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.

at=πθ(ht∣Tt),ot=Call(at),ht+1=ht⊕(at, ot)a_t = \pi_\theta(h_t \mid \mathcal{T}_t), \qquad o_t = \mathrm{Call}(a_t), \qquad h_{t+1} = h_t \oplus (a_t,\, o_t)

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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Ci=0.1 pin ci−1  +  1.25 pin Δi  +  pout oi,ci=ci−1+ΔiC_i = 0.1\,p_{\mathrm{in}}\,c_{i-1} \;+\; 1.25\,p_{\mathrm{in}}\,\Delta_i \;+\; p_{\mathrm{out}}\,o_i, \qquad c_i = c_{i-1} + \Delta_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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nmax⁡=⌊C−Tsystem−Treservetˉtool⌋n_{\max} = \left\lfloor \frac{C - T_{\mathrm{system}} - T_{\mathrm{reserve}}}{\bar{t}_{\mathrm{tool}}} \right\rfloor

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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R=1−∑i=1nwi⋅1[trial i failed]R = 1 - \sum_{i=1}^{n} w_i \cdot \mathbb{1}[\text{trial } i \text{ failed}]

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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sobs=atrue+δcontam+εconfigs_{\mathrm{obs}} = a_{\mathrm{true}} + \delta_{\mathrm{contam}} + \varepsilon_{\mathrm{config}}

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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ttoken  ≳  2 Nactive β+KV(c)BWt_{\mathrm{token}} \;\gtrsim\; \frac{2\,N_{\mathrm{active}}\,\beta + \mathrm{KV}(c)}{\mathrm{BW}}

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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Tturn=Tsystem+Ttools+∑i=1nTresult,i+TexchangeT_{\mathrm{turn}} = T_{\mathrm{system}} + T_{\mathrm{tools}} + \sum_{i=1}^{n} T_{\mathrm{result},i} + T_{\mathrm{exchange}}

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.

All uses →Latest guide →Latest article →