texmath-0.12.5: test/writer/omml/complex1.test
<<< native
[ EArray
[ AlignCenter , AlignCenter ]
[ [ [ EText TextNormal "Bernoulli Trials" ]
, [ EGrouped
[ EGrouped
[ EIdentifier "P"
, ESymbol Open "("
, EIdentifier "E"
, ESymbol Close ")"
]
, ESymbol Rel "="
, EDelimited
"("
")"
[ Right (EFraction NormalFrac (EIdentifier "n") (EIdentifier "k"))
]
, ESubsup (EIdentifier "p") (EGrouped []) (EIdentifier "k")
, ESubsup
(EGrouped
[ ESymbol Open "("
, ENumber "1"
, ESymbol Bin "-"
, EIdentifier "p"
, ESymbol Close ")"
])
(EGrouped [])
(EGrouped [ EIdentifier "n" , ESymbol Bin "-" , EIdentifier "k" ])
]
]
]
, [ [ EText TextNormal "Cauchy-Schwarz Inequality" ]
, [ EGrouped
[ ESubsup
(EDelimited
"("
")"
[ Right
(EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ])
(EIdentifier "n"))
, Right (ESubsup (EIdentifier "a") (EIdentifier "k") (EGrouped []))
, Right (ESubsup (EIdentifier "b") (EIdentifier "k") (EGrouped []))
])
(EGrouped [])
(ENumber "2")
, ESymbol Rel "\8804"
, EDelimited
"("
")"
[ Right
(EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ])
(EIdentifier "n"))
, Right (ESubsup (EIdentifier "a") (EIdentifier "k") (ENumber "2"))
]
, EDelimited
"("
")"
[ Right
(EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ])
(EIdentifier "n"))
, Right (ESubsup (EIdentifier "b") (EIdentifier "k") (ENumber "2"))
]
]
]
]
, [ [ EText TextNormal "Cauchy Formula" ]
, [ EGrouped
[ EIdentifier "f"
, ESymbol Open "("
, EIdentifier "z"
, ESymbol Close ")"
, ESpace (1 % 6)
, ESymbol Bin "\183"
, ESubsup (EIdentifier "Ind") (EIdentifier "\947") (EGrouped [])
, ESymbol Open "("
, EIdentifier "z"
, ESymbol Close ")"
, ESymbol Rel "="
, EFraction
NormalFrac
(ENumber "1")
(EGrouped [ ENumber "2" , EIdentifier "\960" , EIdentifier "i" ])
, EUnderover
False (ESymbol Op "\8750") (EIdentifier "\947") (EGrouped [])
, EFraction
NormalFrac
(EGrouped
[ EIdentifier "f"
, ESymbol Open "("
, EIdentifier "\958"
, ESymbol Close ")"
])
(EGrouped
[ EIdentifier "\958" , ESymbol Bin "-" , EIdentifier "z" ])
, ESpace (1 % 6)
, EIdentifier "d"
, EIdentifier "\958"
]
]
]
, [ [ EText TextNormal "Cross Product" ]
, [ EGrouped
[ ESubsup (EIdentifier "V") (ENumber "1") (EGrouped [])
, ESymbol Bin "\215"
, ESubsup (EIdentifier "V") (ENumber "2") (EGrouped [])
, ESymbol Rel "="
, EDelimited
"|"
"|"
[ Right
(EArray
[ AlignCenter , AlignCenter , AlignCenter ]
[ [ [ EIdentifier "i" ]
, [ EIdentifier "j" ]
, [ EIdentifier "k" ]
]
, [ [ EFraction
NormalFrac
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "X" ])
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "u" ])
]
, [ EFraction
NormalFrac
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "Y" ])
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "u" ])
]
, [ ENumber "0" ]
]
, [ [ EFraction
NormalFrac
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "X" ])
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "v" ])
]
, [ EFraction
NormalFrac
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "Y" ])
(EGrouped [ ESymbol Ord "\8706" , EIdentifier "v" ])
]
, [ ENumber "0" ]
]
])
]
]
]
]
, [ [ EText TextNormal "Vandermonde Determinant" ]
, [ EGrouped
[ EDelimited
"|"
"|"
[ Right
(EArray
[ AlignCenter , AlignCenter , AlignCenter , AlignCenter ]
[ [ [ ENumber "1" ]
, [ ENumber "1" ]
, [ ESymbol Ord "\8943" ]
, [ ENumber "1" ]
]
, [ [ ESubsup (EIdentifier "v") (ENumber "1") (EGrouped []) ]
, [ ESubsup (EIdentifier "v") (ENumber "2") (EGrouped []) ]
, [ ESymbol Ord "\8943" ]
, [ ESubsup (EIdentifier "v") (EIdentifier "n") (EGrouped []) ]
]
, [ [ ESubsup (EIdentifier "v") (ENumber "1") (ENumber "2") ]
, [ ESubsup (EIdentifier "v") (ENumber "2") (ENumber "2") ]
, [ ESymbol Ord "\8943" ]
, [ ESubsup (EIdentifier "v") (EIdentifier "n") (ENumber "2") ]
]
, [ [ ESymbol Rel "\8942" ]
, [ ESymbol Rel "\8942" ]
, [ ESymbol Rel "\8945" ]
, [ ESymbol Rel "\8942" ]
]
, [ [ ESubsup
(EIdentifier "v")
(ENumber "1")
(EGrouped [ EIdentifier "n" , ESymbol Bin "-" , ENumber "1" ])
]
, [ ESubsup
(EIdentifier "v")
(ENumber "2")
(EGrouped [ EIdentifier "n" , ESymbol Bin "-" , ENumber "1" ])
]
, [ ESymbol Ord "\8943" ]
, [ ESubsup
(EIdentifier "v")
(EIdentifier "n")
(EGrouped [ EIdentifier "n" , ESymbol Bin "-" , ENumber "1" ])
]
]
])
]
, ESymbol Rel "="
, EUnderover
False
(ESymbol Op "\8719")
(EGrouped
[ ENumber "1"
, ESymbol Rel "\8804"
, EIdentifier "i"
, ESymbol Rel "<"
, EIdentifier "j"
, ESymbol Rel "\8804"
, EIdentifier "n"
])
(EGrouped [])
, ESymbol Open "("
, ESubsup (EIdentifier "v") (EIdentifier "j") (EGrouped [])
, ESymbol Bin "-"
, ESubsup (EIdentifier "v") (EIdentifier "i") (EGrouped [])
, ESymbol Close ")"
]
]
]
, [ [ EText TextNormal "Lorenz Equations" ]
, [ EArray
[ AlignCenter , AlignCenter , AlignCenter ]
[ [ [ EUnderover
False (EIdentifier "x") (EGrouped []) (ESymbol Accent "\729")
]
, [ ESymbol Rel "=" ]
, [ EGrouped
[ EIdentifier "\963"
, ESymbol Open "("
, EIdentifier "y"
, ESymbol Bin "-"
, EIdentifier "x"
, ESymbol Close ")"
]
]
]
, [ [ EUnderover
False (EIdentifier "y") (EGrouped []) (ESymbol Accent "\729")
]
, [ ESymbol Rel "=" ]
, [ EGrouped
[ EIdentifier "\961"
, EIdentifier "x"
, ESymbol Bin "-"
, EIdentifier "y"
, ESymbol Bin "-"
, EIdentifier "x"
, EIdentifier "z"
]
]
]
, [ [ EUnderover
False (EIdentifier "z") (EGrouped []) (ESymbol Accent "\729")
]
, [ ESymbol Rel "=" ]
, [ EGrouped
[ ESymbol Bin "-"
, EIdentifier "\946"
, EIdentifier "z"
, ESymbol Bin "+"
, EIdentifier "x"
, EIdentifier "y"
]
]
]
]
]
]
, [ [ EText TextNormal "Maxwell's Equations" ]
, [ EDelimited
"{"
""
[ Right
(EArray
[ AlignCenter , AlignCenter , AlignCenter ]
[ [ [ EGrouped
[ ESymbol Ord "\8711"
, ESpace (0 % 1)
, ESymbol Bin "\215"
, EUnderover
False (EIdentifier "B") (EGrouped []) (ESymbol Accent "\8636")
, ESymbol Bin "-"
, ESpace (1 % 6)
, EFraction NormalFrac (ENumber "1") (EIdentifier "c")
, ESpace (1 % 6)
, EFraction
NormalFrac
(EGrouped
[ ESymbol Ord "\8706"
, ESpace (0 % 1)
, EUnderover
False (EIdentifier "E") (EGrouped []) (ESymbol Accent "\8636")
])
(EGrouped
[ ESymbol Ord "\8706" , ESpace (0 % 1) , EIdentifier "t" ])
]
]
, [ ESymbol Rel "=" ]
, [ EGrouped
[ EFraction
NormalFrac
(EGrouped [ ENumber "4" , EIdentifier "\960" ])
(EIdentifier "c")
, ESpace (1 % 6)
, EUnderover
False (EIdentifier "j") (EGrouped []) (ESymbol Accent "\8636")
]
]
]
, [ [ EGrouped
[ ESymbol Ord "\8711"
, ESpace (0 % 1)
, ESymbol Bin "\183"
, EUnderover
False (EIdentifier "E") (EGrouped []) (ESymbol Accent "\8636")
]
]
, [ ESymbol Rel "=" ]
, [ EGrouped
[ ENumber "4" , EIdentifier "\960" , EIdentifier "\961" ]
]
]
, [ [ EGrouped
[ ESymbol Ord "\8711"
, ESpace (0 % 1)
, ESymbol Bin "\215"
, EUnderover
False (EIdentifier "E") (EGrouped []) (ESymbol Accent "\8636")
, ESpace (1 % 6)
, ESymbol Bin "+"
, ESpace (1 % 6)
, EFraction NormalFrac (ENumber "1") (EIdentifier "c")
, ESpace (1 % 6)
, EFraction
NormalFrac
(EGrouped
[ ESymbol Ord "\8706"
, ESpace (0 % 1)
, EUnderover
False (EIdentifier "B") (EGrouped []) (ESymbol Accent "\8636")
])
(EGrouped
[ ESymbol Ord "\8706" , ESpace (0 % 1) , EIdentifier "t" ])
]
]
, [ ESymbol Rel "=" ]
, [ EUnderover
False (ENumber "0") (EGrouped []) (ESymbol Accent "\8636")
]
]
, [ [ EGrouped
[ ESymbol Ord "\8711"
, ESpace (0 % 1)
, ESymbol Bin "\183"
, EUnderover
False (EIdentifier "B") (EGrouped []) (ESymbol Accent "\8636")
]
]
, [ ESymbol Rel "=" ]
, [ ENumber "0" ]
]
])
]
]
]
, [ [ EText TextNormal "Einstein Field Equations" ]
, [ EGrouped
[ ESubsup
(EIdentifier "R")
(EGrouped [ EIdentifier "\956" , EIdentifier "\957" ])
(EGrouped [])
, ESymbol Bin "-"
, EFraction NormalFrac (ENumber "1") (ENumber "2")
, ESpace (1 % 6)
, ESubsup
(EIdentifier "g")
(EGrouped [ EIdentifier "\956" , EIdentifier "\957" ])
(EGrouped [])
, ESpace (1 % 6)
, EIdentifier "R"
, ESymbol Rel "="
, EFraction
NormalFrac
(EGrouped [ ENumber "8" , EIdentifier "\960" , EIdentifier "G" ])
(ESubsup (EIdentifier "c") (EGrouped []) (ENumber "4"))
, ESpace (1 % 6)
, ESubsup
(EIdentifier "T")
(EGrouped [ EIdentifier "\956" , EIdentifier "\957" ])
(EGrouped [])
]
]
]
, [ [ EText TextNormal "Ramanujan Identity" ]
, [ EGrouped
[ EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESymbol Open "("
, ESqrt (EGrouped [ EIdentifier "\966" , ESqrt (ENumber "5") ])
, ESymbol Bin "-"
, EIdentifier "\966"
, ESymbol Close ")"
, ESubsup
(EIdentifier "e")
(EGrouped [])
(EFraction NormalFrac (ENumber "25") (EIdentifier "\960"))
])
, ESymbol Rel "="
, ENumber "1"
, ESymbol Bin "+"
, EFraction
NormalFrac
(ESubsup
(EIdentifier "e")
(EGrouped [])
(EGrouped [ ESymbol Bin "-" , ENumber "2" , EIdentifier "\960" ]))
(EGrouped
[ ENumber "1"
, ESymbol Bin "+"
, EFraction
NormalFrac
(ESubsup
(EIdentifier "e")
(EGrouped [])
(EGrouped [ ESymbol Bin "-" , ENumber "4" , EIdentifier "\960" ]))
(EGrouped
[ ENumber "1"
, ESymbol Bin "+"
, EFraction
NormalFrac
(ESubsup
(EIdentifier "e")
(EGrouped [])
(EGrouped [ ESymbol Bin "-" , ENumber "6" , EIdentifier "\960" ]))
(EGrouped
[ ENumber "1"
, ESymbol Bin "+"
, EFraction
NormalFrac
(ESubsup
(EIdentifier "e")
(EGrouped [])
(EGrouped
[ ESymbol Bin "-" , ENumber "8" , EIdentifier "\960" ]))
(EGrouped
[ ENumber "1" , ESymbol Bin "+" , ESymbol Ord "\8230" ])
])
])
])
]
]
]
, [ [ EText TextNormal "Another Ramanujan identity" ]
, [ EGrouped
[ EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ])
(EIdentifier "\8734")
, EFraction
NormalFrac
(ENumber "1")
(ESubsup
(ENumber "2")
(EGrouped [])
(EGrouped
[ ESymbol Open "\8970"
, EIdentifier "k"
, ESymbol Bin "\183"
, ESpace (0 % 1)
, EIdentifier "\966"
, ESymbol Close "\8971"
]))
, ESymbol Rel "="
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESubsup (ENumber "2") (EGrouped []) (ENumber "0")
, ESymbol Bin "+"
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESubsup (ENumber "2") (EGrouped []) (ENumber "1")
, ESymbol Bin "+"
, ESymbol Ord "\8943"
])
])
]
]
]
, [ [ EText TextNormal "Rogers-Ramanujan Identity" ]
, [ EGrouped
[ ENumber "1"
, ESymbol Bin "+"
, EGrouped
[ EUnderover
False
(ESymbol Op "\8721")
(EGrouped [ EIdentifier "k" , ESymbol Rel "=" , ENumber "1" ])
(EIdentifier "\8734")
, EFraction
NormalFrac
(ESubsup
(EIdentifier "q")
(EGrouped [])
(EGrouped
[ ESubsup (EIdentifier "k") (EGrouped []) (ENumber "2")
, ESymbol Bin "+"
, EIdentifier "k"
]))
(EGrouped
[ ESymbol Open "("
, ENumber "1"
, ESymbol Bin "-"
, EIdentifier "q"
, ESymbol Close ")"
, ESymbol Open "("
, ENumber "1"
, ESymbol Bin "-"
, ESubsup (EIdentifier "q") (EGrouped []) (ENumber "2")
, ESymbol Close ")"
, ESymbol Ord "\8943"
, ESymbol Open "("
, ENumber "1"
, ESymbol Bin "-"
, ESubsup (EIdentifier "q") (EGrouped []) (EIdentifier "k")
, ESymbol Close ")"
])
]
, ESymbol Rel "="
, EGrouped
[ EUnderover
False
(ESymbol Op "\8719")
(EGrouped [ EIdentifier "j" , ESymbol Rel "=" , ENumber "0" ])
(EIdentifier "\8734")
, EFraction
NormalFrac
(ENumber "1")
(EGrouped
[ ESymbol Open "("
, ENumber "1"
, ESymbol Bin "-"
, ESubsup
(EIdentifier "q")
(EGrouped [])
(EGrouped
[ ENumber "5" , EIdentifier "j" , ESymbol Bin "+" , ENumber "2" ])
, ESymbol Close ")"
, ESymbol Open "("
, ENumber "1"
, ESymbol Bin "-"
, ESubsup
(EIdentifier "q")
(EGrouped [])
(EGrouped
[ ENumber "5" , EIdentifier "j" , ESymbol Bin "+" , ENumber "3" ])
, ESymbol Close ")"
])
]
, ESymbol Pun ","
, EText TextNormal "\8287\8202"
, EText TextNormal "\8287\8202"
, EGrouped [ EIdentifier "f" , EIdentifier "o" , EIdentifier "r" ]
, ESpace (2 % 9)
, ESymbol Op "|"
, EIdentifier "q"
, ESymbol Op "|"
, ESymbol Rel "<"
, ENumber "1"
, EIdentifier "."
]
]
]
, [ [ EText TextNormal "Commutative Diagram" ]
, [ EArray
[ AlignCenter , AlignCenter , AlignCenter ]
[ [ [ EIdentifier "H" ]
, [ ESymbol Accent "\8592" ]
, [ EIdentifier "K" ]
]
, [ [ ESymbol Rel "\8595" ]
, [ ESpace (0 % 1) ]
, [ ESymbol Rel "\8593" ]
]
, [ [ EIdentifier "H" ]
, [ ESymbol Accent "\8594" ]
, [ EIdentifier "K" ]
]
]
]
]
]
]
>>> omml
<?xml version='1.0' ?>
<m:oMathPara>
<m:oMathParaPr>
<m:jc m:val="center" />
</m:oMathParaPr>
<m:oMath>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Bernoulli Trials</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>P</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>E</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>n</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>k</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:d>
<m:sSubSup>
<m:e>
<m:r>
<m:t>p</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>k</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:sSubSup>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>p</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>n</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>k</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Cauchy-Schwarz Inequality</m:t>
</m:r>
</m:e>
<m:e>
<m:sSubSup>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:nary>
<m:naryPr>
<m:chr m:val="∑" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>k</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sup>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>k</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
</m:nary>
<m:sSubSup>
<m:e>
<m:r>
<m:t>b</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>k</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
</m:d>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≤</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:nary>
<m:naryPr>
<m:chr m:val="∑" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>k</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sup>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>a</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>k</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
</m:nary>
</m:e>
</m:d>
<m:d>
<m:dPr>
<m:begChr m:val="(" />
<m:endChr m:val=")" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:nary>
<m:naryPr>
<m:chr m:val="∑" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>k</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sup>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>b</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>k</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
</m:nary>
</m:e>
</m:d>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Cauchy Formula</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>f</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>z</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
<m:r>
<m:t> </m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>·</m:t>
</m:r>
<m:sSubSup>
<m:e>
<m:r>
<m:t>Ind</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>γ</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>z</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
<m:r>
<m:t>π</m:t>
</m:r>
<m:r>
<m:t>i</m:t>
</m:r>
</m:den>
</m:f>
<m:nary>
<m:naryPr>
<m:chr m:val="∮" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="1" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>γ</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>f</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>ξ</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>ξ</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>z</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:nary>
<m:r>
<m:t> </m:t>
</m:r>
<m:r>
<m:t>d</m:t>
</m:r>
<m:r>
<m:t>ξ</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Cross Product</m:t>
</m:r>
</m:e>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>V</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>×</m:t>
</m:r>
<m:sSubSup>
<m:e>
<m:r>
<m:t>V</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:d>
<m:dPr>
<m:begChr m:val="|" />
<m:endChr m:val="|" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:t>i</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>j</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>k</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∂</m:t>
</m:r>
<m:r>
<m:t>X</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∂</m:t>
</m:r>
<m:r>
<m:t>u</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∂</m:t>
</m:r>
<m:r>
<m:t>Y</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∂</m:t>
</m:r>
<m:r>
<m:t>u</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∂</m:t>
</m:r>
<m:r>
<m:t>X</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∂</m:t>
</m:r>
<m:r>
<m:t>v</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∂</m:t>
</m:r>
<m:r>
<m:t>Y</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∂</m:t>
</m:r>
<m:r>
<m:t>v</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:d>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Vandermonde Determinant</m:t>
</m:r>
</m:e>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="|" />
<m:endChr m:val="|" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⋯</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>v</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>v</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⋯</m:t>
</m:r>
</m:e>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>v</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>v</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>v</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⋯</m:t>
</m:r>
</m:e>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>v</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⋮</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⋮</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⋱</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⋮</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>v</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>n</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>v</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>n</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⋯</m:t>
</m:r>
</m:e>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>v</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>n</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:d>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:nary>
<m:naryPr>
<m:chr m:val="∏" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="1" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≤</m:t>
</m:r>
<m:r>
<m:t>i</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t><</m:t>
</m:r>
<m:r>
<m:t>j</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>≤</m:t>
</m:r>
<m:r>
<m:t>n</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
</m:e>
</m:nary>
<m:sSubSup>
<m:e>
<m:r>
<m:t>v</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>j</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:sSubSup>
<m:e>
<m:r>
<m:t>v</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>i</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Lorenz Equations</m:t>
</m:r>
</m:e>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:limLow>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="˙" />
</m:accPr>
<m:e>
<m:r>
<m:t>x</m:t>
</m:r>
</m:e>
</m:acc>
</m:e>
<m:lim>
<m:r>
<m:t>​</m:t>
</m:r>
</m:lim>
</m:limLow>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>σ</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>y</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>x</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:limLow>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="˙" />
</m:accPr>
<m:e>
<m:r>
<m:t>y</m:t>
</m:r>
</m:e>
</m:acc>
</m:e>
<m:lim>
<m:r>
<m:t>​</m:t>
</m:r>
</m:lim>
</m:limLow>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>ρ</m:t>
</m:r>
<m:r>
<m:t>x</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>y</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>x</m:t>
</m:r>
<m:r>
<m:t>z</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:limLow>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="˙" />
</m:accPr>
<m:e>
<m:r>
<m:t>z</m:t>
</m:r>
</m:e>
</m:acc>
</m:e>
<m:lim>
<m:r>
<m:t>​</m:t>
</m:r>
</m:lim>
</m:limLow>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>β</m:t>
</m:r>
<m:r>
<m:t>z</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>x</m:t>
</m:r>
<m:r>
<m:t>y</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Maxwell's Equations</m:t>
</m:r>
</m:e>
<m:e>
<m:d>
<m:dPr>
<m:begChr m:val="{" />
<m:endChr m:val="" />
<m:sepChr m:val="" />
<m:grow />
</m:dPr>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∇</m:t>
</m:r>
<m:r>
<m:t>​</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>×</m:t>
</m:r>
<m:limLow>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="↼" />
</m:accPr>
<m:e>
<m:r>
<m:t>B</m:t>
</m:r>
</m:e>
</m:acc>
</m:e>
<m:lim>
<m:r>
<m:t>​</m:t>
</m:r>
</m:lim>
</m:limLow>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t> </m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>c</m:t>
</m:r>
</m:den>
</m:f>
<m:r>
<m:t> </m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∂</m:t>
</m:r>
<m:r>
<m:t>​</m:t>
</m:r>
<m:limLow>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="↼" />
</m:accPr>
<m:e>
<m:r>
<m:t>E</m:t>
</m:r>
</m:e>
</m:acc>
</m:e>
<m:lim>
<m:r>
<m:t>​</m:t>
</m:r>
</m:lim>
</m:limLow>
</m:num>
<m:den>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∂</m:t>
</m:r>
<m:r>
<m:t>​</m:t>
</m:r>
<m:r>
<m:t>t</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
</m:e>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>4</m:t>
</m:r>
<m:r>
<m:t>π</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>c</m:t>
</m:r>
</m:den>
</m:f>
<m:r>
<m:t> </m:t>
</m:r>
<m:limLow>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="↼" />
</m:accPr>
<m:e>
<m:r>
<m:t>j</m:t>
</m:r>
</m:e>
</m:acc>
</m:e>
<m:lim>
<m:r>
<m:t>​</m:t>
</m:r>
</m:lim>
</m:limLow>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∇</m:t>
</m:r>
<m:r>
<m:t>​</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>·</m:t>
</m:r>
<m:limLow>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="↼" />
</m:accPr>
<m:e>
<m:r>
<m:t>E</m:t>
</m:r>
</m:e>
</m:acc>
</m:e>
<m:lim>
<m:r>
<m:t>​</m:t>
</m:r>
</m:lim>
</m:limLow>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>4</m:t>
</m:r>
<m:r>
<m:t>π</m:t>
</m:r>
<m:r>
<m:t>ρ</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∇</m:t>
</m:r>
<m:r>
<m:t>​</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>×</m:t>
</m:r>
<m:limLow>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="↼" />
</m:accPr>
<m:e>
<m:r>
<m:t>E</m:t>
</m:r>
</m:e>
</m:acc>
</m:e>
<m:lim>
<m:r>
<m:t>​</m:t>
</m:r>
</m:lim>
</m:limLow>
<m:r>
<m:t> </m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t> </m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>c</m:t>
</m:r>
</m:den>
</m:f>
<m:r>
<m:t> </m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∂</m:t>
</m:r>
<m:r>
<m:t>​</m:t>
</m:r>
<m:limLow>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="↼" />
</m:accPr>
<m:e>
<m:r>
<m:t>B</m:t>
</m:r>
</m:e>
</m:acc>
</m:e>
<m:lim>
<m:r>
<m:t>​</m:t>
</m:r>
</m:lim>
</m:limLow>
</m:num>
<m:den>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∂</m:t>
</m:r>
<m:r>
<m:t>​</m:t>
</m:r>
<m:r>
<m:t>t</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
</m:e>
<m:e>
<m:limLow>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="↼" />
</m:accPr>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
</m:acc>
</m:e>
<m:lim>
<m:r>
<m:t>​</m:t>
</m:r>
</m:lim>
</m:limLow>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>∇</m:t>
</m:r>
<m:r>
<m:t>​</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>·</m:t>
</m:r>
<m:limLow>
<m:e>
<m:acc>
<m:accPr>
<m:chr m:val="↼" />
</m:accPr>
<m:e>
<m:r>
<m:t>B</m:t>
</m:r>
</m:e>
</m:acc>
</m:e>
<m:lim>
<m:r>
<m:t>​</m:t>
</m:r>
</m:lim>
</m:limLow>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>0</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:d>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Einstein Field Equations</m:t>
</m:r>
</m:e>
<m:e>
<m:sSubSup>
<m:e>
<m:r>
<m:t>R</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>μ</m:t>
</m:r>
<m:r>
<m:t>ν</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>2</m:t>
</m:r>
</m:den>
</m:f>
<m:r>
<m:t> </m:t>
</m:r>
<m:sSubSup>
<m:e>
<m:r>
<m:t>g</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>μ</m:t>
</m:r>
<m:r>
<m:t>ν</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:t> </m:t>
</m:r>
<m:r>
<m:t>R</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>8</m:t>
</m:r>
<m:r>
<m:t>π</m:t>
</m:r>
<m:r>
<m:t>G</m:t>
</m:r>
</m:num>
<m:den>
<m:sSubSup>
<m:e>
<m:r>
<m:t>c</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>4</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:den>
</m:f>
<m:r>
<m:t> </m:t>
</m:r>
<m:sSubSup>
<m:e>
<m:r>
<m:t>T</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>μ</m:t>
</m:r>
<m:r>
<m:t>ν</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Ramanujan Identity</m:t>
</m:r>
</m:e>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>φ</m:t>
</m:r>
<m:rad>
<m:radPr>
<m:degHide m:val="1" />
</m:radPr>
<m:deg />
<m:e>
<m:r>
<m:t>5</m:t>
</m:r>
</m:e>
</m:rad>
</m:e>
</m:rad>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>φ</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
<m:sSubSup>
<m:e>
<m:r>
<m:t>e</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>25</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:t>π</m:t>
</m:r>
</m:den>
</m:f>
</m:sup>
</m:sSubSup>
</m:den>
</m:f>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:sSubSup>
<m:e>
<m:r>
<m:t>e</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>2</m:t>
</m:r>
<m:r>
<m:t>π</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:num>
<m:den>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:sSubSup>
<m:e>
<m:r>
<m:t>e</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>4</m:t>
</m:r>
<m:r>
<m:t>π</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:num>
<m:den>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:sSubSup>
<m:e>
<m:r>
<m:t>e</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>6</m:t>
</m:r>
<m:r>
<m:t>π</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:num>
<m:den>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:sSubSup>
<m:e>
<m:r>
<m:t>e</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>8</m:t>
</m:r>
<m:r>
<m:t>π</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:num>
<m:den>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>…</m:t>
</m:r>
</m:den>
</m:f>
</m:den>
</m:f>
</m:den>
</m:f>
</m:den>
</m:f>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Another Ramanujan identity</m:t>
</m:r>
</m:e>
<m:e>
<m:nary>
<m:naryPr>
<m:chr m:val="∑" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>k</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>∞</m:t>
</m:r>
</m:sup>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:sSubSup>
<m:e>
<m:r>
<m:t>2</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⌊</m:t>
</m:r>
<m:r>
<m:t>k</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>·</m:t>
</m:r>
<m:r>
<m:t>​</m:t>
</m:r>
<m:r>
<m:t>φ</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⌋</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:den>
</m:f>
</m:e>
</m:nary>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:sSubSup>
<m:e>
<m:r>
<m:t>2</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>0</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:sSubSup>
<m:e>
<m:r>
<m:t>2</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⋯</m:t>
</m:r>
</m:den>
</m:f>
</m:den>
</m:f>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Rogers-Ramanujan Identity</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:nary>
<m:naryPr>
<m:chr m:val="∑" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>k</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>∞</m:t>
</m:r>
</m:sup>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:sSubSup>
<m:e>
<m:r>
<m:t>q</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:sSubSup>
<m:e>
<m:r>
<m:t>k</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>k</m:t>
</m:r>
</m:sup>
</m:sSubSup>
</m:num>
<m:den>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:r>
<m:t>q</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:sSubSup>
<m:e>
<m:r>
<m:t>q</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>⋯</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:sSubSup>
<m:e>
<m:r>
<m:t>q</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>k</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:nary>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:nary>
<m:naryPr>
<m:chr m:val="∏" />
<m:limLoc m:val="undOvr" />
<m:subHide m:val="0" />
<m:supHide m:val="0" />
</m:naryPr>
<m:sub>
<m:r>
<m:t>j</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>=</m:t>
</m:r>
<m:r>
<m:t>0</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>∞</m:t>
</m:r>
</m:sup>
<m:e>
<m:f>
<m:fPr>
<m:type m:val="bar" />
</m:fPr>
<m:num>
<m:r>
<m:t>1</m:t>
</m:r>
</m:num>
<m:den>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:sSubSup>
<m:e>
<m:r>
<m:t>q</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>5</m:t>
</m:r>
<m:r>
<m:t>j</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>2</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>(</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>-</m:t>
</m:r>
<m:sSubSup>
<m:e>
<m:r>
<m:t>q</m:t>
</m:r>
</m:e>
<m:sub>
<m:r>
<m:t>​</m:t>
</m:r>
</m:sub>
<m:sup>
<m:r>
<m:t>5</m:t>
</m:r>
<m:r>
<m:t>j</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>+</m:t>
</m:r>
<m:r>
<m:t>3</m:t>
</m:r>
</m:sup>
</m:sSubSup>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>)</m:t>
</m:r>
</m:den>
</m:f>
</m:e>
</m:nary>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>,</m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> </m:t>
</m:r>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t> </m:t>
</m:r>
<m:r>
<m:t>f</m:t>
</m:r>
<m:r>
<m:t>o</m:t>
</m:r>
<m:r>
<m:t>r</m:t>
</m:r>
<m:r>
<m:t> </m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>|</m:t>
</m:r>
<m:r>
<m:t>q</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>|</m:t>
</m:r>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t><</m:t>
</m:r>
<m:r>
<m:t>1</m:t>
</m:r>
<m:r>
<m:t>.</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:nor />
<m:sty m:val="p" />
</m:rPr>
<m:t>Commutative Diagram</m:t>
</m:r>
</m:e>
<m:e>
<m:m>
<m:mPr>
<m:baseJc m:val="center" />
<m:plcHide m:val="1" />
<m:mcs>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
<m:mc>
<m:mcPr>
<m:mcJc m:val="center" />
<m:count m:val="1" />
</m:mcPr>
</m:mc>
</m:mcs>
</m:mPr>
<m:mr>
<m:e>
<m:r>
<m:t>H</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>←</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>K</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>↓</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>​</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>↑</m:t>
</m:r>
</m:e>
</m:mr>
<m:mr>
<m:e>
<m:r>
<m:t>H</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:rPr>
<m:sty m:val="p" />
</m:rPr>
<m:t>→</m:t>
</m:r>
</m:e>
<m:e>
<m:r>
<m:t>K</m:t>
</m:r>
</m:e>
</m:mr>
</m:m>
</m:e>
</m:mr>
</m:m>
</m:oMath>
</m:oMathPara>