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.

T50(t)  =  T0⋅2 (t−t0)/τ,τ≈7 monthsT_{50}(t) \;=\; T_0 \cdot 2^{\,(t - t_0)/\tau}, \qquad \tau \approx 7 \text{ months}

1 published occurrence

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

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T50(t)≈T50(t0)⋅2(t−t0)/τ,τ≈7 monthsT_{50}(t) \approx T_{50}(t_0)\cdot 2^{(t-t_0)/\tau}, \qquad \tau \approx 7\text{ months}

1 published occurrence

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

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T(t)  ≈  T0⋅2t−t0τ,τ≈7 monthsT(t) \;\approx\; T_0 \cdot 2^{\frac{t - t_0}{\tau}}, \qquad \tau \approx 7\ \text{months}

1 published occurrence

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

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Δˉ=1T∑t=1T(AcctFP−AcctQ)\bar{\Delta} = \frac{1}{T}\sum_{t=1}^{T}\left(\mathrm{Acc}_t^{FP} - \mathrm{Acc}_t^{Q}\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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Pˉturbine=247.2 MW15≈16.5 MW per unit\bar{P}_{\mathrm{turbine}} = \frac{247.2\ \mathrm{MW}}{15} \approx 16.5\ \mathrm{MW\ per\ unit}

1 published occurrence

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

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Δmax⁡=max⁡t(AcctFP−AcctQ)\Delta_{\max} = \max_{t}\left(\mathrm{Acc}_t^{FP} - \mathrm{Acc}_t^{Q}\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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A^i,t  =  r~i  =  ri−mean({r1,…,rG})std({r1,…,rG})\hat A_{i,t} \;=\; \tilde r_i \;=\; \frac{r_i - \mathrm{mean}(\{r_1,\ldots,r_G\})}{\mathrm{std}(\{r_1,\ldots,r_G\})}

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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L(θ)=Lnew(θ)+λ∑iFi(θi−θi∗)2\mathcal{L}(\theta) = \mathcal{L}_{\mathrm{new}}(\theta) + \lambda \sum_{i} F_i\left(\theta_i - \theta_i^{*}\right)^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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L(x)=∥x−x^(x)∥22+λ∥f(x)∥1,x^(x)=Wd f(x)+bd\mathcal{L}(x) = \lVert x - \hat{x}(x) \rVert_2^2 + \lambda \lVert f(x) \rVert_1, \qquad \hat{x}(x) = W_d\, f(x) + b_d

2 published occurrences

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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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