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Matches in Wikidata for { ?s <http://www.wikidata.org/prop/statement/P2534> ?o ?g. }

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Q106008771-0c6ee6cd-485d-3f6c-c0c2-96f90f82da49 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \nu ={\frac {1}{T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>T</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu ={\frac {1}{T}}}</annotation> </semantics> </math>" @default.
Q106010255-dc866987-4da0-0761-2ad2-e66b0c25efbe P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle b={\frac {\mu _{\mathrm {n} }}{\mu _{\mathrm {p} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b={\frac {\mu _{\mathrm {n} }}{\mu _{\mathrm {p} }}}}</annotation> </semantics> </math>" @default.
Q1060137-c8d97c8c-42eb-21dc-5ad5-6c5a605e8886 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle -{\frac {\partial S}{\partial t}}=H\left({\boldsymbol {q}},{\frac {\partial S}{\partial {\boldsymbol {q}}}},t\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>H</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">q</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">q</mi> </mrow> </mrow> </mfrac> </mrow> <mo>,</mo> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {\partial S}{\partial t}}=H\left({\boldsymbol {q}},{\frac {\partial S}{\partial {\boldsymbol {q}}}},t\right)}</annotation> </semantics> </math>" @default.
Q106015299-be0e68c3-44e4-7925-8882-db92876d1ed4 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \rho ={\frac {a}{\cos(\theta /2)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mrow> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho ={\frac {a}{\cos(\theta /2)}}}</annotation> </semantics> </math>" @default.
Q106015299-dd8b3615-42e8-5f1a-98a8-5910e92fbbc2 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle (x^{2}+y^{2}-2a^{2})^{2}=x^{2}(x^{2}+y^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x^{2}+y^{2}-2a^{2})^{2}=x^{2}(x^{2}+y^{2})}</annotation> </semantics> </math>" @default.
Q106041131-A11DAB16-519D-47D8-B330-6A8FC6FBFAA3 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \mathbf {T} (t)={\frac {\mathbf {r} ^{\prime }(t)}{|\mathbf {r} ^{\prime }(t)|}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">T</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {T} (t)={\frac {\mathbf {r} ^{\prime }(t)}{|\mathbf {r} ^{\prime }(t)|}}}</annotation> </semantics> </math>" @default.
Q106076968-663fd110-40fd-89a5-8f32-303c447b6ee5 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle x=2r\sin ^{2}{\frac {y}{2r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mn>2</mn> <mi>r</mi> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>y</mi> <mrow> <mn>2</mn> <mi>r</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=2r\sin ^{2}{\frac {y}{2r}}}</annotation> </semantics> </math>" @default.
Q106080-183B4A42-A2EA-41AA-801D-DC861C6E07C3 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle T_{g}={\frac {H_{d}}{S_{d}+R\ln({\frac {1-f_{c}}{f_{c}}})}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> <mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> <mo>+</mo> <mi>R</mi> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mfrac> </mrow> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{g}={\frac {H_{d}}{S_{d}+R\ln({\frac {1-f_{c}}{f_{c}}})}}}</annotation> </semantics> </math>" @default.
Q106097176-f3790390-489e-5e79-95cc-a2bd1d1bbc12 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle L={\sqrt {D\tau }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>D</mi> <mi>τ</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L={\sqrt {D\tau }}}</annotation> </semantics> </math>" @default.
Q106103200-38111301-4b8b-7835-fac3-9550086b0670 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle B_{\mathrm {c} }={\sqrt {\frac {2\mu _{0}(G_{\mathrm {n} }-G_{\mathrm {s} })}{V}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>2</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mi>V</mi> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{\mathrm {c} }={\sqrt {\frac {2\mu _{0}(G_{\mathrm {n} }-G_{\mathrm {s} })}{V}}}}</annotation> </semantics> </math>" @default.
Q1061180-75879cf7-4344-4510-d0aa-0250f108eb24 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \mathrm {C} =\sum _{n=1}^{\infty }\sum _{k=10^{n-1}}^{10^{n}-1}{\frac {k}{10^{kn-9\sum _{k=0}^{n-1}10^{k}(n-k)}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>k</mi> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mi>n</mi> <mo>−</mo> <mn>9</mn> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </munderover> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {C} =\sum _{n=1}^{\infty }\sum _{k=10^{n-1}}^{10^{n}-1}{\frac {k}{10^{kn-9\sum _{k=0}^{n-1}10^{k}(n-k)}}}}</annotation> </semantics> </math>" @default.
Q1061251-3EC896F0-79B7-47C2-8242-3CB9670AC782 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle P_{mag}={\frac {B^{2}}{2\mu _{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{mag}={\frac {B^{2}}{2\mu _{0}}}}</annotation> </semantics> </math>" @default.
Q106177828-a099ed2a-4328-c67a-8194-d5d9abceaffd P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \varkappa _{\mathrm {GL} }={\frac {\lambda }{\xi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϰ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">G</mi> <mi mathvariant="normal">L</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mi>ξ</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varkappa _{\mathrm {GL} }={\frac {\lambda }{\xi }}}</annotation> </semantics> </math>" @default.
Q10621500-290a2249-41a8-49f4-9e77-ec4e55e2f420 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle S_{BC}:S_{AC}:S_{AB}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>C</mi> </mrow> </msub> <mo>:</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>C</mi> </mrow> </msub> <mo>:</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{BC}:S_{AC}:S_{AB}}</annotation> </semantics> </math>" @default.
Q10621500-f9434e1b-4f01-8343-81d1-e49e2ff205be P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \cos(B)\cos(C):\cos(A)\cos(C):\cos(A)\cos(B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>C</mi> <mo stretchy="false">)</mo> <mo>:</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>C</mi> <mo stretchy="false">)</mo> <mo>:</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos(B)\cos(C):\cos(A)\cos(C):\cos(A)\cos(B)}</annotation> </semantics> </math>" @default.
Q1062242-70ECA665-C0F4-4596-8848-545DEB3100D7 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle F(X)\rightarrow \prod _{\alpha \in A}F(X_{\alpha }){{{} \atop \longrightarrow } \atop {\longrightarrow \atop {}}}\prod _{\alpha ,\beta \in A}F(X_{\alpha }\times _{X}X_{\beta })}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <munder> <mo>∏</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mo>∈</mo> <mi>A</mi> </mrow> </munder> <mi>F</mi> <mo stretchy="false">(</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac linethickness="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac linethickness="0"> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mo stretchy="false">⟶</mo> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac linethickness="0"> <mo stretchy="false">⟶</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> </mfrac> </mrow> </mfrac> </mrow> <munder> <mo>∏</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>∈</mo> <mi>A</mi> </mrow> </munder> <mi>F</mi> <mo stretchy="false">(</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <msub> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(X)\rightarrow \prod _{\alpha \in A}F(X_{\alpha }){{{} \atop \longrightarrow } \atop {\longrightarrow \atop {}}}\prod _{\alpha ,\beta \in A}F(X_{\alpha }\times _{X}X_{\beta })}</annotation> </semantics> </math>" @default.
Q106247681-039b031d-493f-7437-b4e1-bfc2f6168bbd P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle M_{\mathrm {e} }=\operatorname {lb} {n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>lb</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{\mathrm {e} }=\operatorname {lb} {n}}</annotation> </semantics> </math>" @default.
Q106268500-636979e8-4214-261f-db5c-48410c45940c P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle T={\frac {1}{r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T={\frac {1}{r}}}</annotation> </semantics> </math>" @default.
Q106282183-26d2dcc2-4128-5674-4b0c-89c2339058bb P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle T_{\mathrm {b} }={\frac {1}{r_{\mathrm {b} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\mathrm {b} }={\frac {1}{r_{\mathrm {b} }}}}</annotation> </semantics> </math>" @default.
Q1062932-474eebd4-4604-8a70-b0f5-a672f969333b P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle a^{x}=b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mo>=</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{x}=b}</annotation> </semantics> </math>" @default.
Q1062958-0695f5a8-4235-f009-4693-64bedd767211 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \;_{j}\phi _{k}\left[{\begin{matrix}a_{1}&a_{2}&\ldots &a_{j}\\b_{1}&b_{2}&\ldots &b_{k}\end{matrix}};q,z\right]=\sum _{n=0}^{\infty }{\frac {(a_{1},a_{2},\ldots ,a_{j};q)_{n}}{(b_{1},b_{2},\ldots ,b_{k},q;q)_{n}}}\left((-1)^{n}q^{n \choose 2}\right)^{1+k-j}z^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mrow> <mo>[</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mo>…</mo> </mtd> <mtd> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mo>…</mo> </mtd> <mtd> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mrow> <mo>;</mo> <mi>q</mi> <mo>,</mo> <mi>z</mi> </mrow> <mo>]</mo> </mrow> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>;</mo> <mi>q</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <mo stretchy="false">(</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>,</mo> <mi>q</mi> <mo>;</mo> <mi>q</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> <mfrac linethickness="0"> <mi>n</mi> <mn>2</mn> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>+</mo> <mi>k</mi> <mo>−</mo> <mi>j</mi> </mrow> </msup> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;_{j}\phi _{k}\left[{\begin{matrix}a_{1}&a_{2}&\ldots &a_{j}\\b_{1}&b_{2}&\ldots &b_{k}\end{matrix}};q,z\right]=\sum _{n=0}^{\infty }{\frac {(a_{1},a_{2},\ldots ,a_{j};q)_{n}}{(b_{1},b_{2},\ldots ,b_{k},q;q)_{n}}}\left((-1)^{n}q^{n \choose 2}\right)^{1+k-j}z^{n}}</annotation> </semantics> </math>" @default.
Q1062958-2bb40dc4-45e9-e8bf-423f-5e964c20e59d P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle (a_{1},a_{2},\ldots ,a_{m};q)_{n}=(a_{1};q)_{n}(a_{2};q)_{n}\ldots (a_{m};q)_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>;</mo> <mi>q</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>;</mo> <mi>q</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>;</mo> <mi>q</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>…</mo> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>;</mo> <mi>q</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a_{1},a_{2},\ldots ,a_{m};q)_{n}=(a_{1};q)_{n}(a_{2};q)_{n}\ldots (a_{m};q)_{n}}</annotation> </semantics> </math>" @default.
Q1063380-07bf3364-4547-ec83-6985-a99474ac6644 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \mathrm {PH} =\bigcup _{k\in \mathbb {N} }\Delta _{k}^{\mathrm {P} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">H</mi> </mrow> <mo>=</mo> <munder> <mo>⋃</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mrow> </munder> <msubsup> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {PH} =\bigcup _{k\in \mathbb {N} }\Delta _{k}^{\mathrm {P} }}</annotation> </semantics> </math>" @default.
Q106344792-9368877a-4e0f-a8c0-b69f-3d2c8a9132c7 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle E_{\mathrm {b} }=P_{\mathrm {c} }T_{\mathrm {b} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\mathrm {b} }=P_{\mathrm {c} }T_{\mathrm {b} }}</annotation> </semantics> </math>" @default.
Q106368657-c3b9f163-4637-521f-f2dd-7b3ac83b4738 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle L_{I}=10\lg {\frac {I}{I_{0}}}\mathrm {dB} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> <mi>lg</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>I</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{I}=10\lg {\frac {I}{I_{0}}}\mathrm {dB} }</annotation> </semantics> </math>" @default.
Q106378242-28934d11-4396-1e97-223a-753ae513a067 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle D_{a}=\log _{a}{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{a}=\log _{a}{n}}</annotation> </semantics> </math>" @default.
Q1064181-70296F95-A83D-4E6D-9603-0D1725D707B7 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \sum _{k=0}^{n}(-2)^{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mo stretchy="false">(</mo> <mo>−</mo> <mn>2</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=0}^{n}(-2)^{k}}</annotation> </semantics> </math>" @default.
Q1064181-8fdf0e55-44bd-3a1d-cba2-aaec36202f33 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \sum _{n=0}^{\infty }(-2)^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mo stretchy="false">(</mo> <mo>−</mo> <mn>2</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{n=0}^{\infty }(-2)^{n}}</annotation> </semantics> </math>" @default.
Q1064218-34c0374f-4df5-3c41-2c6d-3236968b208e P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle A=QUQ^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>Q</mi> <mi>U</mi> <msup> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=QUQ^{-1}}</annotation> </semantics> </math>" @default.
Q106432207-d0a1b67e-4d17-9065-6ce0-909fdea43b71 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle H_{\mathrm {r} }={\frac {H}{H_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>H</mi> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{\mathrm {r} }={\frac {H}{H_{0}}}}</annotation> </semantics> </math>" @default.
Q106432457-7e6c3269-4d0e-fe4d-09e8-28f05c9c9b3e P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle r={\frac {R}{H_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>R</mi> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {R}{H_{0}}}}</annotation> </semantics> </math>" @default.
Q1064357-17106b6c-4aa9-9ba4-6341-76a628bd8bbf P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle g(n,k)={\begin{cases}(g(n-1,k)+k){\bmod {n}}&n>1\\0&n=1\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mi>k</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mo stretchy="false">(</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>k</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo lspace="thickmathspace" rspace="thickmathspace">mod</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </mrow> </mtd> <mtd> <mi>n</mi> <mo>></mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(n,k)={\begin{cases}(g(n-1,k)+k){\bmod {n}}&n>1\\0&n=1\end{cases}}}</annotation> </semantics> </math>" @default.
Q1064434-34a308ca-494a-1554-abb8-eec376980c99 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle m^{*}={\frac {\hbar ^{2}k}{\frac {\mathrm {d} \varepsilon }{\mathrm {d} k}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>k</mi> </mrow> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ε</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>k</mi> </mrow> </mfrac> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m^{*}={\frac {\hbar ^{2}k}{\frac {\mathrm {d} \varepsilon }{\mathrm {d} k}}}}</annotation> </semantics> </math>" @default.
Q106448630-079965c9-4051-0c21-c46d-ae904aad0a15 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\begin{aligned}I(x,y)&=\operatorname {lb} {\frac {1}{p(x,y)}}\,\mathrm {Sh} \\&=\lg {\frac {1}{p(x,y)}}\,\mathrm {Hart} \\&=\ln {\frac {1}{p(x,y)}}\,\mathrm {nat} \end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>I</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>lb</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">h</mi> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>lg</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">t</mi> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">t</mi> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}I(x,y)&=\operatorname {lb} {\frac {1}{p(x,y)}}\,\mathrm {Sh} \\&=\lg {\frac {1}{p(x,y)}}\,\mathrm {Hart} \\&=\ln {\frac {1}{p(x,y)}}\,\mathrm {nat} \end{aligned}}}</annotation> </semantics> </math>" @default.
Q106449009-fcc80de6-4266-0ff1-77a7-6c0936757b70 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle I(x\vert y)=I(x,y)-I(y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo fence="false" stretchy="false">|</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>I</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>I</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I(x\vert y)=I(x,y)-I(y)}</annotation> </semantics> </math>" @default.
Q1064493-350714d0-4452-c02a-a7c7-46a5e600bb0d P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle P={\frac {q^{2}a^{2}}{6\pi \varepsilon _{0}c^{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>6</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\frac {q^{2}a^{2}}{6\pi \varepsilon _{0}c^{3}}}}</annotation> </semantics> </math>" @default.
Q1064500-D7188AE3-DBA1-4B5B-82A0-F32906DD2C10 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle (M,\omega )\qquad (\omega \in \Omega ^{2}(M),\;\mathrm {d} \omega =0,\;\forall (x,v)\in \mathrm {T} M\setminus M\colon \omega _{x}(v,-)\neq 0)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mspace width="2em" /> <mo stretchy="false">(</mo> <mi>ω</mi> <mo>∈</mo> <msup> <mi mathvariant="normal">Ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>M</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ω</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="thickmathspace" /> <mi mathvariant="normal">∀</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> <mi>M</mi> <mo class="MJX-variant">∖</mo> <mi>M</mi> <mo>:</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>v</mi> <mo>,</mo> <mo>−</mo> <mo stretchy="false">)</mo> <mo>≠</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (M,\omega )\qquad (\omega \in \Omega ^{2}(M),\;\mathrm {d} \omega =0,\;\forall (x,v)\in \mathrm {T} M\setminus M\colon \omega _{x}(v,-)\neq 0)}</annotation> </semantics> </math>" @default.
Q106453686-2d80a951-4c47-6f16-53e4-a9b14ca4a055 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle H(Y\vert X)=H(X\vert Y)+H(Y)-H(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo stretchy="false">(</mo> <mi>Y</mi> <mo fence="false" stretchy="false">|</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>H</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo fence="false" stretchy="false">|</mo> <mi>Y</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>H</mi> <mo stretchy="false">(</mo> <mi>Y</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>H</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H(Y\vert X)=H(X\vert Y)+H(Y)-H(X)}</annotation> </semantics> </math>" @default.
Q106460818-16cb832b-4840-dd21-41d0-79e8e4598e24 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle T(X,Y)=\sum _{i=1}^{n}\sum _{j=1}^{m}p(x_{i},y_{j})T(x_{i},y_{j})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </munderover> <mi>p</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>T</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T(X,Y)=\sum _{i=1}^{n}\sum _{j=1}^{m}p(x_{i},y_{j})T(x_{i},y_{j})}</annotation> </semantics> </math>" @default.
Q106460846-53c335ee-4478-0689-1c06-ee923c84e692 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle H'=\lim _{m\to \infty }{\frac {H_{m}}{m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>H</mi> <mo>′</mo> </msup> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mi>m</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H'=\lim _{m\to \infty }{\frac {H_{m}}{m}}}</annotation> </semantics> </math>" @default.
Q106466934-fa5aea86-45f9-f6c3-4256-17fd1255dcd6 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle H^{*}={\frac {H'}{t(X)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>H</mi> <mo>′</mo> </msup> <mrow> <mi>t</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H^{*}={\frac {H'}{t(X)}}}</annotation> </semantics> </math>" @default.
Q106483683-3bf8189a-48cd-ca5c-b0ed-261b1a4dd396 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle T'=\lim _{m\to \infty }{\frac {T_{m}}{m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>T</mi> <mo>′</mo> </msup> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mi>m</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T'=\lim _{m\to \infty }{\frac {T_{m}}{m}}}</annotation> </semantics> </math>" @default.
Q106492181-2dfb77c2-4f32-2a2c-47f9-b5164123b79b P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle T^{*}={\frac {T'}{\sum _{i=1}^{n}\sum _{j=1}^{m}p(x_{i},y_{j})t(x_{i},y_{j})}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>T</mi> <mo>′</mo> </msup> <mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </munderover> <mi>p</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T^{*}={\frac {T'}{\sum _{i=1}^{n}\sum _{j=1}^{m}p(x_{i},y_{j})t(x_{i},y_{j})}}}</annotation> </semantics> </math>" @default.
Q106505959-cbbf6d50-49dc-7af6-cc2b-11992b0807a3 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle C'=\max {T'}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mo>′</mo> </msup> <mo>=</mo> <mo movablelimits="true" form="prefix">max</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>T</mi> <mo>′</mo> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C'=\max {T'}}</annotation> </semantics> </math>" @default.
Q1065144-EE0DC894-466E-4AC2-A944-28533E814A57 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle |A\setminus B|\leq 2|B\setminus A|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>A</mi> <mo class="MJX-variant">∖</mo> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>≤</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>B</mi> <mo class="MJX-variant">∖</mo> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |A\setminus B|\leq 2|B\setminus A|}</annotation> </semantics> </math>" @default.
Q1065257-06573551-4cbe-e5f4-ded2-1a02ea7445e7 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \forall a,b,c\in \mathbb {R} ^{\mathbb {N} }\colon \left(\left(\lim _{n\to \infty }a_{n}=\lim _{n\to \infty }c_{n}\land \forall n\colon a_{n}\leq b_{n}\leq c_{n}\right)\implies \lim _{n\to \infty }b_{n}=\lim _{n\to \infty }a_{n}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo>∈</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mrow> </msup> <mo>:</mo> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>∧</mo> <mi mathvariant="normal">∀</mi> <mi>n</mi> <mo>:</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>≤</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>≤</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mspace width="thickmathspace" /> <mo stretchy="false">⟹</mo> <mspace width="thickmathspace" /> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a,b,c\in \mathbb {R} ^{\mathbb {N} }\colon \left(\left(\lim _{n\to \infty }a_{n}=\lim _{n\to \infty }c_{n}\land \forall n\colon a_{n}\leq b_{n}\leq c_{n}\right)\implies \lim _{n\to \infty }b_{n}=\lim _{n\to \infty }a_{n}\right)}</annotation> </semantics> </math>" @default.
Q106535954-ee8021b5-4cfa-1eb7-960d-5e09ca60cc1f P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {An}}={\frac {m_{\mathrm {a} }}{m_{\mathrm {b} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">A</mi> <mi class="MJX-tex-mathit" mathvariant="italic">n</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {An}}={\frac {m_{\mathrm {a} }}{m_{\mathrm {b} }}}}</annotation> </semantics> </math>" @default.
Q1065997-5e3f21d4-48a3-120e-b7dc-60bda6ae36fe P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \mathrm {p} ^{+}\to \mathrm {e} ^{+}+\pi ^{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo stretchy="false">→</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo>+</mo> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {p} ^{+}\to \mathrm {e} ^{+}+\pi ^{0}}</annotation> </semantics> </math>" @default.
Q1066266-253C0110-8CC1-4E32-844E-D3C21081CA76 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \operatorname {grad} (\mathbf {A} )=\nabla \mathbf {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>grad</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {grad} (\mathbf {A} )=\nabla \mathbf {A} }</annotation> </semantics> </math>" @default.
Q106639293-4c7a76ea-4e5a-45dc-54ae-a0f3299611df P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \mathrm {d} \theta ={\mathcal {C}}\,\mathrm {d} s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>θ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">C</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \theta ={\mathcal {C}}\,\mathrm {d} s}</annotation> </semantics> </math>" @default.
Q106639597-cb97c377-400c-9a66-e458-aca2567a8f3a P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathcal {R}}={\frac {1}{\mathcal {C}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {R}}={\frac {1}{\mathcal {C}}}}</annotation> </semantics> </math>" @default.
Q1066449-4250B9B5-C2B7-4261-B9F7-AD1DE33CD83A P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \mathbf {R} ^{1,3}\rtimes \mathrm {SO} (1,3)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>,</mo> <mn>3</mn> </mrow> </msup> <mo>⋊</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">O</mi> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {R} ^{1,3}\rtimes \mathrm {SO} (1,3)}</annotation> </semantics> </math>" @default.
Q106653384-c7b2bcf7-415d-c6ca-1da4-40d65a91e4e0 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle (a,b]=\{x\in \mathbb {R} \mid a<x\leq b\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mo fence="false" stretchy="false">{</mo> <mi>x</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo>∣</mo> <mi>a</mi> <mo><</mo> <mi>x</mi> <mo>≤</mo> <mi>b</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a,b]=\{x\in \mathbb {R} \mid a<x\leq b\}}</annotation> </semantics> </math>" @default.
Q106653385-ab586a0a-4872-f9c3-6331-22ffd81f0535 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle [a,b)=\{x\in \mathbb {R} \mid a\leq x<b\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo fence="false" stretchy="false">{</mo> <mi>x</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo>∣</mo> <mi>a</mi> <mo>≤</mo> <mi>x</mi> <mo><</mo> <mi>b</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [a,b)=\{x\in \mathbb {R} \mid a\leq x<b\}}</annotation> </semantics> </math>" @default.
Q1067155-2111BDD7-92BD-4F01-92A2-7B07105C2EFE P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle S(x)=\sum _{k=0}^{n}a_{k}\phi _{k}(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S(x)=\sum _{k=0}^{n}a_{k}\phi _{k}(x)}</annotation> </semantics> </math>" @default.
Q1067186-e40a5e1e-4e9c-66b6-1607-68138cbbea32 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle D_{i}=|x_{i}-m(X)|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>−</mo> <mi>m</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{i}=|x_{i}-m(X)|}</annotation> </semantics> </math>" @default.
Q1067478-937DBC91-5783-481F-A475-CF96576935FB P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle V_{j+1}=65539\cdot V_{j}\,{\bmod {\,}}2^{31}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>65539</mn> <mo>⋅</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo lspace="thickmathspace" rspace="thickmathspace">mod</mo> <mrow class="MJX-TeXAtom-ORD"> <mspace width="thinmathspace" /> </mrow> </mrow> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>31</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{j+1}=65539\cdot V_{j}\,{\bmod {\,}}2^{31}}</annotation> </semantics> </math>" @default.
Q1068085-98EC0F41-51A1-4BAC-81D7-D628DBAFFD07 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \lbrace (x,y)\in X\times Y\mid Tx=y\rbrace }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mi>X</mi> <mo>×</mo> <mi>Y</mi> <mo>∣</mo> <mi>T</mi> <mi>x</mi> <mo>=</mo> <mi>y</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lbrace (x,y)\in X\times Y\mid Tx=y\rbrace }</annotation> </semantics> </math>" @default.
Q106808950-e898ca5b-4df0-4a57-8e1f-08a6bb72c269 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \sum _{k=2}^{n}\tau (\rho _{A_{1}A_{k}})\leq \tau (\rho _{A_{1}(A_{2}\dotsm A_{n})})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mi>τ</mi> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> </msub> <mo stretchy="false">)</mo> <mo>≤</mo> <mi>τ</mi> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>⋯</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=2}^{n}\tau (\rho _{A_{1}A_{k}})\leq \tau (\rho _{A_{1}(A_{2}\dotsm A_{n})})}</annotation> </semantics> </math>" @default.
Q1068118-40af2f8d-4bfa-fb14-a25e-0e8914b31ecf P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \int _{X}(\liminf _{n\to \infty }f_{n})\,\mathrm {d} \mu \leq \liminf _{n\to \infty }\int _{X}f_{n}\,\mathrm {d} \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">(</mo> <munder> <mo movablelimits="true" form="prefix">lim inf</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>μ</mi> <mo>≤</mo> <munder> <mo movablelimits="true" form="prefix">lim inf</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{X}(\liminf _{n\to \infty }f_{n})\,\mathrm {d} \mu \leq \liminf _{n\to \infty }\int _{X}f_{n}\,\mathrm {d} \mu }</annotation> </semantics> </math>" @default.
Q1068385-b1cf27d9-4d8e-0f59-af00-28a8e90fe468 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle g(\varphi )=G_{\text{equator}}\left(1+\left({\frac {5}{2}}m-f\right)\sin ^{2}\varphi \right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>equator</mtext> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </mrow> <mi>m</mi> <mo>−</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(\varphi )=G_{\text{equator}}\left(1+\left({\frac {5}{2}}m-f\right)\sin ^{2}\varphi \right)}</annotation> </semantics> </math>" @default.
Q1068463-ec3c09d4-4e8d-7fa0-3b3e-9fc50e9cb2b6 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\boldsymbol {p}}={\begin{pmatrix}E/c\\p_{x}\\p_{y}\\p_{z}\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">p</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {p}}={\begin{pmatrix}E/c\\p_{x}\\p_{y}\\p_{z}\end{pmatrix}}}</annotation> </semantics> </math>" @default.
Q106886041-2c14e20f-4f61-be58-9398-ccd566794744 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle k={\frac {M}{\theta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>M</mi> <mi>θ</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k={\frac {M}{\theta }}}</annotation> </semantics> </math>" @default.
Q1068976-A0F19DE9-F3AB-404A-A82A-BD30722CE03A P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\hbox{I}}({\hbox{V}}(J))={\sqrt {J}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>I</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>V</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>J</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>J</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hbox{I}}({\hbox{V}}(J))={\sqrt {J}}}</annotation> </semantics> </math>" @default.
Q106959133-e24e682d-4544-998b-17df-20f49117faaf P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle E_{\mathrm {e} ,\mathrm {o} }=\int \limits _{4\pi }L_{\mathrm {e} }\mathrm {d} \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> </mrow> </mrow> </msub> <mo>=</mo> <munder> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> <mi>π</mi> </mrow> </munder> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\mathrm {e} ,\mathrm {o} }=\int \limits _{4\pi }L_{\mathrm {e} }\mathrm {d} \Omega }</annotation> </semantics> </math>" @default.
Q107018545-82cfd41c-46bf-168d-90df-ae005db9d7ea P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle V_{\mathrm {mes} ;m}(\lambda )={\frac {1}{M(m)}}(mV(\lambda )+(1-m)V'(\lambda ))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">s</mi> </mrow> <mo>;</mo> <mi>m</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>M</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mi>V</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>m</mi> <mo stretchy="false">)</mo> <msup> <mi>V</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\mathrm {mes} ;m}(\lambda )={\frac {1}{M(m)}}(mV(\lambda )+(1-m)V'(\lambda ))}</annotation> </semantics> </math>" @default.
Q1071013-3608e3c5-4a17-74ac-771d-da4b6c7deba1 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\frac {\mathrm {d} H}{\mathrm {d} t}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>H</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} H}{\mathrm {d} t}}=0}</annotation> </semantics> </math>" @default.
Q1071077-ca540ca9-4ce3-a827-be92-0962f4108005 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {n\#=\prod _{i=1}^{\pi (n)}p_{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi mathvariant="normal">#</mi> <mo>=</mo> <munderover> <mo>∏</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </munderover> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {n\#=\prod _{i=1}^{\pi (n)}p_{i}}}</annotation> </semantics> </math>" @default.
Q1071123-4744AFDE-A44F-430F-9FFE-5519C60C781E P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\frac {8!\times 3^{7}\times 24!^{2}}{4!^{6}\times 24}}\approx 7.40\times 10^{45}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>8</mn> <mo>!</mo> <mo>×</mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mo>×</mo> <mn>24</mn> <msup> <mo>!</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>4</mn> <msup> <mo>!</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mo>×</mo> <mn>24</mn> </mrow> </mfrac> </mrow> <mo>≈</mo> <mn>7.40</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>45</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {8!\times 3^{7}\times 24!^{2}}{4!^{6}\times 24}}\approx 7.40\times 10^{45}}</annotation> </semantics> </math>" @default.
Q1071270-23b2214c-415b-a145-98af-db8bfff8895f P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \int _{a}^{b}f(\phi (x))\phi '(x)\,\mathrm {d} x=\int _{\phi (a)}^{\phi (b)}f(t)\,\mathrm {d} t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <msup> <mi>ϕ</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>x</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{a}^{b}f(\phi (x))\phi '(x)\,\mathrm {d} x=\int _{\phi (a)}^{\phi (b)}f(t)\,\mathrm {d} t}</annotation> </semantics> </math>" @default.
Q10713659-F1A8EF29-E7D5-4950-9D83-680E48CD601E P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle ({\boldsymbol {a}}+{\boldsymbol {b}})_{i}=a_{i}+b_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">a</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">b</mi> </mrow> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\boldsymbol {a}}+{\boldsymbol {b}})_{i}=a_{i}+b_{i}}</annotation> </semantics> </math>" @default.
Q1071534-8BCD9D74-169C-4F1B-9A47-B9FB8AAA69F1 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \lambda =\alpha {\frac {\gamma }{M_{\mathrm {s} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>=</mo> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>γ</mi> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda =\alpha {\frac {\gamma }{M_{\mathrm {s} }}}}</annotation> </semantics> </math>" @default.
Q107164637-b17f6842-4e1e-3765-e030-d474c9c94240 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle I_{\mathrm {P} }=L_{\mathrm {v} }A_{\mathrm {P} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">v</mi> </mrow> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\mathrm {P} }=L_{\mathrm {v} }A_{\mathrm {P} }}</annotation> </semantics> </math>" @default.
Q1071743-c96f339a-49ca-94d5-926b-ea3826f1d40f P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\boldsymbol {\Phi }}(u,v)=(x(u,v),y(u,v),z(u,v))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Φ</mi> </mrow> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mi>y</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mi>z</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\Phi }}(u,v)=(x(u,v),y(u,v),z(u,v))}</annotation> </semantics> </math>" @default.
Q1071795-a52b2a31-41e6-7e76-cabf-1e35074ee17c P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \forall C,D\in \operatorname {Open} (X)\left(X\setminus C\cap X\setminus D=\varnothing \implies \exists U,V\in \operatorname {Open} (X)\colon \left(X\setminus C\subseteq U\land X\setminus D\subseteq V\land U\cap V=\varnothing \right)\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>C</mi> <mo>,</mo> <mi>D</mi> <mo>∈</mo> <mi>Open</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo class="MJX-variant">∖</mo> <mi>C</mi> <mo>∩</mo> <mi>X</mi> <mo class="MJX-variant">∖</mo> <mi>D</mi> <mo>=</mo> <mi class="MJX-variant">∅</mi> <mspace width="thickmathspace" /> <mo stretchy="false">⟹</mo> <mspace width="thickmathspace" /> <mi mathvariant="normal">∃</mi> <mi>U</mi> <mo>,</mo> <mi>V</mi> <mo>∈</mo> <mi>Open</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>:</mo> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo class="MJX-variant">∖</mo> <mi>C</mi> <mo>⊆</mo> <mi>U</mi> <mo>∧</mo> <mi>X</mi> <mo class="MJX-variant">∖</mo> <mi>D</mi> <mo>⊆</mo> <mi>V</mi> <mo>∧</mo> <mi>U</mi> <mo>∩</mo> <mi>V</mi> <mo>=</mo> <mi class="MJX-variant">∅</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall C,D\in \operatorname {Open} (X)\left(X\setminus C\cap X\setminus D=\varnothing \implies \exists U,V\in \operatorname {Open} (X)\colon \left(X\setminus C\subseteq U\land X\setminus D\subseteq V\land U\cap V=\varnothing \right)\right)}</annotation> </semantics> </math>" @default.
Q1071846-836C98F6-73A2-40D9-BA5B-725EAFB921FC P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \nabla ^{2}f=\nabla \cdot \nabla f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>f</mi> <mo>=</mo> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mi mathvariant="normal">∇</mi> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla ^{2}f=\nabla \cdot \nabla f}</annotation> </semantics> </math>" @default.
Q107203920-860e2cc5-4387-42ed-41f0-879cbcb8fce7 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \varphi \left(\operatorname {E} [X]\right)\leq \operatorname {E} \left[\varphi (X)\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">E</mi> <mo>⁡</mo> <mo stretchy="false">[</mo> <mi>X</mi> <mo stretchy="false">]</mo> </mrow> <mo>)</mo> </mrow> <mo>≤</mo> <mi mathvariant="normal">E</mi> <mo>⁡</mo> <mrow> <mo>[</mo> <mrow> <mi>φ</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi \left(\operatorname {E} [X]\right)\leq \operatorname {E} \left[\varphi (X)\right]}</annotation> </semantics> </math>" @default.
Q107205-64dda55d-4a63-a3b7-0d2c-bc52aa1d72e6 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle 10^{6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{6}}</annotation> </semantics> </math>" @default.
Q107209392-57cd583f-44de-81c2-8fa5-3dafd1b8ecd3 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle a(n)=prime(n)\oplus n^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>p</mi> <mi>r</mi> <mi>i</mi> <mi>m</mi> <mi>e</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>⊕</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a(n)=prime(n)\oplus n^{2}}</annotation> </semantics> </math>" @default.
Q1072412-d5f35cea-4773-3c5f-9a2b-6afe623a9a76 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\begin{aligned}&f_{n}\colon A\to \mathbb {R} \\&\left(\forall n\geq 1\forall x\in A\colon |f_{n}(x)|\leq |M_{n}|\right)\land \left(\sum _{n=1}^{\infty }|M_{n}|<\infty \right)\implies \exists \sum _{n=1}^{\infty }|f_{n}|\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>:</mo> <mi>A</mi> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">∀</mi> <mi>n</mi> <mo>≥</mo> <mn>1</mn> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo>∈</mo> <mi>A</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>≤</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>∧</mo> <mrow> <mo>(</mo> <mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo><</mo> <mi mathvariant="normal">∞</mi> </mrow> <mo>)</mo> </mrow> <mspace width="thickmathspace" /> <mo stretchy="false">⟹</mo> <mspace width="thickmathspace" /> <mi mathvariant="normal">∃</mi> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&f_{n}\colon A\to \mathbb {R} \\&\left(\forall n\geq 1\forall x\in A\colon |f_{n}(x)|\leq |M_{n}|\right)\land \left(\sum _{n=1}^{\infty }|M_{n}|<\infty \right)\implies \exists \sum _{n=1}^{\infty }|f_{n}|\end{aligned}}}</annotation> </semantics> </math>" @default.
Q1072476-0B9195FF-522F-47DE-BCE4-E6C972323EE7 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\cfrac {\mathrm {d} ^{2}w(x)}{\mathrm {d} x^{2}}}={\frac {M(x)}{E(x)I(x)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>w</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mstyle> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>M</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>E</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mi>I</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\cfrac {\mathrm {d} ^{2}w(x)}{\mathrm {d} x^{2}}}={\frac {M(x)}{E(x)I(x)}}}</annotation> </semantics> </math>" @default.
Q1072483-95507ef0-4a2e-bd26-f76f-4d47ef25e113 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \left\{{\begin{aligned}x&=&v\cos(u)\\y&=&v\sin(u)\\z&=&u\end{aligned}}\right.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>{</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> </mtd> <mtd> <mi>v</mi> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>u</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> </mtd> <mtd> <mi>v</mi> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>u</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> </mtd> <mtd> <mi>u</mi> </mtd> </mtr> </mtable> </mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\{{\begin{aligned}x&=&v\cos(u)\\y&=&v\sin(u)\\z&=&u\end{aligned}}\right.}</annotation> </semantics> </math>" @default.
Q1072885-E1B7F210-4FC4-4823-A0EB-2671F64DC99C P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \operatorname {E} (R_{p})=\sum _{i}w_{i}\operatorname {E} (R_{i})\quad }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">E</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi mathvariant="normal">E</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mspace width="1em" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {E} (R_{p})=\sum _{i}w_{i}\operatorname {E} (R_{i})\quad }</annotation> </semantics> </math>" @default.
Q1073808-1ba8933c-4c04-9a9d-1db3-f2827a104e66 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle RV+ERV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mi>V</mi> <mo>+</mo> <mi>E</mi> <mi>R</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RV+ERV}</annotation> </semantics> </math>" @default.
Q107428-a04ad46c-4a23-ff1c-2f35-0481e3dbf367 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle 10^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{3}}</annotation> </semantics> </math>" @default.
Q1074289-5379C003-59F7-4060-9191-AF41F396107D P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle x(t)=A\sin(2\pi ft)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(t)=A\sin(2\pi ft)}</annotation> </semantics> </math>" @default.
Q1074845-4bbf07cc-4cc8-ee42-7414-94fdce56302f P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \sum _{n=1}^{\infty }1/4^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{n=1}^{\infty }1/4^{n}}</annotation> </semantics> </math>" @default.
Q1074845-c975ef12-4edb-819c-22b8-3dc1a7f24231 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle 1/4+1/16+1/64+1/256+\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> <mo>+</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>16</mn> <mo>+</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>64</mn> <mo>+</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>256</mn> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/4+1/16+1/64+1/256+\cdots }</annotation> </semantics> </math>" @default.
Q10754052-81927f55-40f3-b07c-40ab-a0d1a203389f P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \left({\overline {\boldsymbol {A}}}\right)_{ik}={\overline {\left({\boldsymbol {A}}\right)_{ik}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">A</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">A</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>k</mi> </mrow> </msub> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\overline {\boldsymbol {A}}}\right)_{ik}={\overline {\left({\boldsymbol {A}}\right)_{ik}}}}</annotation> </semantics> </math>" @default.
Q1075846-b175be62-433b-0b24-a6e5-d51672faa939 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\frac {\left({\frac {3}{2}}\right)^{4}}{2^{2}}}={\frac {3^{4}}{2^{6}}}={\frac {81}{64}}\approx 407{,}82\;\mathrm {Cent} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>81</mn> <mn>64</mn> </mfrac> </mrow> <mo>≈</mo> <mn>407</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>82</mn> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\left({\frac {3}{2}}\right)^{4}}{2^{2}}}={\frac {3^{4}}{2^{6}}}={\frac {81}{64}}\approx 407{,}82\;\mathrm {Cent} }</annotation> </semantics> </math>" @default.
Q1076349-77B5C3BD-7E6D-42D8-AA45-A7F09D0207D0 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle H(\sigma )=-\sum _{\langle i~j\rangle }J_{ij}\sigma _{i}\sigma _{j}-\mu \sum _{j}h_{j}\sigma _{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo stretchy="false">(</mo> <mi>σ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mo fence="false" stretchy="false">⟨</mo> <mi>i</mi> <mtext> </mtext> <mi>j</mi> <mo fence="false" stretchy="false">⟩</mo> </mrow> </munder> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>−</mo> <mi>μ</mi> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H(\sigma )=-\sum _{\langle i~j\rangle }J_{ij}\sigma _{i}\sigma _{j}-\mu \sum _{j}h_{j}\sigma _{j}}</annotation> </semantics> </math>" @default.
Q107645914-46aa65af-4c1a-9a8f-250e-bfa8e5a629c0 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle S=A\cos {\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mi>A</mi> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=A\cos {\alpha }}</annotation> </semantics> </math>" @default.
Q1077037-C40ABB2E-DBC8-4457-94C7-69B70A389033 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle T=KP_{pre}d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mi>K</mi> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>r</mi> <mi>e</mi> </mrow> </msub> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T=KP_{pre}d}</annotation> </semantics> </math>" @default.
Q1077153-b90c0a22-465b-fa18-ce95-8efe4801c7ad P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\frac {PV}{T}}=k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>P</mi> <mi>V</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mo>=</mo> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {PV}{T}}=k}</annotation> </semantics> </math>" @default.
Q1077153-fad8fded-4951-b3ff-b7da-e6f8fdafb476 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\frac {P_{1}V_{1}}{T_{1}}}={\frac {P_{2}V_{2}}{T_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {P_{1}V_{1}}{T_{1}}}={\frac {P_{2}V_{2}}{T_{2}}}}</annotation> </semantics> </math>" @default.
Q1077442-52818B0B-C3AF-4E68-A69E-91E2A2C16E1C P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle (A\to B)\iff (\neg B\to \neg A)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">→</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mo stretchy="false">⟺</mo> <mspace width="thickmathspace" /> <mo stretchy="false">(</mo> <mi mathvariant="normal">¬</mi> <mi>B</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">¬</mi> <mi>A</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A\to B)\iff (\neg B\to \neg A)}</annotation> </semantics> </math>" @default.
Q107752223-36efa2f2-46f1-645a-8684-723e8a6d7018 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle R_{Sh}^{-1}={\frac {3\pi }{16}}{\frac {n{{e}^{2}}{{d}^{2}}}{{p}_{F}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mi>h</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mi>π</mi> </mrow> <mn>16</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> </msub> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{Sh}^{-1}={\frac {3\pi }{16}}{\frac {n{{e}^{2}}{{d}^{2}}}{{p}_{F}}},}</annotation> </semantics> </math>" @default.
Q1077769-1CDD0A61-55AA-4118-82DB-09B58BFE9A4B P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle P=1/W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=1/W}</annotation> </semantics> </math>" @default.
Q107780-65f64d83-4482-8e98-88c8-f949ca11f653 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \Phi _{\mathrm {v} }={\frac {\mathrm {d} Q_{\mathrm {v} }}{\mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">v</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">v</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi _{\mathrm {v} }={\frac {\mathrm {d} Q_{\mathrm {v} }}{\mathrm {d} t}}}</annotation> </semantics> </math>" @default.
Q1077811-8c28a1c0-4f0a-1c53-594b-f96d1d6476dd P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \forall x\,\exists P\,\forall y\,y\in P\Leftrightarrow y\subseteq x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mspace width="thinmathspace" /> <mi mathvariant="normal">∃</mi> <mi>P</mi> <mspace width="thinmathspace" /> <mi mathvariant="normal">∀</mi> <mi>y</mi> <mspace width="thinmathspace" /> <mi>y</mi> <mo>∈</mo> <mi>P</mi> <mo stretchy="false">⇔</mo> <mi>y</mi> <mo>⊆</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x\,\exists P\,\forall y\,y\in P\Leftrightarrow y\subseteq x}</annotation> </semantics> </math>" @default.

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