in this paper we consider the group algebra $r(c_2times‎ ‎d_infty)$‎. ‎it is shown that $r(c_2times d_infty)$ can be‎ ‎represented by a $4times 4$ block circulant matrix‎. ‎it is also‎ ‎shown that $mathcal{u}(mathbb{z}_2(c_2times d_infty))$ is‎ ‎infinitely generated‎.

groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.

A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $ mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (...

In this paper we present an analytical solution for the eigenmodes and corresponding electric field of a composite system made nanorod in vicinity plasmonic semi-infinite metallic system. To be specific, choose Silver as material both metal. The is composed two sub-systems with different symmetries: rod has symmetry, while interface rectangular one. Using boundary integral method, proposed by E...

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 $xin r$.

In generalized semi-infinite programming the feasible set is known to be not closed in general. In this paper, under natural and generic assumptions, the closure of the feasible set is described in explicit terms.