In this paper, we compute the number of distinct centralizers some classes finite rings. We then characterize all rings with $n$ for any positive integer $n \le 5$. Further give connections between a ring and its commutativity degree.

in recent years, the number of research works devoted to applying the highly accurate numerical schemes, in particular compact finite difference schemes, to numerical simulation of complex flow fields with multi-scale structures, is increasing. the use of compact finite-difference schemes are the simple and powerful ways to reach the objectives of high accuracy and low computational cost. compa...

Let $H$, $L$ and $X$ be subgroups of a finite group$G$. Then $H$ is said to be $X$-permutable with $L$ if for some$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is emph{$X$-quasipermutable } (emph{$X_{S}$-quasipermutable}, respectively) in $G$ provided $G$ has a subgroup$B$ such that $G=N_{G}(H)B$ and $H$ $X$-permutes with $B$ and with all subgroups (with all Sylowsubgroups, respectively) $...

In this paper, without using the classification of finite simple groups, we determine the structure of  finite simple groups whose Sylow 3-subgroups are of the order 9. More precisely, we classify finite simple groups whose Sylow 3-subgroups are elementary abelian of order 9.

in this study, focuses on applying the hp-version for forward modeling. the eit forward solver is normally based on the conventional finite element method (hfem). in h-fem, the polynomial order p of the element shape functions is constant and the element size h, is decreased. to accurately simulate the forward solution with the hfem, a mesh with large number of nodes and elements is usually need...

We discuss intrinsic aspects of Krupka’s approach to finite–order variational sequences. We give intrinsic isomorphisms of the quotient subsheaves of the short finite– order variational sequence with sheaves of forms on jet spaces of suitable order, obtaining a new finite–order (short exact) variational sequence which is made by sheaves of polynomial differential operators. Moreover, we present...

We show that two families of germs of real-analytic subsets in Cn are formally equivalent if and only if they are equivalent of any finite order. We further apply the same technique to obtain analogous statements for equivalences of real-analytic self-maps and vector fields under conjugations. On the other hand, we provide an example of two sets of germs of smooth curves that are equivalent of ...

Duality and chirality are examples of operations of order 2 on hypermaps. James showed that the groups of all operations on hypermaps and on oriented hypermaps can be identified with the outer automorphism groups Out∆ ∼= PGL2(Z) and Out∆ ∼= GL2(Z) of the groups ∆ = C2 ∗ C2 ∗ C2 and ∆ + = F2. We will consider the elements of finite order in these two groups, and the operations they induce. MSC c...