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.

qτ=Pr⁡(failure and severity>τ)=(1−p)⋅Pr⁡(C>τ∣failure)q_\tau = \Pr(\text{failure and severity} > \tau) = (1-p)\cdot \Pr(C > \tau \mid \text{failure})

1 published occurrence

View equation in context

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

All uses →Latest guide →Latest article →
Qdevice∗=(Cdev+U)/(ccloud−cd)Q^{*}_{\mathrm{device}} = (C_{\mathrm{dev}} + U) / (c_{\mathrm{cloud}} - c_{d})

1 published occurrence

View equation in context

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 →
Qdevice∗=Cdev+Uccloud−cdQ^{*}_{\mathrm{device}} = \frac{C_{\mathrm{dev}} + U}{c_{\mathrm{cloud}} - c_{d}}

1 published occurrence

View equation in context

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 →
Qdistill∗=Cdistillcteacher−cstudentQ^{*}_{\mathrm{distill}} = \frac{C_{\mathrm{distill}}}{c_{\mathrm{teacher}} - c_{\mathrm{student}}}

1 published occurrence

View equation in context

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 →
S(g)=1(1−p)+p/g,lim⁡g→∞S(g)=11−pS(g) = \frac{1}{(1-p) + p/g}, \qquad \lim_{g \to \infty} S(g) = \frac{1}{1-p}

1 published occurrence

View equation in context

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 →
Ttotal=Tparent+∑i=1kTsubagenti,Tparent≪∑i=1kTsubagentiT_{\mathrm{total}} = T_{\mathrm{parent}} + \sum_{i=1}^{k} T_{\mathrm{subagent}_i}, \qquad T_{\mathrm{parent}} \ll \sum_{i=1}^{k} T_{\mathrm{subagent}_i}

1 published occurrence

View equation in context

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 →
TCdevice=Cdev+U+Q⋅cd,TCcloud=Q⋅ccloudTC_{\mathrm{device}} = C_{\mathrm{dev}} + U + Q \cdot c_{d}, \qquad TC_{\mathrm{cloud}} = Q \cdot c_{\mathrm{cloud}}

1 published occurrence

View equation in context

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 →
TCdistill=Cdistill+Q⋅cstudentTC_{\mathrm{distill}} = C_{\mathrm{distill}} + Q \cdot c_{\mathrm{student}}

1 published occurrence

View equation in context

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 →