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.

1676 equations across 1477 symbols.

PˉGPU,2=PtotalN2=2,000 MW555,000≈3.6 kW per GPU\bar{P}_{\text{GPU},2} = \frac{P_{\text{total}}}{N_2} = \frac{2{,}000\ \text{MW}}{555{,}000} \approx 3.6\ \text{kW per GPU}

1 published occurrence

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This equation gives an approximation: it relates the quantities while allowing an approximation.

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x2i−1′=x2i−1cos⁡(mθi)−x2isin⁡(mθi)x2i′=x2i−1sin⁡(mθi)+x2icos⁡(mθi)\begin{aligned} x'_{2i-1} &= x_{2i-1}\cos(m\theta_i) - x_{2i}\sin(m\theta_i) \\ x'_{2i} &= x_{2i-1}\sin(m\theta_i) + x_{2i}\cos(m\theta_i) \end{aligned}

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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ΔW=BA,B∈Rd×r, A∈Rr×k, r≪min⁡(d,k)\Delta W = BA, \qquad B \in \mathbb{R}^{d \times r},\ A \in \mathbb{R}^{r \times k},\ r \ll \min(d, 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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Δ(C)=m(Mclean→C←corrupt)−m(Mclean)\Delta(\mathcal{C}) = m\big(M_{\mathrm{clean} \to \mathcal{C} \leftarrow \mathrm{corrupt}}\big) - m\big(M_{\mathrm{clean}}\big)

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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DK⋅DK⋅M⋅DF⋅DF+M⋅N⋅DF⋅DFDK⋅DK⋅M⋅N⋅DF⋅DF=1N+1DK2\frac{D_K \cdot D_K \cdot M \cdot D_F \cdot D_F + M \cdot N \cdot D_F \cdot D_F}{D_K \cdot D_K \cdot M \cdot N \cdot D_F \cdot D_F} = \frac{1}{N} + \frac{1}{D_K^2}

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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