A natural definition of the Markov property for multi-parameter random processes (random fields) is the following. Let {Xt, tEIR N} be a multiparameter process. For any set D in N. N, let a D denote the a-field generated by {Xt, tED}. The field {Xt, tEN. u} is said to be Markov (or Markov of degree 1 [6], or sharp Markov) if, for any bounded open set D with smooth boundary, oD and ape are condi...

We give a basic introduction to the properties of Gauss’ hypergeometric functions, with an emphasis on the determination of the monodromy group of the Gaussian hyperegeometric equation. Initially this document started as an informal introduction to Gauss’ hypergeometric functions for those who want to have a quick idea of some main facts on hypergeometric functions. It is the startig of a book ...

We study the thermodynamic properties associated with black hole horizon and cosmological horizon for the Gauss-Bonnet solution in de Sitter space. When the Gauss-Bonnet coefficient is positive, a locally stable small black hole appears in the case of spacetime dimension d = 5, the stable small black hole disappears and the Gauss-Bonnet black hole is always unstable quantum mechanically when d ...

In this paper multigrid technique is adapted for solving standing one-dimensional wave equation with radiation boundary conditions. Solver, consisting of wave cycle and ray cycle, uses Gauss-Seidel and Kaczmarz relaxation sweeps and is aimed to work efficiently for all error components.

We give a uniform short proof of the fact that the intersection of every non-central conjugacy class in a Chevalley group and a big Gauss cell is non-empty and that this intersection contains elements with any prescribed semisimple part. The interest in this property stems at least in part from its relation to Ore's and Thompson's conjectures in the theory of nite groups.