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vv

This entry links every published equation using this exact notation. Its meaning may change between equations.

Meanings in context

Used in 40 equations

⟨H⟩ℏc2 b⋅v=Mℏ b⋅v+⟨HNR⟩ℏc2 b⋅v.\frac{\langle H\rangle}{\hbar c^2}\,\mathbf b\cdot\mathbf v=\frac{M}{\hbar}\,\mathbf b\cdot\mathbf v+\frac{\langle H_{\rm NR}\rangle}{\hbar c^2}\,\mathbf b\cdot\mathbf v.

The Clock That Comes Back Wrong by Exactly Its Mass · Equation 59

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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mop=ℏc2 ∂Δϕ∂Δτ,mop[LG]=ℏ ∂Φ∂(b⋅v).m_{\rm op}=\frac{\hbar}{c^2}\,\frac{\partial\Delta\phi}{\partial\Delta\tau},\qquad m_{\rm op}[\mathcal L_{\rm G}]=\hbar\,\frac{\partial\Phi}{\partial(\mathbf b\cdot\mathbf v)}.

The Clock That Comes Back Wrong by Exactly Its Mass · Equation 70

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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⟨σv⟩3α  ∝  ΓαΓ Γrad  exp⁡ ⁣(−ERkBT)\langle \sigma v \rangle_{3\alpha} \;\propto\; \frac{\Gamma_\alpha}{\Gamma}\,\Gamma_{\mathrm{rad}}\; \exp\!\left(-\frac{E_R}{k_{B}T}\right)

The Resonance That Selected Carbon, and the Universes That Couldn't · Equation 1

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

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qA(v)≷qB(v),where the sign can flip as the operating-point vector v varies.q_A(v) \gtrless q_B(v), \quad \text{where the sign can flip as the operating-point vector } v \text{ varies}.

The Hardest Unsolved Problems in Frontier AI Model Comparisons · Equation 17

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

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