Live mathematical reference

Mathematical compendium

A live index of the equations in published articles. Each entry leads to its article, equation guide, and the terms explained there. New or edited published articles appear automatically.

1680 equations across 1484 symbols.

Δln⁡L  =  η Δln⁡Y⏟productivity  −  ∫II+ΔIs(x) dx⏟displacement  +  ∫NN+ΔNs(x) dx⏟reinstatement\Delta \ln L \;=\; \underbrace{\eta \, \Delta \ln Y}_{\text{productivity}} \;-\; \underbrace{\int_{I}^{I+\Delta I} s(x)\,dx}_{\text{displacement}} \;+\; \underbrace{\int_{N}^{N+\Delta N} s(x)\,dx}_{\text{reinstatement}}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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Δln⁡w  =  Δln⁡ ⁣(YL)  +  Δln⁡sL\Delta \ln w \;=\; \Delta \ln\!\left(\frac{Y}{L}\right) \;+\; \Delta \ln s_{L}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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δKi′=∑jΛij δKj,Λij=∂Ki′∂Kj∣K∗\delta K'_i = \sum_j \Lambda_{ij} \, \delta K_j, \qquad \Lambda_{ij} = \frac{\partial K'_i}{\partial K_j} \Big|_{K^{*}}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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Δstot[Γ]=kBln⁡PF[Γ]PR[Γ†]\Delta s_{\mathrm{tot}}[\Gamma] = k_{\mathrm B}\ln \frac{\mathcal P_{\mathrm F}[\Gamma]} {\mathcal P_{\mathrm R}[\Gamma^\dagger]}

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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Δ(C)=m ⁣(Mclean with C set to aCcorrupt)−m ⁣(Mclean)\Delta(\mathcal{C}) = m\!\left(M_{\mathrm{clean}} \text{ with } \mathcal{C} \text{ set to } a_{\mathcal{C}}^{\mathrm{corrupt}}\right) - m\!\left(M_{\mathrm{clean}}\right)

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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Q˙=m˙ cp ΔT=ρ V˙ cp ΔT\dot{Q} = \dot{m}\,c_p\,\Delta T = \rho\,\dot{V}\,c_p\,\Delta T

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Cooling power equals fluid mass flow × specific heat capacity × temperature rise. Density converts volume flow into mass flow.

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x˙i=xi(fi−fˉ)+∑jMjixj−∑jMijxi\dot{x}_i = x_i(f_i-\bar f) + \sum_j M_{ji}x_j - \sum_j M_{ij}x_i

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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Var⁡(Jτ)⟨Jτ⟩2≥2⟨Στ⟩\frac{\operatorname{Var}(J_\tau)}{\langle J_\tau\rangle^2} \ge \frac{2}{\langle\Sigma_\tau\rangle}

1 published occurrence

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This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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σEE  =  AE  ⊕  B  ⊕  C\frac{\sigma_E}{E} \;=\; \frac{A}{\sqrt{E}} \;\oplus\; B \;\oplus\; C

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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PF(W)PR(−W)=exp⁡[β(W−ΔF)]\frac{P_{\mathrm F}(W)}{P_{\mathrm R}(-W)} = \exp\left[\beta(W-\Delta F)\right]

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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