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...verline{\Phi}_{10}\,,\Phi_{02}=\overline{\Phi}_{20}\,,\Phi_{12}=\overline{\Phi}_{21}\}</math> and the NP curvature scalar <math>\Lambda</math>. Physically ...ab}m^a n^b\,, \quad\; \Phi_{21}:=\frac{1}{2}R_{ab}\bar{m}^a n^b=\overline{\Phi}_{12}\,.</math> ...

\varepsilon_{\alpha\beta} & = \frac{1}{2}(u^0_{\alpha,\beta}+u^0_{\beta,\alpha}) - \frac{x_3}{2}~(\varphi_{\alpha,\beta}+\varphi_{\beta,\alpha}) \\ ...

...he right, the difference between the unlensed angular position <math>\vec{\beta}</math> and the observed position <math>\vec{\theta}</math> is this deflect :<math>\vec{\beta}=\vec{\theta}-\vec{\alpha}(\vec{\theta}) = \vec{\theta} - \frac{D_{ds}}{D_s ...

...th> [[scale parameter|scale]] (positive, [[real number|real]])<br/><math> \beta \,</math> [[shape parameter|shape]] (positive, [[real number|real]])| pdf =<math>\frac{\beta}{2\alpha\Gamma(1/\beta)} \; ...

.../math> is the [[differential form|two-form]] [[Kalb–Ramond field]], <math>\phi</math> is the [[dilaton]], and <math>A_\mu^a</math> is a Yang–Mills gauge f ...^\mu C)_{\alpha \beta}P_\mu + (P\gamma^{\mu\nu\rho\sigma\delta}C)_{\alpha \beta}Z_{\mu\nu\rho\sigma \delta}. ...

...mbda = \lambda^++\lambda^-</math>. Lastly, there a [[scalar field]] <math>\phi</math>. ...=1</math> multiplet <math>(g_{\mu\nu}, B_{\mu\nu}, \psi^+_\mu, \lambda^-, \phi)</math>, along with four additional fields <math>(C_{\mu\nu\rho}, C_\mu, \p ...

...pha \rangle = \frac{(\beta, \alpha)}{(\alpha, \alpha)} \, \forall \alpha, \beta \in E. </math> ...lity]]: A Lie algebra <math>\mathfrak{g}</math> is solvable [[iff]] <math>\kappa( \mathfrak{g}, [\mathfrak{g},\mathfrak{g}] ) = 0</math>.}} ...

<math display = "block">\eta = a \exp\left[\frac{1}{2} \varepsilon \beta k C_w \left(\frac{U}{C_w}\right)^2 t \right] \exp[i(kx - \omega t)]</math> where <math>\varepsilon = (\rho_a / \rho_w)</math>, <math>\beta</math> is the scale parameter, <math>C_w</math> is the phase speed of free ...

...\frac{\sin \alpha}{\sin \beta} < \frac\alpha\beta < \frac{\tan\alpha}{\tan\beta}.</math> \beta & \mathrm{beta} & 2 & \kappa & \mathrm{kappa} & 20 & \sigma & \mathrm{sigma} & 200 \\ ...

:<math>g_{ab}=-g_{tt}dt^2+g_{rr}dr^2+g_{\theta\theta}d\theta^2+g_{\phi\phi}d\phi^2\,,</math> ...heta=\sqrt{g_{\theta\theta}}d\theta\,,\;\;\omega_\phi=\sqrt{g_{\phi\phi}}d\phi\,,</math> ...

...e pV cell, rather than electric power. The energy efficiency (<math>\eta_{\phi}</math>) is quantified by the ratio of the band gap and optical phonon ener \eta_{\phi}=\Delta E_{e,g}/E_{p,\mathrm{O}}. ...

...1 e^ {2 {\xi} {\theta} } } {1+ {\epsilon e^{\frac {3}{2}\xi \theta}} cos {\phi} } </math>, where <math> \epsilon </math> is orbital eccentricity, and <math> \phi </math> is radial phase angle that is related to the revolving angle <math> ...

...bf{r},\mathbf{s}) + \frac{\sigma}{4\pi}\int_{4\pi}I(\mathbf{r},\mathbf{s})\Phi (\mathbf{s},\mathbf{s'})d\Omega '</math> <math>\sum_{j=1}^n w_j I(\mathbf{r},\mathbf{s_j})\Phi (\mathbf{s_j},\mathbf{s_i})</math> ...

:<math>Z = \sum_i e^{-\beta E_i},</math> where the sum runs over all possible [[microstate]]s, and <math>\beta =1/(k_B T)</math> is the inverse temperature, <math>k_B</math> is the [[Bol ...

...&dq=florence+eliza+allen+%22florence+eliza+allen%22&pg=PA3 |title=Phi Beta Kappa: Alpha of Wisconsin; Catalogue |date=1917 |publisher=University of Wisconsi [[Category:Phi Beta Kappa]] ...

N_{\alpha\beta,\alpha} = 0 M_{\alpha\beta,\alpha\beta} - q = 0 ...

# <math> \frac{D_g u_g}{Dt} - f_{0}v_a - \beta y v_g = 0 </math> (x component of quasi-geostrophic momentum equation) # <math> \frac{D_g v_g}{Dt} + f_{0}u_a + \beta y u_g = 0 </math> (y component of quasi-geostrophic momentum equation) ...

...\left( 1-\frac{2M}{r} \right)^{-1}dr^2+r^2 \left(d\theta^2+\sin^2\theta\,d\phi^2\right).</math>|{{EquationRef|1}}}} ...1-\frac{2M}{r} \right) du^2- 2du dr + r^2\left(d\theta^2 + \sin^2\theta\,d\phi^2\right);</math>|{{EquationRef|3}}}} ...

| <math>\displaystyle u_{tt}-u_{xx}-2 \alpha (u u_x)_{x}-\beta u_{xxtt}=0</math> |<math>u_t + 2\kappa u_x - u_{xxt} + 3 u u_x = 2 u_x u_{xx} + u u_{xxx}\,</math> ...

<math display="block">S[g]= \int {1 \over 2\kappa} R \sqrt{-g} \, \mathrm{d}^4x </math> <math display="block">S[g]= \int {1 \over 2\kappa} f(R) \sqrt{-g} \, \mathrm{d}^4x </math> ...