/r/g,"right "),mask=mask.replace(/c/g,"center "),node.setAttribute("columnalign",mask),node.setAttribute("displaystyle","false"),isIE)return[node,result[1],null];var lspace=LMcreateElementMathML("mspace");lspace.setAttribute("width","0.167em");var rspace=LMcreateElementMathML("mspace");rspace.setAttribute("width","0.167em");var node1=LMcreateMmlNode("mrow",lspace);return node1.appendChild(node),node1.appendChild(rspace),[node1,result[1],null]}return result=LMparseExpr("{"+str,!0,!0),node=LMcreateMmlNode("mtable",result[0]),isIE?node.setAttribute("columnspacing","0.25em"):node.setAttribute("columnspacing","0.167em"),node.setAttribute("columnalign","right center left"),node.setAttribute("displaystyle","true"),node=LMcreateMmlNode("mrow",node),[node,result[1],null];case TEXT:return i="{"==str.charAt(0)?str.indexOf("}"):0,-1==i&&(i=str.length),st=str.slice(1,i)," "==st.charAt(0)&&(node=LMcreateElementMathML("mspace"),node.setAttribute("width","0.33em"),newFrag.appendChild(node)),newFrag.appendChild(LMcreateMmlNode(symbol.tag,document.createTextNode(st)))," "==st.charAt(st.length-1)&&(node=LMcreateElementMathML("mspace"),node.setAttribute("width","0.33em"),newFrag.appendChild(node)),str=LMremoveCharsAndBlanks(str,i+1),[LMcreateMmlNode("mrow",newFrag),str,null];case UNARY:if(result=LMparseSexpr(str),null==result[0])return[LMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),str];if("boolean"==typeof symbol.func&&symbol.func){if(st=str.charAt(0),"^"==st||"_"==st||","==st)return[LMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),str,symbol.tag];if(node=LMcreateMmlNode("mrow",LMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output))),isIE){var space=LMcreateElementMathML("mspace");space.setAttribute("width","0.167em"),node.appendChild(space)}return node.appendChild(result[0]),[node,result[1],symbol.tag]}if("\\sqrt"==symbol.input){if(isIE){var space=LMcreateElementMathML("mspace");return space.setAttribute("height","1.2ex"),space.setAttribute("width","0em"),node=LMcreateMmlNode(symbol.tag,result[0]),node.appendChild(space),[node,result[1],symbol.tag]}return[LMcreateMmlNode(symbol.tag,result[0]),result[1],symbol.tag]}if("boolean"==typeof symbol.acc&&symbol.acc){node=LMcreateMmlNode(symbol.tag,result[0]);var output=symbol.output;isIE&&("\\hat"==symbol.input?output="̂":"\\widehat"==symbol.input?output="^":"\\bar"==symbol.input?output="¯":"\\grave"==symbol.input?output="̀":"\\tilde"==symbol.input&&(output="̃"));var node1=LMcreateMmlNode("mo",document.createTextNode(output));return"\\vec"!=symbol.input&&"\\check"!=symbol.input||node1.setAttribute("maxsize","1.2"),isIE&&"\\bar"==symbol.input&&node1.setAttribute("maxsize","0.5"),"\\underbrace"==symbol.input||"\\underline"==symbol.input?node1.setAttribute("accentunder","true"):node1.setAttribute("accent","true"),node.appendChild(node1),"\\overbrace"!=symbol.input&&"\\underbrace"!=symbol.input||(node.ttype=UNDEROVER),[node,result[1],symbol.tag]}if(!isIE&&"undefined"!=typeof symbol.codes)for(i=0;i<result[0].childNodes.length;i++)if("mi"==result[0].childNodes[i].nodeName||"mi"==result[0].nodeName){st="mi"==result[0].nodeName?result[0].firstChild.nodeValue:result[0].childNodes[i].firstChild.nodeValue;for(var newst=[],j=0;j<st.length;j++)newst+=st.charCodeAt(j)>64&&st.charCodeAt(j)<91?symbol.codes[st.charCodeAt(j)-65]:st.charCodeAt(j)>96&&st.charCodeAt(j)<123?symbol.codes[st.charCodeAt(j)-71]:st.charAt(j);"mi"==result[0].nodeName?result[0]=LMcreateElementMathML("mo").appendChild(document.createTextNode(newst)):result[0].replaceChild(LMcreateElementMathML("mo").appendChild(document.createTextNode(newst)),result[0].childNodes[i])}return node=LMcreateMmlNode(symbol.tag,result[0]),node.setAttribute(symbol.atname,symbol.atval),"\\scriptstyle"!=symbol.input&&"\\scriptscriptstyle"!=symbol.input||node.setAttribute("displaystyle","false"),[node,result[1],symbol.tag];case BINARY:return result=LMparseSexpr(str),null==result[0]?[LMcreateMmlNode("mo",document.createTextNode(symbol.input)),str,null]:(result2=LMparseSexpr(result[1]),null==result2[0]?[LMcreateMmlNode("mo",document.createTextNode(symbol.input)),str,null]:("\\root"!=symbol.input&&"\\stackrel"!=symbol.input||newFrag.appendChild(result2[0]),newFrag.appendChild(result[0]),"\\frac"==symbol.input&&newFrag.appendChild(result2[0]),[LMcreateMmlNode(symbol.tag,newFrag),result2[1],symbol.tag]));case INFIX:return str=LMremoveCharsAndBlanks(str,symbol.input.length),[LMcreateMmlNode("mo",document.createTextNode(symbol.output)),str,symbol.tag];default:return[LMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),str,symbol.tag]}}function LMparseIexpr(str){var symbol,sym1,sym2,node,result,tag,underover;if(str=LMremoveCharsAndBlanks(str,0),sym1=LMgetSymbol(str),result=LMparseSexpr(str),node=result[0],str=result[1],tag=result[2],symbol=LMgetSymbol(str),symbol.ttype==INFIX)if(str=LMremoveCharsAndBlanks(str,symbol.input.length),result=LMparseSexpr(str),null==result[0]&&(result[0]=LMcreateMmlNode("mo",document.createTextNode("□"))),str=result[1],tag=result[2],"_"==symbol.input||"^"==symbol.input){if(sym2=LMgetSymbol(str),tag=null,underover=sym1.ttype==UNDEROVER||node.ttype==UNDEROVER,"_"==symbol.input&&"^"==sym2.input){str=LMremoveCharsAndBlanks(str,sym2.input.length);var res2=LMparseSexpr(str);str=res2[1],tag=res2[2],node=LMcreateMmlNode(underover?"munderover":"msubsup",node),node.appendChild(result[0]),node.appendChild(res2[0])}else"_"==symbol.input?(node=LMcreateMmlNode(underover?"munder":"msub",node),node.appendChild(result[0])):(node=LMcreateMmlNode(underover?"mover":"msup",node),node.appendChild(result[0]));node=LMcreateMmlNode("mrow",node)}else node=LMcreateMmlNode(symbol.tag,node),"\\atop"!=symbol.input&&"\\choose"!=symbol.input||node.setAttribute("linethickness","0ex"),node.appendChild(result[0]),"\\choose"==symbol.input&&(node=LMcreateMmlNode("mfenced",node));return[node,str,tag]}function LMparseExpr(str,rightbracket,matrix){var symbol,node,result,i,tag,newFrag=document.createDocumentFragment();do if(str=LMremoveCharsAndBlanks(str,0),result=LMparseIexpr(str),node=result[0],str=result[1],tag=result[2],symbol=LMgetSymbol(str),void 0!=node){if(("mn"==tag||"mi"==tag)&&null!=symbol&&"boolean"==typeof symbol.func&&symbol.func){var space=LMcreateElementMathML("mspace");space.setAttribute("width","0.167em"),node=LMcreateMmlNode("mrow",node),node.appendChild(space)}newFrag.appendChild(node)}while(symbol.ttype!=RIGHTBRACKET&&null!=symbol&&""!=symbol.output);if(tag=null,symbol.ttype==RIGHTBRACKET){"\\right"==symbol.input&&(str=LMremoveCharsAndBlanks(str,symbol.input.length),symbol=LMgetSymbol(str),null!=symbol&&"."==symbol.input&&(symbol.invisible=!0),null!=symbol&&(tag=symbol.rtag)),null!=symbol&&(str=LMremoveCharsAndBlanks(str,symbol.input.length));var len=newFrag.childNodes.length;if(matrix&&len>0&&"mrow"==newFrag.childNodes[len-1].nodeName&&len>1&&"mo"==newFrag.childNodes[len-2].nodeName&&"&"==newFrag.childNodes[len-2].firstChild.nodeValue){var pos=[],m=newFrag.childNodes.length;for(i=0;matrix&&m>i;i+=2){pos[i]=[],node=newFrag.childNodes[i];for(var j=0;j<node.childNodes.length;j++)"&"==node.childNodes[j].firstChild.nodeValue&&(pos[i][pos[i].length]=j)}var row,frag,n,k,table=document.createDocumentFragment();for(i=0;m>i;i+=2){for(row=document.createDocumentFragment(),frag=document.createDocumentFragment(),node=newFrag.firstChild,n=node.childNodes.length,k=0,j=0;n>j;j++)"undefined"!=typeof pos[i][k]&&j==pos[i][k]?(node.removeChild(node.firstChild),row.appendChild(LMcreateMmlNode("mtd",frag)),k++):frag.appendChild(node.firstChild);row.appendChild(LMcreateMmlNode("mtd",frag)),newFrag.childNodes.length>2&&(newFrag.removeChild(newFrag.firstChild),newFrag.removeChild(newFrag.firstChild)),table.appendChild(LMcreateMmlNode("mtr",row))}return[table,str]}"boolean"==typeof symbol.invisible&&symbol.invisible||(node=LMcreateMmlNode("mo",document.createTextNode(symbol.output)),newFrag.appendChild(node))}return[newFrag,str,tag]}function LMparseMath(str){var node=LMcreateElementMathML("mstyle");if(""!=mathcolor&&node.setAttribute("mathcolor",mathcolor),""!=mathfontfamily&&node.setAttribute("fontfamily",mathfontfamily),node.appendChild(LMparseExpr(str.replace(/^\s+/g,""),!1,!1)[0]),node=LMcreateMmlNode("math",node),showasciiformulaonhover&&node.setAttribute("title",str.replace(/\s+/g," ")),""!=mathfontfamily&&(isIE||"serif"!=mathfontfamily)){var fnode=LMcreateElementXHTML("font");return fnode.setAttribute("face",mathfontfamily),fnode.appendChild(node),fnode}return node}function LMstrarr2docFrag(arr,linebreaks){for(var newFrag=document.createDocumentFragment(),expr=!1,i=0;i<arr.length;i++){if(expr)newFrag.appendChild(LMparseMath(arr[i]));else{var arri=linebreaks?arr[i].split("\n\n"):[arr[i]];newFrag.appendChild(LMcreateElementXHTML("span").appendChild(document.createTextNode(arri[0])));for(var j=1;j<arri.length;j++)newFrag.appendChild(LMcreateElementXHTML("p")),newFrag.appendChild(LMcreateElementXHTML("span").appendChild(document.createTextNode(arri[j])))}expr=!expr}return newFrag}function LMprocessNodeR(n,linebreaks){var mtch,str,arr,frg,i;if(0==n.childNodes.length){if(8==n.nodeType&&!linebreaks||"form"==n.parentNode.nodeName||"FORM"==n.parentNode.nodeName||"textarea"==n.parentNode.nodeName||"TEXTAREA"==n.parentNode.nodeName||"pre"==n.parentNode.nodeName||"PRE"==n.parentNode.nodeName)return 0;if(str=n.nodeValue,null!=str){for(str=str.replace(/\r\n\r\n/g,"\n\n"),str=str.replace(/\x20+/g," "),str=str.replace(/\s*\r\n/g," "),mtch=-1!=str.indexOf("$"),str=str.replace(/([^\\])\$/g,"$1 $"),str=str.replace(/^\$/," $"),arr=str.split(" $"),i=0;i<arr.length;i++)arr[i]=arr[i].replace(/\\\$/g,"$");if(arr.length>1||mtch){if(checkForMathML){checkForMathML=!1;var nd=LMisMathMLavailable();LMnoMathML=null!=nd,LMnoMathML&&notifyIfNoMathML&&(alertIfNoMathML?alert("To view the ASCIIMathML 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