let $r$ be an infinite ring. here we prove that if $0_r$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin x}$ for every infinite subset $x$ of $r$, then $r$ satisfies the polynomial identity $x^n=0$. also we prove that if $0_r$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in x}$ for every infinite subset $x$ of $r$, then $x^n=x$ for all $xin r$.

Generalizations of the series exp and log to noncommutative nonassociative and other types of algebras were regarded by M. Lazard, and recently by V. Drensky and L. Gerritzen. There is a unique power series exp(x) in one non-associative variable x such that exp(x) exp(x) = exp(2x), exp(0) = 1. We call the unique series H = H(x, y) in two non-associative variables satisfying exp(H) = exp(x) exp(...

In this study we describe parallel iterative and direct solution strategies for viscous flow computation using domain decomposition. Both stream function vorticity and primitive variable formulations are considered. The basic ideas associated with the element-by-element approach and subdomain approach can also be extended to other cell or control-volume approximate formulations. Numerical resul...

In this paper, we investigate a nonlinear partial differential equation, arising from a model of cellular proliferation. This model describes the production of blood cells in the bone marrow. It is represented by a partial differential equation with a retardation of the maturation variable and a distributed temporal delay. Our aim is to prove that the behaviour of primitive cells influences the...

We propose an extension to the pixel pipeline of current programmable rasterization hardware to include the possibility to freely locate the rasterization position of fragments and pixels. The corresponding new primitive name is Vragment (variable fragment). We show how this new functionality could lead to new and wider classes of algorithms in computer graphics, especially in image processing,...

one of the most important characteristics of the eternal religion is the adaptation of its decrees with the changes of the human’s life in the transition of time. so, it is necessary for us to review the second decrees as the flexible dimensions of the decrees. according to the causes of some decrees’ change, altering the decree’s subject leads to the change of the primitive decrees into the se...