Let $R$ be a prime ring with center $Z$ and $f\ne 0$ a right generalized $(\alpha,\beta)$-derivation of $R$. If $f(x)^n\in Z$ for all $x\in L$, a nonzero ideal of $R$, and for some fixed positive integer $n$, then $R$ is either commutative or is an order in a $4$-dimensional simple algebra.

Most papers written on the subject of the relationship between groups and near-rings are concerned with the structure of those near-rings which are associated in some way with particular groups. The theme of this paper is in the other direction: recapturing information about the group from the near-rings associated with it. So far most of the work has been concerned with one particular case: obtaining information about Inn G from I(G). We also will concern ourselves mainly with this situation, although we will provide a very general framework. In the next section we set up the background. The second section gives a view of the results we used as our starting point. Finally we present our contribution to date.

We construct retractions with positive lower Hausdorff norms and small Hausdorff norms in Banach spaces of real continuous functions which domains are not necessarily bounded or finite dimensional. Moreover, we give precise formulas for the lower Hausdorff norms and the Hausdorff norms of such maps.

Let $X$ be a reflexive Banach space of functions analytic on a bounded plane domain $G$ such that for every $\lambda$ in $G$ the functional of evaluation at $\lambda$ is bounded. Assume further that $X$ contains the constants and admits multiplication by the independent variable $z$, $M_{z}$, as a bounded operator. We give sufficient conditions for $M_{z}$ to be reflexive.

An $L(2,1)$-labelling of a graph $G$ is an assignment of non-negative integers to the vertices of $G$ such that vertices at distance at most two get different numbers and adjacent vertices get numbers which are at least two apart. The $L(2,1)$-labelling number of $G$, denoted by $\lambda(G)$, is the minimum range of labels over all such labellings. In this paper, we first discuss some necessary and sufficient conditions for unit interval graph $G$ to have $\lambda(G)=2\chi(G)-2$ and then characterize all unit interval graphs $G$ of order no more than $3\chi(G)-1$, where $\chi(G)$ is the chromatic number of $G$. Finally, we discuss some subgraphs of unit interval graphs $G$ on more than $2\chi(G)+1$ vertices with $\lambda(G) = 2\chi(G)$.

We show that in certain cases a $\Phi$-derivation on a Banach algebra with a nilpotent separating ideal leaves each primitive ideal invariant. We also obtain some sufficient conditions for the separating ideal of a $\Phi$-derivation to be nilpotent.

In this paper we introduce new sequence space $m(M,A,\phi ,p)$ defined by combining an Orlicz function and an infinite matrix. We study its different properties and obtain some inclusion relations involving the space $m(M,A,\phi ,p)$.

In this paper we introduce an iterative process to find a common element of the set of fixed points of a strict pseudo-contraction and the set of solutions of the variational inequality problem for a monotone and Lipschitz continuous mapping. The iterative process is based on the so-called modified extragradient method. We obtain a weak convergence theorem for two sequences generated by this process. Using this theorem, we also construct an iterative process to find a common element of the set of fixed points of a strict pseudo-contraction and the set of zeroes of a monotone and Lipschitz continuous mapping.

We study an initial boundary value problem for a heat equation with strong absorption. We first prove that the solution of this problem stays positive for any finite time and converges to the unique steady state for a large class of initial data. This gives an example in which the dead-core is developed in infinite time. Then some estimates of the dead-core rate(s) are derived. Finally, we provide the uniformly exponential rate of convergence of the solution to the unique steady state.

In this article we give sufficient conditions on kernels of singular integral operators on product spaces to be bounded on weighted $L^p$-spaces for $2\lt p \lt \infty$. Applications include the weighted norm inequalities of holomorphic functional calculi of elliptic operators on product spaces.

A module $M$ is called ECS if every ec-closed submodule of $M$ is a direct summand. It was shown that the ECS property lies strictly between CS and P-extending properties. We studied modules $M$ such that every homomorphism from an ec-closed submodule of $M$ to $M$ can be lifted to $M$. Although such modules share some of the properties of ECS-modules, it is shown that they form a substantially bigger class of modules.

We construct infinite-dimensional Banach spaces and infinitely generated Banach algebras of functions that, except for 0, satisfy some kind of special or pathological property. Three of these structures are: a Banach algebra of everywhere continuous bounded functions which are not Riemannintegrable ; a Banach space of Lebesgue-integrable functions that are not Riemann-integrable; an algebra of continuous unbounded functions defined on an arbitrary non-compact metric space.

Shih and Ho have proved a global convergent theorem for boolean network: if a map from $\{0,1\}^{n}$ to itself defines a boolean network has the conditions: (1) each column of the discrete Jacobian matrix of each element of $\{0,1\}^{n}$ is either a unit vector or a zero vector; (2) all the boolean eigenvalues of the discrete Jacobian matrix of this map evaluated at each element of $\{0,1\}^{n}$ are zero, then it has a unique fixed point and this boolean network is global convergent to the fixed point. The purpose of this paper is to give a global convergent theorem for XOR boolean network, it is a counterpart of the global convergent theorem for boolean network.

Let $(T_1,\dots,T_N)$ be a $N-$tuple of positive operators with respect a Markushevich basis which are defined on a Hausdorff topological vector space. In this work we extend the notion of weak local quasinilpotence to $N-$tuples of operators (not-necessarily commuting). Under the hypothesis of existence of positive vectors, joint weak locally quasinilpotent we will obtain the existence of common invariant subspaces.

In this paper, we prove a common fixed point theorem for weakly compatible mappings satisfying an implicit relation. Our theorem generalizes many fixed point theorems.

In this paper we consider the group $C^*$-algebras of some solvable Lie groups involving cyclic symmetries and obtain some results on their %algebraic structure, stable rank, and connected stable rank for $C^*$-algebras.

Given a graph $G=(V,E)$ and a set $T$ of non-negative integers containing $0$, a $T$-coloring of $G$ is an integer function $f$ of the vertices of $G$ such that $|f(u)-f(v)| \notin T$ whenever $uv \in E$. The edge-span of a $T$-coloring $f$ is the maximum value of $|f(u)-f(v)|$ over all edges $uv$, and the $T$-edge-span of a graph $G$ is the minimum value of the edge-span among all possible $T$-colorings of $G$. This paper discusses the $T$-edge span of the folded hypercube network of dimension $n$ for the $k$-multiple-of-$s$ set, $T=\{ 0$, $s$, $2s$, $\dots$, $ks\} \cup S$, where $s$ and $k \geq 1$ and $S \subseteq \{ s+1, s+2, \dots , ks-1 \}$.

In this paper, we consider the risk reserve process with claims. In order to have the non-ruin probability in finite time, we use the skeleton process studied by T.Mikosch. Furthermore, we find a general formula that derives the non-ruin probability for the model in which the claim inter-arrival time has an exponential distribution and the claim size has an exponential distribution with distinct rate.

In this paper, we study mixed boundary value problem for secondorder impulsive differential equations with a parameter. By using critical point theory, several new existence results are obtained. This is one of the first times that impulsive boundary value problems are studied by means of variational methods.