Equation (1) is the equation of momentum balance. Equation (2) is the equation of continuity for incompressible fluids. In order to study the blending within the micromixer, the convection–diffusion equation will be used. It is delineate by the subsequent Eq. (3)8: $$\frac{\partial c}{...
. This is the only parameter in the theory, and input from experiment is needed to determine it. The results from the Belle experiment [21] provide this information. Then the BS equation of Eq. (1) is solved, and poles of the T
oradvected, along the fluid's velocity field. In fact, the velocity of a fluid carriesitselfalong just as it carries the dye. The first term on the right-hand side of Equation 1 represents
Taking the time derivative of (2.5) and replacing a¨/a by the right-hand side of (2.6) leads to the continuity equation ρ˙+3H(ρ+p)=0, (2.7) with H=a˙/a the Hubble parameter. Friedmann’s equations have two nice properties that follow by considering the linear combination of ...
Before doing so, let us remark that the right-hand side of the equation above is the simplest expression that reduces to the original \({\nu }_{mx}^{I}\)’s for vanishing sector Chern number while being still additive. Next, we impose the invariance under large gauge transformations to...
To test the hypotheses suggested in this study, we used a two-stage procedure of structural equation modeling (SEM) approach (Anderson & Gerbing, 1988) using Mplus program. The following criteria was adopted to evaluate the model fit: root mean square error of approximation (RMSEA) < .08;...
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by expanding both sides of the equation. Multiplying \((s^2-2p_0s+|p|^2)^{-1}\) from the left, \((p^2-2s_0p+|s|^2)^{-1}\) from the right and plugging it into (102), gives $$\begin{aligned}{} & {} \int _{\partial (S_\varphi \cap {\mathbb {C}}_J)}g(s)...
Physics has up to now missed to express in mathematical terms the fundamental idea of events of a path in time and space uniquely succeeding one another. A
Thus,by a theorem of Lebesgue,a=u a.e.in B1.We now take u≡a,after changing the values of u on a zero measure set.Letsatisfy,for some positive integer k,By(2.5),we have,for some dimensional constant C, Switching the roles ofandleads to ...