Sentence examples for formula to the first from inspiring English sources

Applying Itô's formula to the first equation of model (5) leads to begin{aligned} dbigl(ln(mu/Lambda E bigr) =&frac{alpha 1-p Lambda}{mu} frac{I}{E}- frac{alpha(1-p) I^{2}}{E}- alpha(1-p) I- biggl(beta+ gamma_{1}+mu+frac{1}{2}sigma_{1}^{2} biggr) &-sigma_{1},dB_{1}(t).

If the condition (alpha delta formula to the first equation of model (4) leads to begin{aligned} dln frac{1}{x}= biggl -varepsilon frac{1}{x}-omega y +delta +0.5 sigma^{2} y^{2} biggl -varepsilon,dB(t).

The application of gamma reduction formula to the second of the two gamma functions will reduce the integrand to f RW ( v ) = β α 2 K 1 2 πj ∫ L Γ 1 - 1 β + s ′ Λ k b - s ′ d s ′, (23).

(20) Hence, applying Itô's formula to the second equation of model (5) leads to d( ln I =frac{alpha pLambda}{mu}-gamma_{2}-mu- frac {1}{2}sigma_{2}^{2}+ frac{E}{I}- alpha p E- alpha 1-p) I-sigmalpha 1-p{2}(t).

Applying Itô's formula to the third equation of stochastic differential system (2), one has dln I t)= biggl[-d-frac{sigma^{2}S^{2}}{2}-a_{33}I+beta S biggr],dt+ sigma S,dB_{2}(t).

Hence, should there be some δ ≠ 0 such that U x s + a U s s − p U y s + δ U y = F x s + a F s s − p F y s + δ F y = 0. so that we may apply l'Hôspital's rule with respect to p in the following formula to obtain the first identity below.

To reduce this to a tractable form in Meijer G-function, apply gamma duplication formula to the arguments of first gamma function.

The heliostat consists of a number of grouped slave mirrors, which are able to move according to a proposed formula to eliminate the first order aberration.

The author proposes an experimental formula to obtain the third-order elastic constants of steels.

Aligned left, select cell AB1458 and enter the formula with quotes ="So if "&AE1457&" Spheroids are wanted, then adjust the series in the chart formula bar to the first "&AE1456*AE1457&" rows".

Apply the second Green formula to the subharmonic function (u t,Phi)) and v t,Phi)= biggl(frac{1}{t^{gamma-1}}-frac{t^{aleph ^{R^{chi}} biggr)varphi=psi(t) varphi in the domain (mathfrak{C}_{n}(Gamma;(r,R))).