Let k be a perfect field of virtual cohomological dimension ≤ 2. Let G be a connected linear algebraic group over k such that Gsc satisfies a Hasse principle over k. Let X be a principal homogeneous space under G over k. We show that if X admits a zero cycle of degree one, then X has a k-rational point. Introduction The following question of Serre [10, p. 192] is open in general. Q: Let k be a ...

a complete linear theory in four dimensional space-time is constructed for propagation and coupling of electromagnetic waves in the most general case, i.e. media where all three space directions are in homogeneous and where temporal changes, anisotropy and absorbtion are also included. the only condition is that the properties of the medium should be slowly varying, although it is assumed that ...

This paper concerned with the dispersion of Love wave in a fiber-reinforced medium lying over a heterogeneous half-space. The heterogeneity is caused by the consideration of quadratic variation in density and directional rigidity of lower half-space. The irregularity has been considered in the form of rectangle at the interface of the fiber-reinforced layer and heterogeneous half-space. The dis...

This paper deals with Markovian models which are deened on a nite-dimensional discrete state space, and possess a stationary state distribution of a product-form. We view the space of such models as a mathematical object, and explore its structure. We focus on models on an orthant Z n + , which are homogeneous within subsets of Z n + called walls, and permit only state transitions whose k k 1-l...

Many problems, not only in computer vision and visualization, lead to a system of linear equations or and fast and robust solution is required. A vast majority of computational problems in computer vision, visualization and computer graphics are three dimensional in principle. This paper presents equivalence of the cross–product operation and solution of a system of linear equations or using pr...