formulae expressing explicitly the coefficients of an expansion of double jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. extension to expansion of triple jacobi polynomials is given. the results for the special cases of double and triple ultraspher...

By means of the modified method test functions, we obtain sufficient conditions absence nontrivial solutions for some classes semilinear elliptic inequalities higher order and quasilinear containing nonhomogeneous terms (independent unknown function).

The aim of this paper is to provide general results for predicting progress in a physical mapping project by anchoring random clones, when clones and anchors are not homogeneously distributed along the genome. A complete physical map of the DNA of an organism consists of overlapping clones spanning the entire genome. Several schemes can be used to construct such a map, depending on the way that...

Meshless methods based on the local Petrov-Galerkin approach are proposed for solution of steady and transient heat conduction problem in a continuously nonhomogeneous anisotropic medium. Fundamental solution of the governing partial differential equations and the Heaviside step function are used as the test functions in the local weak form. It is leading to derive local boundary integral equat...

Abstract In this paper, we study the Cauchy problems for quasilinear hyperbolic inequalities with nonlocal singular source term and prove nonexistence of global weak solutions in homogeneous nonhomogeneous cases by test function method.

In this paper, we investigate the nonhomogeneous boundary value problem for steady Navier--Stokes equations in a helically symmetric spatial domain. When data is assumed to be helical invariant and satisfies compatibility condition, prove has at least one solution.