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.

N206N238=eλ238t−1,N207N235=eλ235t−1\frac{N_{206}}{N_{238}} = e^{\lambda_{238} t} - 1, \qquad \frac{N_{207}}{N_{235}} = e^{\lambda_{235} t} - 1

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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log⁡(Ngroup)=α+β⋅log⁡(VneocortexVrest of brain)\log(N_{\text{group}}) = \alpha + \beta \cdot \log\left(\frac{V_{\text{neocortex}}}{V_{\text{rest of brain}}}\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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Var⁡ ⁣[∂θiE(θ)]∼O ⁣(2−n)\operatorname{Var}\!\left[\partial_{\theta_i} E(\theta)\right] \sim O\!\left(2^{-n}\right)

1 published occurrence

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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mismatch confirmed  ⟺  mechanism specified  ∧  novelty dated  ∧  causal link demonstrated\text{mismatch confirmed} \iff \text{mechanism specified} \;\land\; \text{novelty dated} \;\land\; \text{causal link demonstrated}

1 published occurrence

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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T(E)≈exp⁡(−2ℏ∫x1x22m[V(x)−E] dx)T(E) \approx \exp\left(-\frac{2}{\hbar}\int_{x_1}^{x_2}\sqrt{2m\left[V(x)-E\right]}\,dx\right)

1 published occurrence

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

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