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.

g(i)∼πsuper(g∣task),at(i)∼πworker(i)(a∣o≤t(i), ht(i), g(i))g^{(i)} \sim \pi_{\text{super}}(g \mid \text{task}), \qquad a_t^{(i)} \sim \pi_{\text{worker}}^{(i)}\bigl(a \mid o_{\le t}^{(i)},\ h_t^{(i)},\ g^{(i)}\bigr)

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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K(t)=1 ⁣[O(t)≥o∗]⋅1 ⁣[W(t)≥w∗]K(t) = \mathbb{1}\!\left[O(t) \ge o^{*}\right] \cdot \mathbb{1}\!\left[W(t) \ge w^{*}\right]

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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Leff(τ)=max⁡{ n≤W : S(n)≥τ⋅S0 }L_{\mathrm{eff}}(\tau) = \max\left\{\, n \le W \ :\ S(n) \ge \tau \cdot S_0 \,\right\}

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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Lsequential(k)≈k lˉ,Lparallel(k)≈lˉ+ϵ(k)L_{\text{sequential}}(k) \approx k\,\bar{l}, \qquad L_{\text{parallel}}(k) \approx \bar{l} + \epsilon(k)

1 published occurrence

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

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