The application of homotopy analysis method to solve nonlinear differential equation governing Jeffery–Hamel flow

In this paper Jeffery–Hamel flow has been studied and its nonlinear ordinary differential equation has been solved through homotopy analysis method (HAM). The obtained solution in comparison with the numerical ones represents a remarkable accuracy. The results also indicate that HAM can provide us with a convenient way to control and adjust the convergence region.     

Neuromodulation by soy diets or equol: Anti-depressive &; anti-obesity-like influences,age- &; hormone-dependent effects

Background  

Soy-derived isoflavones potentially protect against obesity and depression. In five different studies we examined the influence of soy-containing diets or equol injections on depression, serotonin levels, body weight gain (BW) and white adipose tissue (WAT) deposition in female Long-Evans rats at various stages of life [rats were intact, ovariectomized or experienced natural ovarian failure (NOF)].     

Anisotropic solutions of the Einstein-Boltzmann equations. II. Some exact properties of the equations

A covariant harmonic analysis is used to determine exact properties of the Einstein-Boltzmann equations. In particular, it is shown that if there are a finite number of harmonic components, or if the first and second harmonic components are zero, then the solutions are kinematically very restricted in many circumstances. Implications for the understanding of the microscopic foundations of perfect fluids and of transport coefficients are discussed.     

Two comments and a problem for David Davies’ performance theory

This paper considers the view, recently put forward by David Davies in Art and Performance, that works of art should be identified with the generative performances that result in the object, rather than with the object. It attempts to disarm two of Davies arguments by, first, providing a criterion by which the contextualist can accommodate all and only the relevant generative properties as properties of the work, and, second, providing an alternative explanation for his modal intuitions. Finally, it draws attention to Davies’ difficulties in providing a clear criterion for the identity of the work of art.     

An exact anisotropic solution of the Einstein-Liouville equations

A family of exact solutions of the Einstein-Liouville equations are presented, in which the space-time geometry is that of ak=0 ork=+1 Robertson-Walker space-time but the particle distribution function is anisotropic (and can be inhomogeneous). In some of these solutions, the fluid average (barycentric) velocity is not the timelike eigenvector of the fluid stress tensor. Then a “fundamental observer” moving with the average (barycentric) velocity will not observe these universes to be isotropic.     

A study of some exact solutions to Einstein's field equations which yield separable Hamilton-Jacobi equations

Exact solutions to Einstein's field equations, which give rise to a Stäckel-separable Hamilton-Jacobi equation of the form $$,y,z)\left[ {X(x)\left( {\frac{{\partial S}}{{\partial x}}} \right)^2 - 2\left( {\frac{{\partial S}}{{\partial x}}} \right)\left( {\frac{{\partial S}}{{\partial t}}} \right) - 2\left( {\frac{{\partial S}}{{\partial y}}} \right)\left( {\frac{{\partial S}}{{\partial t}}} \right) + Z(z)\left( {\frac{{\partial S}}{{\partial z}}} \right)^2 - 2\left( {\frac{{\partial S}}{{\partial z}}} \right)\left( {\frac{{\partial S}}{{\partial t}}} \right) - F(x,y,z)\left( {\frac{{\partial S}}{{\partial t}}} \right)^2 } \right] = \lambda $$ are considered. It is shown that there are no solutions for whichD is a function ofx orz, orx andz. The exact solutions are of Petrov typeN and are plane polarized waves without rotation. Some of the solutions are given explicitly, up to two arbitary functions. For these solutions the Hamilton-Jacobi equation is reduced to an uncoupled set of first-order ordinary differential equations.