in this paper, the ritz-galerkin method in bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (mhd) flow of third grade fluid between the two plates. the properties of the bernstein  polynomials together with the ritz-galerkin method are used to reduce the solution of the mhd couette flow of non-newtonian fluid in a porous medium to the solution o...

If V is a nonsingular real algebraic set we say Ht(V;Z2) * s algebraic if it is generated by nonsingular algebraic subsets of V. Let V be a 3-dimensional nonsingular real algebraic set. Then, we prove that any immersed surface in V can be isotoped to an algebraic subset if and only if Ht (V: Z 2 ) / = 1,2 are algebraic. This isotopy above carries the natural stratification of the immersed surfa...

1. INTRODUCTION. There is something fascinating about procedures for solving low degree polynomial equations. On one hand, we all know that while general solutions (using radicals) are impossible beyond the fourth degree, they have been found for quadratics, cubics, and quartics. On the other hand, the standard solutions for the the cubic and quartic are complicated, and the methods seem ad hoc...

A new approach for investigating polynomial solutions of differential equations is proposed. It is based on elementary linear algebra. Any differential operator of the form L(y) = k=N ∑ k=0 ak(x)y, where ak is a polynomial of degree ≤ k, over an infinite ground field F has all eigenvalues in F in the space of polynomials of degree at most n, for all n. If these eigenvalues are distinct, then th...