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 $xin r$.

this paper uses the l1−norm and the concept of the non-dominated vector, topropose a method to find a well-dispersed subset of non-dominated (wdsnd) vectorsof a multi-objective mixed integer linear programming (momilp) problem.the proposed method generalizes the proposed approach by tohidi and razavyan[tohidi g., s. razavyan (2014), determining a well-dispersed subset of non-dominatedvectors of...

We study the following question: for given d ⩾ 2 , n and k ⩽ what is largest value c ( ) such that from any set of unit vectors in R we may select with corresponding signs ±1 so their signed sum has norm at least ? The problem dual to classical vector minimization balancing questions, which have been studied over a century. give asymptotically sharp estimates general case. In several special ca...

We study finite groups G having a normal subgroup H and \(D \subset \setminus H, D \cap D^{-1}=\emptyset ,\) such that the multiset \(\{ xy^{-1}:x,y \in D\}\) has every non-identity element occur same number of times (such is called DRAD difference set). show there are no order \(4p^2\), where p an odd prime.

Let be a domain, or more generally, Lipschitz domain with small local constant. In this paper it is shown that if u function harmonic in and continuous , which vanishes relatively open subset ; moreover, the normal derivative of positive surface measure; then identically zero. © 2021 The Authors. Communications on Pure Applied Mathematics published by Wiley Periodicals LLC.

INTRODUCTION To investigate the relationship between CD4(+)CD25(+)CD127(dim) regulatory T cells (Tregs) and immune imbalance in acquired severe aplastic anemia (SAA). METHODS The quantity of CD4(+)CD25(+)CD127(dim) Tregs in 44 SAA patients and 23 normal controls were measured by flow cytometry. Correlations between Tregs and T cell subsets, dendritic cell (DC) subsets, granulocyte counts and ...

BACKGROUND Lymphocyte subsets enumeration is considered prominent in the management of primary and acquired immunodeficiency disorders. Because of local variations due to race, age, gender, and environmental conditions on lymphocyte subsets, and to improve the accuracy of interpretation of laboratory findings, reference intervals must be determined in every population. OBJECTIVE To establish ...