LaTeX Search - Latex Code: "\epsilon" AND "2\pi"

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Exact Results (28)

Exact Results are those equations that conform exactly to the given search string.

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3 results	Delamination of thin bonded cement-based overlays: analytical analysis Materials and Structures (2010):1-9, April 23, 2010
EXACT	$\epsilon ={\frac{1}{ 2\pi }}\ln{\frac{1-\beta}{1+\beta}}$ View Latex Code \epsilon ={\frac{1}{ 2\pi }}\ln{\frac{1-\beta}{1+\beta}}

EXACT	$\sigma_{22}+i\sigma_{12}={\frac{K} {\sqrt{ 2\pi r}}}\;r^{i \epsilon }$ View Latex Code \sigma_{22}+i\sigma_{12}={\frac{K} {\sqrt{ 2\pi r}}}\;r^{i \epsilon }

EXACT	$\sigma_{22}=Re\left({\frac{K}{\sqrt{ 2\pi r}}}\,r^{i \epsilon }\right)$ View Latex Code \sigma_{22}=Re\left({\frac{K}{\sqrt{ 2\pi r}}}\,r^{i \epsilon }\right)

1 result	Transient dynamics in altered disturbance regimes: recovery may start quickly, then slow Theoretical Ecology (2009) 2:79-87, April 23, 2009
EXACT	$\epsilon (x,t) \propto \sin( 2\pi t/32) \left[\sin( 2\pi x/32) + \sin( 2\pi x/16)\right]$ View Latex Code $ \epsilon (x,t) \propto \sin( 2\pi t/32) \left[\sin( 2\pi x/32) + \sin( 2\pi x/16)\right]$

2 results	Dimensional Effects on Densities of States and Interactions in Nanostructures Nanoscale Research Letters (2010):1-9, July 02, 2010
EXACT	$\Upphi(r)={\frac{q}{4\pi \epsilon _\ast r}}+{\frac{q} { 2\pi \epsilon _\ast}} \sum_{n=1}^\infty\left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^{n} {\frac{1}{\sqrt{r^2+n^2L^2}}}.$ View Latex Code \Upphi(r)={\frac{q}{4\pi \epsilon _\ast r}}+{\frac{q} { 2\pi \epsilon _\ast}} \sum_{n=1}^\infty\left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^{n} {\frac{1}{\sqrt{r^2+n^2L^2}}}.

EXACT	$\begin{aligned} q_n&=\left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^n q,\quad Q_n={\frac{2 \epsilon } { \epsilon _\ast+ \epsilon }} \left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^n q,\\ \|z\|\le L/2:\quad \Upphi=&{\frac{q} {4\pi \epsilon _\ast}} \sum_{n=-\infty}^\infty \left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^{\|n\|} {\frac{1} {\sqrt{r^2+(z-nL)^2}}},\\ z>L/2:\quad \Upphi=&{\frac{q}{ 2\pi ( \epsilon _\ast+ \epsilon )}} \sum_{n=0}^\infty\left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^n {\frac{1}{\sqrt{r^2+(z+nL)^2}}}. \end{aligned}$ View Latex Code \begin{aligned} q_n&=\left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^n q,\quad Q_n={\frac{2 \epsilon } { \epsilon _\ast+ \epsilon }} \left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^n q,\\ \|z\|\le L/2:\quad \Upphi=&{\frac{q} {4\pi \epsilon _\ast}} \sum_{n=-\infty}^\infty \left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^{\|n\|} {\frac{1} {\sqrt{r^2+(z-nL)^2}}},\\ z>L/2:\quad \Upphi=&{\frac{q}{ 2\pi ( \epsilon _\ast+ \epsilon )}} \sum_{n=0}^\infty\left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^n {\frac{1}{\sqrt{r^2+(z+nL)^2}}}. \end{aligned}

1 result	Multiple-path Quantum Interference Effects in a Double-Aharonov-Bohm Interferometer Nanoscale Research Letters (2010):1228-1235, July 01, 2010
EXACT	$\Upgamma_{j}^{\alpha}=\sum_{k}\|V_{\alpha j }\|^{2} 2 \pi \delta( \epsilon - \epsilon _{\alpha k }$ View Latex Code \Upgamma_{j}^{\alpha}=\sum_{k}\|V_{\alpha j }\|^{2} 2 \pi \delta( \epsilon - \epsilon _{\alpha k }

1 result	Modeling Electrolytically Top-Gated Graphene Nanoscale Research Letters (2010):505-511, March 01, 2010
EXACT	$N_0={\frac{\pi}{2}}n_0^2\lambda_{\rm B}={\frac{2e^2}{\pi \epsilon \beta^3(\hbar v_{\rm F})^4}},$ View Latex Code N_0={\frac{\pi}{2}}n_0^2\lambda_{\rm B}={\frac{2e^2}{\pi \epsilon \beta^3(\hbar v_{\rm F})^4}},

2 results	A Model System for Dimensional Competition in Nanostructures: A Quantum Wire on a Surface Nanoscale Research Letters (2008) 3:140-144, May 02, 2008
EXACT	$\begin{aligned} &\left(1+\frac{m}{\mu}\frac{k_x^2} { 2\pi }\int\frac{{\hbox{d}}\kappa}{\kappa^2+k_x^2-(2mE/\hbar^2)-\hbox{i} \epsilon } \right)f(E,k_x,k_y^{\prime})\\ &=-\frac{m}{\mu}\frac{k_x^2}{ 2\pi }\frac{{\hbox{exp}}({\hbox{i}}k^{\prime}_yy_0)}{k^{\prime}_y+k_x^2-(2mE/\hbar^2)-{\hbox{i}} \epsilon }. \end{aligned}$ View Latex Code \begin{aligned} &\left(1+\frac{m}{\mu}\frac{k_x^2} { 2\pi }\int\frac{{\hbox{d}}\kappa}{\kappa^2+k_x^2-(2mE/\hbar^2)-\hbox{i} \epsilon } \right)f(E,k_x,k_y^{\prime})\\ &=-\frac{m}{\mu}\frac{k_x^2}{ 2\pi }\frac{{\hbox{exp}}({\hbox{i}}k^{\prime}_yy_0)}{k^{\prime}_y+k_x^2-(2mE/\hbar^2)-{\hbox{i}} \epsilon }. \end{aligned}

EXACT	$\begin{aligned} &\left[1+\frac{m\hbar}{2\mu}k_x^2\left(\frac{\Uptheta(\hbar^2k_x^2-2mE)}{\sqrt{\hbar^2k_x^2-2mE}}+\hbox{i}\frac {\Uptheta(2mE-\hbar^2k_x^2)}{\sqrt{2mE-\hbar^2k_x^2}} \right)\right]f(E,k_x,k_y^{\prime})\\ &=-\frac{m}{\mu}\frac{k_x^2}{ 2\pi } \frac{{\hbox{exp}}({\hbox{i}}k^{\prime}_yy_0)}{ k^{\prime2}_y+k_x^2-(2mE/\hbar^2)-\hbox{i} \epsilon }. \end{aligned}$ View Latex Code \begin{aligned} &\left[1+\frac{m\hbar}{2\mu}k_x^2\left(\frac{\Uptheta(\hbar^2k_x^2-2mE)}{\sqrt{\hbar^2k_x^2-2mE}}+\hbox{i}\frac {\Uptheta(2mE-\hbar^2k_x^2)}{\sqrt{2mE-\hbar^2k_x^2}} \right)\right]f(E,k_x,k_y^{\prime})\\ &=-\frac{m}{\mu}\frac{k_x^2}{ 2\pi } \frac{{\hbox{exp}}({\hbox{i}}k^{\prime}_yy_0)}{ k^{\prime2}_y+k_x^2-(2mE/\hbar^2)-\hbox{i} \epsilon }. \end{aligned}

1 result	Microwave applicator for hyperthermia treatment on in vivo melanoma model Medical & Biological Engineering & Computing (2010):285-292, February 10, 2010
EXACT	$f_{\rm r}=\frac{k_{1}c}{ 2\pi \sqrt{ \epsilon _{\rm r}}}$ View Latex Code f_{\rm r}=\frac{k_{1}c}{ 2\pi \sqrt{ \epsilon _{\rm r}}}

1 result	Comparison of Non-Newtonian Constitutive Laws in Hydrodynamic Lubrication Tribology Letters (2010):1-9, March 24, 2010
EXACT	$F_{ \epsilon }=R L \int\limits_{0}^{ 2\pi } p \cos(\theta) {\text{d}}\theta,\quad F_{\phi}=R L \int\limits_{0}^{ 2\pi } p \sin(\theta) {\text{d}}\theta.$ View Latex Code F_{ \epsilon }=R L \int\limits_{0}^{ 2\pi } p \cos(\theta) {\text{d}}\theta,\quad F_{\phi}=R L \int\limits_{0}^{ 2\pi } p \sin(\theta) {\text{d}}\theta.

1 result	Extended MHD Modelling with the Ten-Moment Equations Journal of Fusion Energy (2008) 27:36-43, February 04, 2008
EXACT	$\Uplambda_{ab}=12\pi \epsilon _0 (m_aT_b + m_bT_a)/(m_a+m_b)\lambda_D$ View Latex Code \Uplambda_{ab}=12\pi \epsilon _0 (m_aT_b + m_bT_a)/(m_a+m_b)\lambda_D

1 result	Electron transport in GaN(ZB) and AlN(WZ) Journal of Materials Science (2007) 42:396-400, January 17, 2007
EXACT	$\tau _{\rm imp}(t)\simeq \frac{128\sqrt{ 2\pi m_{\rm e}^{\ast }}(k_{\rm B}T_{\rm e}^{\ast }(t))^{3/2}}{{\mathcal N}_{\rm I}({\mathcal Z}e^{2}/ \epsilon _{0})^{2}G(t)},$ View Latex Code \tau _{\rm imp}(t)\simeq \frac{128\sqrt{ 2\pi m_{\rm e}^{\ast }}(k_{\rm B}T_{\rm e}^{\ast }(t))^{3/2}}{{\mathcal N}_{\rm I}({\mathcal Z}e^{2}/ \epsilon _{0})^{2}G(t)},

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