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.

1709 equations across 1439 symbols.

Cox′  =  2πεoxln⁡ ⁣(ro/ri)C'_{\text{ox}} \;=\; \frac{2\pi\varepsilon_{\text{ox}}}{\ln\!\left(r_{\text{o}}/r_{\text{i}}\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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τ=Kp(qd−q)+Kd(q˙d−q˙)+τff\tau = K_p (q_d - q) + K_d (\dot{q}_d - \dot{q}) + \tau_{ff}

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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φent=φLL+φRR−φLR−φRL\varphi_{\text{ent}} = \varphi_{LL} + \varphi_{RR} - \varphi_{LR} - \varphi_{RL}

1 published occurrence

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This alternating sum isolates the branch-phase difference that local phase choices cannot remove. In the ideal balanced state, it controls whether the two path qubits are entangled.

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E[tokens per round]=1−αγ+11−α\mathbb{E}[\text{tokens per round}] = \frac{1-\alpha^{\gamma+1}}{1-\alpha}

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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I=FLOPs performedbytes read and writtenI = \frac{\text{FLOPs performed}}{\text{bytes read and written}}

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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hv(k+1)=ϕ(hv(k),⨁u∈N(v)ψ(hv(k),hu(k),euv))h_v^{(k+1)} = \phi\left(h_v^{(k)}, \bigoplus_{u \in \mathcal{N}(v)} \psi\left(h_v^{(k)}, h_u^{(k)}, e_{uv}\right)\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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xt=αˉt x0+1−αˉt ϵ,x^0=fθ(xt,t)x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \hat{x}_0 = f_\theta(x_t, 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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Leff=LSM+∑iciΛ2 Oi\mathcal{L}_{\text{eff}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}}\,\mathcal{O}_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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