In this paper we present a method of obtaining finitely based linear representations of possibly infinitely based semigroups. Let R{x1, x2, . . . } be a free associative algebra over a commutative ring R with the countable set of free generators {x1, x2, . . . }. An endomorphism α of R{x1, x2, . . . } is called a semigroup endomorphism if x1α, x2α, . . . are monomials (i.e. finite products of x...

In this paper, we consider the probability density function (pdf) of a non-central χ distribution with odd number of degrees of freedom ν. This pdf is represented in the literature as an infinite sum. Consequently, we present three alternative expressions to this pdf. The first expression is in terms of a partial derivative of the hyperbolic cosine function. The second expression, on the other ...

Some, but not all, mutations at H-2 loci can alter, in either direction, histocompatible tumor resistance in the model system of P815-X2 mastocytoma (DBA/2 origin) transplanted into DBA/2J or (C57BL/6 X DBA/2J)F1 mice. This hybrid effect has been shown previously to depend on the immune system. We have examined eight mutants at H-2Kb (bm1, bm4, bm6, bm7, bm8, bm10, bm11, and bm16, two at H-2Db ...

The question of the correct formulation of one spatial problem of Darboux type for the wave equation has been investigated. The correct formulation of that problem in the Sobolev space has been proved for surfaces having a quite definite orientation on which are given the boundary value conditions of the problem of Darboux type. In the space of variables x1, x2, t we consider the wave equation ...

This case-control study aimed to investigate the role of -251 T>A (rs4073) and -781 C>T (rs2227306) polymorphisms in the interleukin-8 (IL-8) gene in the development of glioma in a Chinese population. One hundred and twenty-seven glioma patients and 284 healthy control subjects were recruited to this study between February 2013 and December 2014. The IL-8 -251 T>A (rs4073) and -781 C>T (rs22273...