Matches in Wikidata for { ?s <http://www.wikidata.org/prop/statement/P2534> ?o ?g. }
- P7316-0107e5d4-4e86-07f1-83bf-0833052d805a P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \left\lfloor \log _{10}n\right\rfloor +1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>⌊</mo> <mrow> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡<!-- --></mo> <mi>n</mi> </mrow> <mo>⌋</mo> </mrow> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\lfloor \log _{10}n\right\rfloor +1}</annotation> </semantics> </math>" @default.
- Q1000116-7ce48d19-4ac1-72e7-8cfb-336f2ba261e2 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \left(\forall i\in \mathbb {N} \colon S_{i}\neq \varnothing \right)\implies \prod _{i\in N}S_{i}\neq \varnothing }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">∀<!-- ∀ --></mi> <mi>i</mi> <mo>∈<!-- ∈ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mo>:<!-- : --></mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>≠<!-- ≠ --></mo> <mi class="MJX-variant">∅<!-- ∅ --></mi> </mrow> <mo>)</mo> </mrow> <mspace width="thickmathspace" /> <mo stretchy="false">⟹<!-- ⟹ --></mo> <mspace width="thickmathspace" /> <munder> <mo>∏<!-- ∏ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈<!-- ∈ --></mo> <mi>N</mi> </mrow> </munder> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>≠<!-- ≠ --></mo> <mi class="MJX-variant">∅<!-- ∅ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(\forall i\in \mathbb {N} \colon S_{i}\neq \varnothing \right)\implies \prod _{i\in N}S_{i}\neq \varnothing }</annotation> </semantics> </math>" @default.
- Q1000845-2B005A8C-AF17-48A3-AA05-81B5F3B0F5CD P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle z_{n+1}={z_{n}}^{2}+c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z_{n+1}={z_{n}}^{2}+c}</annotation> </semantics> </math>" @default.
- Q1003136-f4d943af-41cf-4239-828b-2c35cbed58ac P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle M[G]=\{\operatorname {val} (u,G)|u\in M^{(\mathbb {P} )}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo stretchy="false">[</mo> <mi>G</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mo fence="false" stretchy="false">{</mo> <mi>val</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>G</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>u</mi> <mo>∈<!-- ∈ --></mo> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">P</mi> </mrow> <mo stretchy="false">)</mo> </mrow> </msup> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M[G]=\{\operatorname {val} (u,G)|u\in M^{(\mathbb {P} )}\}}</annotation> </semantics> </math>" @default.
- Q1003225-703E0F82-C068-42AA-8422-B847747EB675 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle (X,{\mathcal {B}},\mu ,T)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">B</mi> </mrow> </mrow> <mo>,</mo> <mi>μ<!-- μ --></mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (X,{\mathcal {B}},\mu ,T)}</annotation> </semantics> </math>" @default.
- Q1004053-d84338cc-4ec5-8086-6218-fd813cdfab01 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \lVert A\rVert _{F}={\sqrt {{\text{Tr}}(AA^{*})}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">‖<!-- ‖ --></mo> <mi>A</mi> <msub> <mo fence="false" stretchy="false">‖<!-- ‖ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mtext>Tr</mtext> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lVert A\rVert _{F}={\sqrt {{\text{Tr}}(AA^{*})}}}</annotation> </semantics> </math>" @default.
- Q1004118-C880A7E4-346B-4264-82C6-E886CF429D50 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle BRN={\frac {(g/T_{v})\Delta \theta _{v}\Delta z}{(\Delta U)^{2}+(\Delta V)^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mi>R</mi> <mi>N</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi mathvariant="normal">Δ<!-- Δ --></mi> <msub> <mi>θ<!-- θ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mi>z</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mi>U</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mi>V</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle BRN={\frac {(g/T_{v})\Delta \theta _{v}\Delta z}{(\Delta U)^{2}+(\Delta V)^{2}}}}</annotation> </semantics> </math>" @default.
- Q100793317-c779aaaa-4168-dd27-e2dc-47af0b77880b P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle I_{\mathrm {sp} }={\frac {F_{\mathrm {T} }}{\dot {m}}}}"> <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">s</mi> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo>˙<!-- ˙ --></mo> </mover> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\mathrm {sp} }={\frac {F_{\mathrm {T} }}{\dot {m}}}}</annotation> </semantics> </math>" @default.
- Q100828354-4172527f-4970-6290-c7b6-c3eff8f08e4f P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle F_{\mathrm {T} }=g_{0}I_{\mathrm {sp} }{\dot {m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo>˙<!-- ˙ --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\mathrm {T} }=g_{0}I_{\mathrm {sp} }{\dot {m}}}</annotation> </semantics> </math>" @default.
- Q1008943-F869E713-7F5C-40A0-AD97-465E6270736B P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle [g_{i},g_{j}]=if^{ijk}g_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">]</mo> <mo>=</mo> <mi>i</mi> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> <mi>k</mi> </mrow> </msup> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [g_{i},g_{j}]=if^{ijk}g_{k}}</annotation> </semantics> </math>" @default.
- Q100981463-145EADA1-E6A1-42A5-BAAC-65C9CBA643E1 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \lambda ={\frac {h}{p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ<!-- λ --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mi>p</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda ={\frac {h}{p}}}</annotation> </semantics> </math>" @default.
- Q101038-33C5D62A-D7FE-4C70-B844-5CF4B586BCCB P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\alpha }=(1-D){\bar {\alpha }}(\theta _{i})+D{\bar {\bar {\alpha }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>α<!-- α --></mi> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−<!-- − --></mo> <mi>D</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α<!-- α --></mi> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <msub> <mi>θ<!-- θ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α<!-- α --></mi> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\alpha }=(1-D){\bar {\alpha }}(\theta _{i})+D{\bar {\bar {\alpha }}}}</annotation> </semantics> </math>" @default.
- Q101194075-33411a8b-49ea-f6fc-eaa4-bb461974ddb0 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \alpha _{A}={\frac {1}{A}}{\frac {\mathrm {d} A}{\mathrm {d} T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α<!-- α --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>A</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>A</mi> </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 \alpha _{A}={\frac {1}{A}}{\frac {\mathrm {d} A}{\mathrm {d} T}}}</annotation> </semantics> </math>" @default.
- Q1012683-9B4E60A8-E1DD-4C56-8AF5-E733CC496568 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle e^{+}e^{-}\rightarrow e^{+}e^{-}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> </mrow> </msup> <mo stretchy="false">→<!-- → --></mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{+}e^{-}\rightarrow e^{+}e^{-}}</annotation> </semantics> </math>" @default.
- Q101434718-35334f33-4b7e-cd6b-446a-a60d96b1e6b8 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle L_{\mathrm {e} ,\nu }={\frac {\mathrm {d} L_{\mathrm {e} }}{\mathrm {d} \nu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mo>,</mo> <mi>ν<!-- ν --></mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ν<!-- ν --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{\mathrm {e} ,\nu }={\frac {\mathrm {d} L_{\mathrm {e} }}{\mathrm {d} \nu }}}</annotation> </semantics> </math>" @default.
- Q101435109-468e94b1-453e-87d4-3257-1d6ff0bf2f43 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle E_{\mathrm {e} ,\nu }={\frac {\mathrm {d} E_{\mathrm {e} }}{\mathrm {d} \nu }}}"> <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> <mi>ν<!-- ν --></mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ν<!-- ν --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\mathrm {e} ,\nu }={\frac {\mathrm {d} E_{\mathrm {e} }}{\mathrm {d} \nu }}}</annotation> </semantics> </math>" @default.
- Q101435187-3a5472c9-4090-8f1b-0d50-4cc291823b6c P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle H_{\mathrm {e} ,\nu }={\frac {\mathrm {d} H_{\mathrm {e} }}{\mathrm {d} \nu }}}"> <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">e</mi> </mrow> <mo>,</mo> <mi>ν<!-- ν --></mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ν<!-- ν --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{\mathrm {e} ,\nu }={\frac {\mathrm {d} H_{\mathrm {e} }}{\mathrm {d} \nu }}}</annotation> </semantics> </math>" @default.
- Q101438718-04c8d98f-45c1-9a12-22a9-1b0a2705d52d P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle aA+bB\leftrightarrow cC+dD}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>A</mi> <mo>+</mo> <mi>b</mi> <mi>B</mi> <mo stretchy="false">↔<!-- ↔ --></mo> <mi>c</mi> <mi>C</mi> <mo>+</mo> <mi>d</mi> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle aA+bB\leftrightarrow cC+dD}</annotation> </semantics> </math>" @default.
- Q101459832-72672319-4b07-b1d3-89ca-588260292caf P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle w_{\nu }={\frac {\mathrm {d} w}{\mathrm {d} \nu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν<!-- ν --></mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>w</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ν<!-- ν --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{\nu }={\frac {\mathrm {d} w}{\mathrm {d} \nu }}}</annotation> </semantics> </math>" @default.
- Q101460704-d0745896-4a0d-6854-5fa6-c4e9ef40dc64 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \Phi _{\mathrm {e} ,\nu }={\frac {\mathrm {d} \Phi _{\mathrm {e} }}{\mathrm {d} \nu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Φ<!-- Φ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mo>,</mo> <mi>ν<!-- ν --></mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi mathvariant="normal">Φ<!-- Φ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ν<!-- ν --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi _{\mathrm {e} ,\nu }={\frac {\mathrm {d} \Phi _{\mathrm {e} }}{\mathrm {d} \nu }}}</annotation> </semantics> </math>" @default.
- Q101461777-fd1d240b-4e4c-03ee-66bb-54cf5e8fc4aa P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle I_{\mathrm {e} ,\nu }={\frac {\mathrm {d} I_{\mathrm {e} }}{\mathrm {d} \nu }}}"> <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">e</mi> </mrow> <mo>,</mo> <mi>ν<!-- ν --></mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ν<!-- ν --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\mathrm {e} ,\nu }={\frac {\mathrm {d} I_{\mathrm {e} }}{\mathrm {d} \nu }}}</annotation> </semantics> </math>" @default.
- Q1014878-14DF70DD-EEF8-4DB1-B4FE-AB1A8AD62FAD P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \theta =\sum _{i}p_{i}dq^{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ<!-- θ --></mi> <mo>=</mo> <munder> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>d</mi> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta =\sum _{i}p_{i}dq^{i}}</annotation> </semantics> </math>" @default.
- Q1014918-9356a9fb-4e56-cd45-a226-6b913b7ff41b P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\frac {\partial y}{\partial t}}+y{\frac {\partial y}{\partial x}}=d{\frac {\partial ^{2}y}{\partial x^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial y}{\partial t}}+y{\frac {\partial y}{\partial x}}=d{\frac {\partial ^{2}y}{\partial x^{2}}}}</annotation> </semantics> </math>" @default.
- Q101511180-feb3821a-4154-a62c-cc1b-3994576c6108 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle M_{\mathrm {e} ,\nu }={\frac {\mathrm {d} M_{\mathrm {e} }}{\mathrm {d} \nu }}}"> <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> <mo>,</mo> <mi>ν<!-- ν --></mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ν<!-- ν --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{\mathrm {e} ,\nu }={\frac {\mathrm {d} M_{\mathrm {e} }}{\mathrm {d} \nu }}}</annotation> </semantics> </math>" @default.
- Q101584387-dece1e3a-4200-fffd-dce6-bc2c86d8a6f2 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Bg}}={\frac {c_{\mathrm {D} }\rho v^{2}}{lg\rho _{\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">B</mi> <mi class="MJX-tex-mathit" mathvariant="italic">g</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> </mrow> </mrow> </msub> <mi>ρ<!-- ρ --></mi> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>l</mi> <mi>g</mi> <msub> <mi>ρ<!-- ρ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Bg}}={\frac {c_{\mathrm {D} }\rho v^{2}}{lg\rho _{\mathrm {b} }}}}</annotation> </semantics> </math>" @default.
- Q1017585-5ed4ccaf-4dce-7ca2-a6b6-04dd2c6115ee P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \sum _{i,j}\alpha _{ij}(x)\mathrm {d} x^{i}\wedge \mathrm {d} x^{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </munder> <msub> <mi>α<!-- α --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msup> <mo>∧<!-- ∧ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i,j}\alpha _{ij}(x)\mathrm {d} x^{i}\wedge \mathrm {d} x^{j}}</annotation> </semantics> </math>" @default.
- Q1019460-D0091376-52ED-4E3A-BD44-E83972ABCCB5 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\frac {\partial {\vec {v}}}{\partial t}}+({\vec {v}}\cdot \nabla ){\vec {v}}=-{\frac {1}{\rho _{0}}}\nabla p+\nu \Delta {\vec {v}}-\beta T{\vec {g}},{\frac {\partial T}{\partial t}}+{\vec {v}}\cdot \nabla T=\chi \Delta T,\operatorname {div} {\vec {v}}=0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>⋅<!-- ⋅ --></mo> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>ρ<!-- ρ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mi>p</mi> <mo>+</mo> <mi>ν<!-- ν --></mi> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>−<!-- − --></mo> <mi>β<!-- β --></mi> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>g</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>T</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>⋅<!-- ⋅ --></mo> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mi>T</mi> <mo>=</mo> <mi>χ<!-- χ --></mi> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mi>T</mi> <mo>,</mo> <mi>div</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial {\vec {v}}}{\partial t}}+({\vec {v}}\cdot \nabla ){\vec {v}}=-{\frac {1}{\rho _{0}}}\nabla p+\nu \Delta {\vec {v}}-\beta T{\vec {g}},{\frac {\partial T}{\partial t}}+{\vec {v}}\cdot \nabla T=\chi \Delta T,\operatorname {div} {\vec {v}}=0.}</annotation> </semantics> </math>" @default.
- Q102040931-fd17cb7c-40c5-4834-7134-65adfff3f20a P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle c_{\mathrm {t} }={\frac {F_{\mathrm {T} }}{\rho n^{2}d^{4}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> </mrow> </msub> <mrow> <mi>ρ<!-- ρ --></mi> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{\mathrm {t} }={\frac {F_{\mathrm {T} }}{\rho n^{2}d^{4}}}}</annotation> </semantics> </math>" @default.
- Q102066153-b66e8bdb-4b71-162c-acc5-25c941ecae8c P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Lg}}={\mathit {Re}}\cdot {\mathit {Eu}}}"> <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">L</mi> <mi class="MJX-tex-mathit" mathvariant="italic">g</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">R</mi> <mi class="MJX-tex-mathit" mathvariant="italic">e</mi> </mrow> </mrow> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">u</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Lg}}={\mathit {Re}}\cdot {\mathit {Eu}}}</annotation> </semantics> </math>" @default.
- Q102066153-e9e01d78-4d01-c175-76d1-8e4d7d15f7b3 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Lg}}={\frac {l\Delta p}{\eta v}}}"> <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">L</mi> <mi class="MJX-tex-mathit" mathvariant="italic">g</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>l</mi> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mi>p</mi> </mrow> <mrow> <mi>η<!-- η --></mi> <mi>v</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Lg}}={\frac {l\Delta p}{\eta v}}}</annotation> </semantics> </math>" @default.
- Q1020763-463F5B47-0F6E-49A2-9361-96085C1110D7 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle cs_{1}={\sqrt {\gamma {\frac {P_{L}}{\rho _{L}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>γ<!-- γ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <msub> <mi>ρ<!-- ρ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle cs_{1}={\sqrt {\gamma {\frac {P_{L}}{\rho _{L}}}}}}</annotation> </semantics> </math>" @default.
- Q1021159-FA77636B-D168-42BB-9791-2F287A61620D P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle X^{\flat }=g_{ij}X^{i}\,dx^{j}=X_{j}\,dx^{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">♭<!-- ♭ --></mi> </mrow> </msup> <mo>=</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msup> <mo>=</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi>d</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X^{\flat }=g_{ij}X^{i}\,dx^{j}=X_{j}\,dx^{j}}</annotation> </semantics> </math>" @default.
- Q102310770-03027c8b-4321-fcd2-5fde-0d26c23106a8 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {El}}={\frac {t_{\mathrm {r} }\nu }{r^{2}}}}"> <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">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">l</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mi>ν<!-- ν --></mi> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {El}}={\frac {t_{\mathrm {r} }\nu }{r^{2}}}}</annotation> </semantics> </math>" @default.
- Q1023483-67EF2AB1-2431-48F7-9281-EEF7AC6CE9FC P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle C={\frac {|u|\,\Delta t}{\Delta x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mspace width="thinmathspace" /> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mi>t</mi> </mrow> <mrow> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C={\frac {|u|\,\Delta t}{\Delta x}}}</annotation> </semantics> </math>" @default.
- Q1027067-073a7ae3-4ae6-422c-737e-62ce506baf30 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle B({\mathcal {H}})/K({\mathcal {H}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>K</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B({\mathcal {H}})/K({\mathcal {H}})}</annotation> </semantics> </math>" @default.
- Q102723670-70f28717-461d-d653-c6d3-89c864b74d4a P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Go}}={\frac {vl_{\mathrm {b} }}{\nu }}{\sqrt {\frac {l_{\mathrm {b} }}{r_{\mathrm {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-mathit" mathvariant="italic">G</mi> <mi class="MJX-tex-mathit" mathvariant="italic">o</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> </mrow> <mi>ν<!-- ν --></mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Go}}={\frac {vl_{\mathrm {b} }}{\nu }}{\sqrt {\frac {l_{\mathrm {b} }}{r_{\mathrm {c} }}}}}</annotation> </semantics> </math>" @default.
- Q102761-f22ea70b-4f88-0f5f-04c5-8725efaf6536 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle a,b,h'\in \mathbb {Z} \land (a\neq 0\lor b\neq 0)\land h\in \mathbb {N} \implies \operatorname {lcm} (a,b)=\{h:(a\mid h\land b\mid h)\land (a\mid h'\land b\mid h'\implies h\mid h')\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <msup> <mi>h</mi> <mo>′</mo> </msup> <mo>∈<!-- ∈ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo>∧<!-- ∧ --></mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>≠<!-- ≠ --></mo> <mn>0</mn> <mo>∨<!-- ∨ --></mo> <mi>b</mi> <mo>≠<!-- ≠ --></mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo>∧<!-- ∧ --></mo> <mi>h</mi> <mo>∈<!-- ∈ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mspace width="thickmathspace" /> <mo stretchy="false">⟹<!-- ⟹ --></mo> <mspace width="thickmathspace" /> <mi>lcm</mi> <mo>⁡<!-- --></mo> <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>h</mi> <mo>:</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>∣<!-- ∣ --></mo> <mi>h</mi> <mo>∧<!-- ∧ --></mo> <mi>b</mi> <mo>∣<!-- ∣ --></mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>∧<!-- ∧ --></mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>∣<!-- ∣ --></mo> <msup> <mi>h</mi> <mo>′</mo> </msup> <mo>∧<!-- ∧ --></mo> <mi>b</mi> <mo>∣<!-- ∣ --></mo> <msup> <mi>h</mi> <mo>′</mo> </msup> <mspace width="thickmathspace" /> <mo stretchy="false">⟹<!-- ⟹ --></mo> <mspace width="thickmathspace" /> <mi>h</mi> <mo>∣<!-- ∣ --></mo> <msup> <mi>h</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a,b,h'\in \mathbb {Z} \land (a\neq 0\lor b\neq 0)\land h\in \mathbb {N} \implies \operatorname {lcm} (a,b)=\{h:(a\mid h\land b\mid h)\land (a\mid h'\land b\mid h'\implies h\mid h')\}}</annotation> </semantics> </math>" @default.
- Q1029151-F42D701B-4B2C-4A28-B94E-EBC3667F4CEB P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\text{Doppler Frequency}}=\left({\frac {2\times {\text{Transmit Frequency}}\times {\text{Range Velocity}}}{C}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Doppler Frequency</mtext> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mo>×<!-- × --></mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Transmit Frequency</mtext> </mrow> <mo>×<!-- × --></mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Range Velocity</mtext> </mrow> </mrow> <mi>C</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{Doppler Frequency}}=\left({\frac {2\times {\text{Transmit Frequency}}\times {\text{Range Velocity}}}{C}}\right)}</annotation> </semantics> </math>" @default.
- Q1029234-B852044D-28E9-4504-9543-43FDEDBA0303 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle f_{r}=f_{t}\left({\frac {1+v/{c'}}{1-v/c'}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>c</mi> <mo>′</mo> </msup> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−<!-- − --></mo> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mo>′</mo> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{r}=f_{t}\left({\frac {1+v/{c'}}{1-v/c'}}\right)}</annotation> </semantics> </math>" @default.
- Q1030949-cff98694-4dfd-e20d-6127-2320d654cf1d P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle A^{2}(b^{2}+c^{2}-a^{2})+B^{2}(a^{2}+c^{2}-b^{2})+C^{2}(a^{2}+b^{2}-c^{2})\geq 16Ff}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−<!-- − --></mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−<!-- − --></mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−<!-- − --></mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>≥<!-- ≥ --></mo> <mn>16</mn> <mi>F</mi> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{2}(b^{2}+c^{2}-a^{2})+B^{2}(a^{2}+c^{2}-b^{2})+C^{2}(a^{2}+b^{2}-c^{2})\geq 16Ff}</annotation> </semantics> </math>" @default.
- Q1032070-50E63F27-E4FB-4EDB-8211-6AEFB6752D1A P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\hat {a}}|\alpha \rangle =\alpha |\alpha \rangle ~}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">^<!-- ^ --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>α<!-- α --></mi> <mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo> <mo>=</mo> <mi>α<!-- α --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>α<!-- α --></mi> <mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {a}}|\alpha \rangle =\alpha |\alpha \rangle ~}</annotation> </semantics> </math>" @default.
- Q1032350-ae16229d-44dc-1ebb-39f5-4a6529cc6171 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle L=CA^{h}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mi>C</mi> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=CA^{h}}</annotation> </semantics> </math>" @default.
- Q10338607-9283EB11-6E1B-4DCC-A795-0F0D497F4EB7 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle M_{n}=2^{n}-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>−<!-- − --></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{n}=2^{n}-1}</annotation> </semantics> </math>" @default.
- Q1033906-E2223FE0-917F-4ECF-959D-EFAF663F99E2 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \pi \mathbb {N} \times \mathbb {N} \to \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π<!-- π --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mo>×<!-- × --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi \mathbb {N} \times \mathbb {N} \to \mathbb {N} }</annotation> </semantics> </math>" @default.
- Q1035152-06a07e06-4f48-0db0-360f-70f7879678f9 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle P={1 \over N^{(x-1)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={1 \over N^{(x-1)}}}</annotation> </semantics> </math>" @default.
- Q10351825-eb76fe5d-4e9e-6d42-4f21-9bb09b46a61e P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle S^{2}={\frac {1}{n-1}}\sum _{i=1}^{n}\left(X_{i}-{\bar {X}}\right)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </mfrac> </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> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S^{2}={\frac {1}{n-1}}\sum _{i=1}^{n}\left(X_{i}-{\bar {X}}\right)^{2}}</annotation> </semantics> </math>" @default.
- Q1036595-08613617-4c71-833b-000b-cbed170c8d54 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \operatorname {Bl} _{\mathcal {I}}X=\operatorname {\underline {Proj}} \bigoplus _{n=0}^{\infty }{\mathcal {I}}^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Bl</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">I</mi> </mrow> </mrow> </msub> <mo>⁡<!-- --></mo> <mi>X</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <munder> <mrow> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">j</mi> </mrow> <mo>_<!-- _ --></mo> </munder> </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> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">I</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Bl} _{\mathcal {I}}X=\operatorname {\underline {Proj}} \bigoplus _{n=0}^{\infty }{\mathcal {I}}^{n}}</annotation> </semantics> </math>" @default.
- Q1036748-22D655CD-D668-4616-B021-8BAACD4EC697 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \rho (\pi ^{*},a)=\int _{\Theta }L(\theta ,a)\,\operatorname {d} \pi ^{*}(\theta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ<!-- ρ --></mi> <mo stretchy="false">(</mo> <msup> <mi>π<!-- π --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>,</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Θ<!-- Θ --></mi> </mrow> </msub> <mi>L</mi> <mo stretchy="false">(</mo> <mi>θ<!-- θ --></mi> <mo>,</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi mathvariant="normal">d</mi> <mo>⁡<!-- --></mo> <msup> <mi>π<!-- π --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>θ<!-- θ --></mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho (\pi ^{*},a)=\int _{\Theta }L(\theta ,a)\,\operatorname {d} \pi ^{*}(\theta )}</annotation> </semantics> </math>" @default.
- Q1037559-5665D631-91E1-4E06-A9C8-A9C30A410FBA P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle |Y^{X}/G|={\frac {1}{|G|}}\sum _{g\in G}m^{c(g)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msup> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> </mfrac> </mrow> <munder> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> <mo>∈<!-- ∈ --></mo> <mi>G</mi> </mrow> </munder> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo stretchy="false">(</mo> <mi>g</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |Y^{X}/G|={\frac {1}{|G|}}\sum _{g\in G}m^{c(g)}}</annotation> </semantics> </math>" @default.
- Q103820258-06fdd554-46de-235b-483f-68ec004532ce P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Stk}}_{1}={\frac {\nu }{d^{2}f}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> <mi class="MJX-tex-mathit" mathvariant="italic">k</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ν<!-- ν --></mi> <mrow> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>f</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Stk}}_{1}={\frac {\nu }{d^{2}f}}}</annotation> </semantics> </math>" @default.
- Q103896907-1d4a1b17-46f5-db08-3481-f78b0ffcfb1c P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Stk}}_{2}={\frac {r^{3}gm}{\nu ^{2}}}\left({\frac {1}{\rho }}-{\frac {1}{\rho _{\mathrm {b} }}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> <mi class="MJX-tex-mathit" mathvariant="italic">k</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>g</mi> <mi>m</mi> </mrow> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>ρ<!-- ρ --></mi> </mfrac> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>ρ<!-- ρ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Stk}}_{2}={\frac {r^{3}gm}{\nu ^{2}}}\left({\frac {1}{\rho }}-{\frac {1}{\rho _{\mathrm {b} }}}\right)}</annotation> </semantics> </math>" @default.
- Q103982174-777cacc8-46bc-7653-fe96-4339e4ec1738 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Stk}}_{3}={\frac {v\nu }{gl^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> <mi class="MJX-tex-mathit" mathvariant="italic">k</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mi>ν<!-- ν --></mi> </mrow> <mrow> <mi>g</mi> <msup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Stk}}_{3}={\frac {v\nu }{gl^{2}}}}</annotation> </semantics> </math>" @default.
- Q103982270-2452efcc-4a92-fe42-cf44-7865242ceef0 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\boldsymbol {g}}={\boldsymbol {a}}_{\rm {g}}+{\boldsymbol {a}}_{\rm {cf}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">g</mi> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {g}}={\boldsymbol {a}}_{\rm {g}}+{\boldsymbol {a}}_{\rm {cf}}}</annotation> </semantics> </math>" @default.
- Q103982443-ec204afc-488f-db39-0eee-21ef45864fab P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Stk}}_{4}={\frac {F_{\mathrm {D} }}{\eta vl}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> <mi class="MJX-tex-mathit" mathvariant="italic">k</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> </mrow> </mrow> </msub> <mrow> <mi>η<!-- η --></mi> <mi>v</mi> <mi>l</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Stk}}_{4}={\frac {F_{\mathrm {D} }}{\eta vl}}}</annotation> </semantics> </math>" @default.
- Q104036153-a03bd195-4285-b0b0-1508-031e54065070 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle (\gamma _{0}\cdot \gamma _{1})(t)={\begin{cases}\gamma _{0}(2t)&0\leq t\leq {\tfrac {1}{2}}\\\gamma _{1}(2t-1)&{\tfrac {1}{2}}\leq t\leq 1.\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>γ<!-- γ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅<!-- ⋅ --></mo> <msub> <mi>γ<!-- γ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>t</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> <msub> <mi>γ<!-- γ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mn>2</mn> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mn>0</mn> <mo>≤<!-- ≤ --></mo> <mi>t</mi> <mo>≤<!-- ≤ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>γ<!-- γ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mn>2</mn> <mi>t</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>≤<!-- ≤ --></mo> <mi>t</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 (\gamma _{0}\cdot \gamma _{1})(t)={\begin{cases}\gamma _{0}(2t)&0\leq t\leq {\tfrac {1}{2}}\\\gamma _{1}(2t-1)&{\tfrac {1}{2}}\leq t\leq 1.\end{cases}}}</annotation> </semantics> </math>" @default.
- Q104058296-7f1a1118-4047-4227-fcb6-e330ccf8022b P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mbox{LICQ}}\Rightarrow {\mbox{MFCQ}}\Rightarrow {\mbox{CPLD}}\wedge {\mbox{LICQ}}\Rightarrow {\mbox{CRCQ}}\Rightarrow {\mbox{CPLD}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>LICQ</mtext> </mstyle> </mrow> <mo stretchy="false">⇒<!-- ⇒ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>MFCQ</mtext> </mstyle> </mrow> <mo stretchy="false">⇒<!-- ⇒ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>CPLD</mtext> </mstyle> </mrow> <mo>∧<!-- ∧ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>LICQ</mtext> </mstyle> </mrow> <mo stretchy="false">⇒<!-- ⇒ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>CRCQ</mtext> </mstyle> </mrow> <mo stretchy="false">⇒<!-- ⇒ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>CPLD</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{LICQ}}\Rightarrow {\mbox{MFCQ}}\Rightarrow {\mbox{CPLD}}\wedge {\mbox{LICQ}}\Rightarrow {\mbox{CRCQ}}\Rightarrow {\mbox{CPLD}}}</annotation> </semantics> </math>" @default.
- Q104120010-2E111CCF-A73C-4DB2-B6EF-B7E1ED875BC5 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \omega (n)=\sum _{p|n}1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω<!-- ω --></mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>n</mi> </mrow> </munder> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega (n)=\sum _{p|n}1}</annotation> </semantics> </math>" @default.
- Q104120010-406244D0-0E15-4519-A03A-6A1ABCEED38B P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \omega (n)=\omega (p_{1}^{\alpha _{1}}p_{2}^{\alpha _{2}}\cdots p_{k}^{\alpha _{k}})=\sum _{p|n}1=k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω<!-- ω --></mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ω<!-- ω --></mi> <mo stretchy="false">(</mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>α<!-- α --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msubsup> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>α<!-- α --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msubsup> <mo>⋯<!-- ⋯ --></mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>α<!-- α --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> </msubsup> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>n</mi> </mrow> </munder> <mn>1</mn> <mo>=</mo> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega (n)=\omega (p_{1}^{\alpha _{1}}p_{2}^{\alpha _{2}}\cdots p_{k}^{\alpha _{k}})=\sum _{p|n}1=k}</annotation> </semantics> </math>" @default.
- Q104145165-4e4ba50a-4e1c-e9c7-d00b-dc0a83d9d060 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \ \mathrm {d} \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo>=</mo> <msubsup> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>θ<!-- θ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>θ<!-- θ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msubsup> <mi>τ<!-- τ --></mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>θ<!-- θ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \ \mathrm {d} \theta }</annotation> </semantics> </math>" @default.
- Q104145185-4055db33-44f0-a784-b090-65f38d7d2da7 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle P={\boldsymbol {M}}\cdot {\boldsymbol {\omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">M</mi> </mrow> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω<!-- ω --></mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\boldsymbol {M}}\cdot {\boldsymbol {\omega }}}</annotation> </semantics> </math>" @default.
- Q104145274-a0ac155a-4020-c171-219f-44c467ec4d2a P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle B={\frac {F}{I\ell }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>F</mi> <mrow> <mi>I</mi> <mi>ℓ<!-- ℓ --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B={\frac {F}{I\ell }}}</annotation> </semantics> </math>" @default.
- Q104155936-B036104E-F47B-4144-97CA-6AA457C43369 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \Omega (n)=\Omega (p_{1}^{\alpha _{1}}p_{2}^{\alpha _{2}}\cdots p_{k}^{\alpha _{k}})=\sum _{k}\alpha _{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω<!-- Ω --></mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">Ω<!-- Ω --></mi> <mo stretchy="false">(</mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>α<!-- α --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msubsup> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>α<!-- α --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msubsup> <mo>⋯<!-- ⋯ --></mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>α<!-- α --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> </msubsup> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munder> <msub> <mi>α<!-- α --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega (n)=\Omega (p_{1}^{\alpha _{1}}p_{2}^{\alpha _{2}}\cdots p_{k}^{\alpha _{k}})=\sum _{k}\alpha _{k}}</annotation> </semantics> </math>" @default.
- Q1041630-f60c4879-4d68-f4e2-7d8d-15a16eb77eeb P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathcal {L}}=-{\frac {1}{4}}f^{2}\operatorname {tr} (L_{\mu }L^{\mu })+{\frac {1}{32g^{2}}}\operatorname {tr} [L_{\mu },L_{\nu }][L^{\mu },L^{\nu }]\qquad (L_{\mu }=U^{\dagger }\partial _{\mu }U)}"> <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">L</mi> </mrow> </mrow> <mo>=</mo> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>tr</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ<!-- μ --></mi> </mrow> </msub> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ<!-- μ --></mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>32</mn> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>tr</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">[</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ<!-- μ --></mi> </mrow> </msub> <mo>,</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν<!-- ν --></mi> </mrow> </msub> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ<!-- μ --></mi> </mrow> </msup> <mo>,</mo> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν<!-- ν --></mi> </mrow> </msup> <mo stretchy="false">]</mo> <mspace width="2em" /> <mo stretchy="false">(</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ<!-- μ --></mi> </mrow> </msub> <mo>=</mo> <msup> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>†<!-- † --></mo> </mrow> </msup> <msub> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ<!-- μ --></mi> </mrow> </msub> <mi>U</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}=-{\frac {1}{4}}f^{2}\operatorname {tr} (L_{\mu }L^{\mu })+{\frac {1}{32g^{2}}}\operatorname {tr} [L_{\mu },L_{\nu }][L^{\mu },L^{\nu }]\qquad (L_{\mu }=U^{\dagger }\partial _{\mu }U)}</annotation> </semantics> </math>" @default.
- Q104175687-9cd40a4a-47f2-3cc7-95ad-74ad422e5b4d P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Fr}}^{*}={\frac {gl}{\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">F</mi> <mi class="MJX-tex-mathit" mathvariant="italic">r</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>g</mi> <mi>l</mi> </mrow> <mi>α<!-- α --></mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Fr}}^{*}={\frac {gl}{\alpha }}}</annotation> </semantics> </math>" @default.
- Q104209862-20ad75e5-4c90-8d60-59ff-5c1de403168f P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Be}}_{1}={\frac {\Delta pl^{2}}{\eta \alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">B</mi> <mi class="MJX-tex-mathit" mathvariant="italic">e</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mi>p</mi> <msup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>η<!-- η --></mi> <mi>α<!-- α --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Be}}_{1}={\frac {\Delta pl^{2}}{\eta \alpha }}}</annotation> </semantics> </math>" @default.
- Q104212301-43c534e5-42da-4870-c3f2-0d34f2adcba4 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\boldsymbol {F}}={\frac {\mathrm {d} {\boldsymbol {p}}}{\mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">F</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">p</mi> </mrow> </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 {\boldsymbol {F}}={\frac {\mathrm {d} {\boldsymbol {p}}}{\mathrm {d} t}}}</annotation> </semantics> </math>" @default.
- Q104217085-6de6e3be-4412-3005-4e86-5a9ffa643d27 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle f(x)={\frac {1}{\sqrt {2\pi }}}\mathrm {e} ^{-{\frac {x^{2}}{2}}}}"> <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>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> <mi>π<!-- π --></mi> </msqrt> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>2</mn> </mfrac> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)={\frac {1}{\sqrt {2\pi }}}\mathrm {e} ^{-{\frac {x^{2}}{2}}}}</annotation> </semantics> </math>" @default.
- Q104217205-267f3a39-4362-634e-394e-0345abd7a28b P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle Q={\frac {C_{\mathrm {pt} }}{m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> <mi>m</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q={\frac {C_{\mathrm {pt} }}{m}}}</annotation> </semantics> </math>" @default.
- Q104223516-2df88757-49df-5783-11b4-3820a536f153 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\boldsymbol {\tau }}=I{\boldsymbol {\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">τ<!-- τ --></mi> </mrow> <mo>=</mo> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">α<!-- α --></mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\tau }}=I{\boldsymbol {\alpha }}}</annotation> </semantics> </math>" @default.
- Q104379084-288697c1-449d-6459-46f4-5c7ff375b03b P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle K_{Q}={\frac {\Phi }{v^{3}l^{2}\rho }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">Φ<!-- Φ --></mi> <mrow> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <msup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>ρ<!-- ρ --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{Q}={\frac {\Phi }{v^{3}l^{2}\rho }}}</annotation> </semantics> </math>" @default.
- Q104379986-ae724067-4db3-fafc-054a-d155d0ed59d2 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Po}}={\frac {Q_{\mathrm {m} }l^{2}}{\lambda \Delta T}}}"> <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">P</mi> <mi class="MJX-tex-mathit" mathvariant="italic">o</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <msup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>λ<!-- λ --></mi> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mi>T</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Po}}={\frac {Q_{\mathrm {m} }l^{2}}{\lambda \Delta T}}}</annotation> </semantics> </math>" @default.
- Q1043944-AE56B630-17FE-4202-9A98-E43D04EB150B P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle P_{\text{stagnation}}={\tfrac {1}{2}}\rho v^{2}+P_{\text{static}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>stagnation</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mi>ρ<!-- ρ --></mi> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>static</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\text{stagnation}}={\tfrac {1}{2}}\rho v^{2}+P_{\text{static}}}</annotation> </semantics> </math>" @default.
- Q104407222-b7f2d445-4ef7-0ac1-47a2-e7a642962bc8 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Sk}}={\frac {\varepsilon \sigma T^{3}l}{\lambda }}}"> <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">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">k</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ε<!-- ε --></mi> <mi>σ<!-- σ --></mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>l</mi> </mrow> <mi>λ<!-- λ --></mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Sk}}={\frac {\varepsilon \sigma T^{3}l}{\lambda }}}</annotation> </semantics> </math>" @default.
- Q1044340-0713E88C-6925-49DE-A67C-16B289B080B3 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle WCI=(10{\sqrt {v}}-v+10.5)\cdot (33-T_{\mathrm {a} })}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mi>C</mi> <mi>I</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>v</mi> </msqrt> </mrow> <mo>−<!-- − --></mo> <mi>v</mi> <mo>+</mo> <mn>10.5</mn> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mo stretchy="false">(</mo> <mn>33</mn> <mo>−<!-- − --></mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle WCI=(10{\sqrt {v}}-v+10.5)\cdot (33-T_{\mathrm {a} })}</annotation> </semantics> </math>" @default.
- Q104438608-40147822-4788-6ebf-2caa-87632a53ef45 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \chi _{\mathrm {mol} }={\frac {M}{\rho }}\kappa }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>χ<!-- χ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>M</mi> <mi>ρ<!-- ρ --></mi> </mfrac> </mrow> <mi>κ<!-- κ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi _{\mathrm {mol} }={\frac {M}{\rho }}\kappa }</annotation> </semantics> </math>" @default.
- Q10452359-9464c023-460e-4c53-5850-3ff837022521 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \{g\in G|g\bullet x=x\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mi>g</mi> <mo>∈<!-- ∈ --></mo> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>g</mi> <mo>∙<!-- ∙ --></mo> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{g\in G|g\bullet x=x\}}</annotation> </semantics> </math>" @default.
- Q104542186-e8469ee5-46a0-7c1a-db1b-29f3e631b0d1 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Fo}}^{*}={\frac {Dt}{l^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">F</mi> <mi class="MJX-tex-mathit" mathvariant="italic">o</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>D</mi> <mi>t</mi> </mrow> <msup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Fo}}^{*}={\frac {Dt}{l^{2}}}}</annotation> </semantics> </math>" @default.
- Q104542217-71d0eec0-4827-599d-103d-47a26e3b1b3b P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Pe}}^{*}={\frac {vl}{D}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> <mi class="MJX-tex-mathit" mathvariant="italic">e</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mi>l</mi> </mrow> <mi>D</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Pe}}^{*}={\frac {vl}{D}}}</annotation> </semantics> </math>" @default.
- Q104578635-5a9b5d87-47c3-ce9f-dd67-4b7ee49115e9 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\begin{array}{lcl}{\mathit {Gr}}^{*}&=&{\frac {l^{3}g\beta \Delta x}{\nu ^{2}}}\\\beta &=&-{\frac {1}{\rho }}\left({\frac {\partial \rho }{\partial x}}\right)_{T,p}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left center left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">G</mi> <mi class="MJX-tex-mathit" mathvariant="italic">r</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>g</mi> <mi>β<!-- β --></mi> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mi>x</mi> </mrow> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>β<!-- β --></mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>ρ<!-- ρ --></mi> </mfrac> </mrow> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>ρ<!-- ρ --></mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{lcl}{\mathit {Gr}}^{*}&=&{\frac {l^{3}g\beta \Delta x}{\nu ^{2}}}\\\beta &=&-{\frac {1}{\rho }}\left({\frac {\partial \rho }{\partial x}}\right)_{T,p}\end{array}}}</annotation> </semantics> </math>" @default.
- Q1045966-27F091A5-9F2A-4C4D-9FB2-DAAF83B31E46 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {2n \choose n}={\frac {(2n)!}{(n!)^{2}}}{\text{ for all }}n\geq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mrow> <mn>2</mn> <mi>n</mi> </mrow> <mi>n</mi> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>n</mi> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>!</mo> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext> for all </mtext> </mrow> <mi>n</mi> <mo>≥<!-- ≥ --></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {2n \choose n}={\frac {(2n)!}{(n!)^{2}}}{\text{ for all }}n\geq 0}</annotation> </semantics> </math>" @default.
- Q104598868-317f5c0b-4561-8fd2-8eeb-c50c20598667 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\begin{array}{lcl}{\mathit {Nu}}^{*}&=&{\frac {k'l}{\rho D}}\\k'&=&{\frac {q_{m}}{A}}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left center left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> <mi class="MJX-tex-mathit" mathvariant="italic">u</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>k</mi> <mo>′</mo> </msup> <mi>l</mi> </mrow> <mrow> <mi>ρ<!-- ρ --></mi> <mi>D</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msup> <mi>k</mi> <mo>′</mo> </msup> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mi>A</mi> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{lcl}{\mathit {Nu}}^{*}&=&{\frac {k'l}{\rho D}}\\k'&=&{\frac {q_{m}}{A}}\end{array}}}</annotation> </semantics> </math>" @default.
- Q104627433-4de814a7-4e68-d60c-dfc7-8453f7398394 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\begin{array}{lcl}{\mathit {St}}^{*}&=&{\frac {k'}{\rho v}}\\k'&=&{\frac {q_{m}}{A}}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left center left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>k</mi> <mo>′</mo> </msup> <mrow> <mi>ρ<!-- ρ --></mi> <mi>v</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msup> <mi>k</mi> <mo>′</mo> </msup> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mi>A</mi> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{lcl}{\mathit {St}}^{*}&=&{\frac {k'}{\rho v}}\\k'&=&{\frac {q_{m}}{A}}\end{array}}}</annotation> </semantics> </math>" @default.
- Q104627433-e1987e43-431d-156b-569d-0b842b6c8f93 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {St}}^{*}={\frac {{\mathit {Nu}}^{*}}{{\mathit {Pe}}^{*}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> <mi class="MJX-tex-mathit" mathvariant="italic">u</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> <mi class="MJX-tex-mathit" mathvariant="italic">e</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {St}}^{*}={\frac {{\mathit {Nu}}^{*}}{{\mathit {Pe}}^{*}}}}</annotation> </semantics> </math>" @default.
- Q104638971-f40d8095-489a-01bc-c9da-9857c565697c P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Gz}}^{*}={\frac {vd}{D}}={\frac {d}{l}}{\mathit {Pe}}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">G</mi> <mi class="MJX-tex-mathit" mathvariant="italic">z</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mi>d</mi> </mrow> <mi>D</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mi>l</mi> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> <mi class="MJX-tex-mathit" mathvariant="italic">e</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Gz}}^{*}={\frac {vd}{D}}={\frac {d}{l}}{\mathit {Pe}}^{*}}</annotation> </semantics> </math>" @default.
- Q104654483-123f10a3-4e6a-ddd8-09dc-3c6fae688f9b P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle j^{*}={\frac {k}{v}}\left({\frac {\nu }{D}}\right)^{2/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>k</mi> <mi>v</mi> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ν<!-- ν --></mi> <mi>D</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j^{*}={\frac {k}{v}}\left({\frac {\nu }{D}}\right)^{2/3}}</annotation> </semantics> </math>" @default.
- Q104654483-7702677c-4cc3-cec2-1bef-6da4fb55df6e P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle j^{*}={\mathit {St}}^{*}{\mathit {Sc}}^{2/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">c</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j^{*}={\mathit {St}}^{*}{\mathit {Sc}}^{2/3}}</annotation> </semantics> </math>" @default.
- Q104655916-5cedd583-4758-8eb6-1a4c-cea60a3e7f96 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \chi _{\mathrm {mass} }={\frac {\kappa }{\rho }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>χ<!-- χ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>κ<!-- κ --></mi> <mi>ρ<!-- ρ --></mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi _{\mathrm {mass} }={\frac {\kappa }{\rho }}}</annotation> </semantics> </math>" @default.
- Q1046711-B25987FC-799A-4269-9D0F-31F0AF1C9475 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \vartheta (x)=\sum _{p\leq x}\log p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϑ<!-- ϑ --></mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>≤<!-- ≤ --></mo> <mi>x</mi> </mrow> </munder> <mi>log</mi> <mo>⁡<!-- --></mo> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vartheta (x)=\sum _{p\leq x}\log p}</annotation> </semantics> </math>" @default.
- Q10470221-00ac6ab8-48d7-ab13-9488-c0aca2e549a1 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \Delta f={\frac {B}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mi>f</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>B</mi> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta f={\frac {B}{2}}}</annotation> </semantics> </math>" @default.
- Q1047080-2dcbc649-4f16-e440-a56d-9ac67bbee873 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \Omega (M)=\Gamma \left(\bigwedge \mathrm {T} ^{*}M\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω<!-- Ω --></mi> <mo stretchy="false">(</mo> <mi>M</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">Γ<!-- Γ --></mi> <mrow> <mo>(</mo> <mrow> <mo>⋀<!-- ⋀ --></mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mi>M</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega (M)=\Gamma \left(\bigwedge \mathrm {T} ^{*}M\right)}</annotation> </semantics> </math>" @default.
- Q104713187-a2aa6e55-4802-cec4-d2e9-def581991196 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Bi}}^{*}={\frac {kl}{D_{\mathrm {int} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">B</mi> <mi class="MJX-tex-mathit" mathvariant="italic">i</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <mi>l</mi> </mrow> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Bi}}^{*}={\frac {kl}{D_{\mathrm {int} }}}}</annotation> </semantics> </math>" @default.
- Q1047416-F46ED6EB-B368-44BF-9169-F66CF78928B3 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle L={{w_{\max }-{\bar {w}}} \over w_{\max }}~~~~~~~~~~(1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>w</mi> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> </mrow> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> </mfrac> </mrow> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L={{w_{\max }-{\bar {w}}} \over w_{\max }}~~~~~~~~~~(1)}</annotation> </semantics> </math>" @default.
- Q1047481-3cbe5ae6-46f9-3b76-51b6-41134c6013a3 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle R(x):=\max(x,0)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>:=</mo> <mo movablelimits="true" form="prefix">max</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R(x):=\max(x,0)}</annotation> </semantics> </math>" @default.
- Q1047481-ec38faf3-44ac-41d3-6ed1-879ef71a9116 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle R:=\mathrm {id} ^{+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>:=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R:=\mathrm {id} ^{+}}</annotation> </semantics> </math>" @default.
- Q1047481-eea00623-472e-332d-1b09-aa6f2a41c566 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle R(x):={\begin{cases}x,&x\geq 0;\\0,&x<0\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo stretchy="false">(</mo> <mi>x</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> <mi>x</mi> <mo>,</mo> </mtd> <mtd> <mi>x</mi> <mo>≥<!-- ≥ --></mo> <mn>0</mn> <mo>;</mo> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> <mo>,</mo> </mtd> <mtd> <mi>x</mi> <mo><</mo> <mn>0</mn> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R(x):={\begin{cases}x,&x\geq 0;\\0,&x<0\end{cases}}}</annotation> </semantics> </math>" @default.
- Q104774294-b435f27b-4b35-7ed8-899a-f7ede6bd0616 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Ex}}={\frac {gd}{v^{2}}}\left(1-{\frac {\rho _{\mathrm {b} }}{\rho }}\right)}"> <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">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>g</mi> <mi>d</mi> </mrow> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ<!-- ρ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> <mi>ρ<!-- ρ --></mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Ex}}={\frac {gd}{v^{2}}}\left(1-{\frac {\rho _{\mathrm {b} }}{\rho }}\right)}</annotation> </semantics> </math>" @default.
- Q104785959-b87b9870-43f9-8e32-0d2c-a4f4c9c5a611 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Be}}^{*}={\frac {\Delta pl^{2}}{\eta D}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">B</mi> <mi class="MJX-tex-mathit" mathvariant="italic">e</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ<!-- Δ --></mi> <mi>p</mi> <msup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>η<!-- η --></mi> <mi>D</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Be}}^{*}={\frac {\Delta pl^{2}}{\eta D}}}</annotation> </semantics> </math>" @default.
- Q104815730-1f862104-4e45-2118-f5fd-657d82c87501 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\mathit {Ca}}={\frac {d^{2}\rho g}{\gamma }}}"> <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">C</mi> <mi class="MJX-tex-mathit" mathvariant="italic">a</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>ρ<!-- ρ --></mi> <mi>g</mi> </mrow> <mi>γ<!-- γ --></mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {Ca}}={\frac {d^{2}\rho g}{\gamma }}}</annotation> </semantics> </math>" @default.
- Q104831-3ad4d7dd-4fe4-0bcb-1a81-c536ac06aefb P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle I_{\mathrm {v} }={\frac {\mathrm {d} \Phi _{\mathrm {v} }}{\mathrm {d} \Omega }}}"> <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">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 mathvariant="normal">Φ<!-- Φ --></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 mathvariant="normal">Ω<!-- Ω --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\mathrm {v} }={\frac {\mathrm {d} \Phi _{\mathrm {v} }}{\mathrm {d} \Omega }}}</annotation> </semantics> </math>" @default.
- Q104841296-a154ab7c-434a-9cf9-8573-a4dc9ebda234 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \forall \alpha \in V''\exists v\in V\forall \lambda \in V'\colon \alpha (\lambda )=\lambda (v)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀<!-- ∀ --></mi> <mi>α<!-- α --></mi> <mo>∈<!-- ∈ --></mo> <msup> <mi>V</mi> <mo>″</mo> </msup> <mi mathvariant="normal">∃<!-- ∃ --></mi> <mi>v</mi> <mo>∈<!-- ∈ --></mo> <mi>V</mi> <mi mathvariant="normal">∀<!-- ∀ --></mi> <mi>λ<!-- λ --></mi> <mo>∈<!-- ∈ --></mo> <msup> <mi>V</mi> <mo>′</mo> </msup> <mo>:<!-- : --></mo> <mi>α<!-- α --></mi> <mo stretchy="false">(</mo> <mi>λ<!-- λ --></mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>λ<!-- λ --></mi> <mo stretchy="false">(</mo> <mi>v</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall \alpha \in V''\exists v\in V\forall \lambda \in V'\colon \alpha (\lambda )=\lambda (v)}</annotation> </semantics> </math>" @default.