# SEARCH CONTENT

## You are looking at 1 - 10 of 4,082 items :

• Differential Equations and Dynamical Systems
• General Mathematics
Clear All

## Abstract

Let G be a group with identity e, R be a G-graded commutative ring with a nonzero unity 1 and M be a G-graded R-module. In this article, we introduce and study the concept of almost graded multiplication modules as a generalization of graded multiplication modules; a graded R-module M is said to be almost graded multiplication if whenever $a∈h(R)$ satisfies $AnnR(aM)=AnnR(M)$, then $(0:Ma)={0}$. Also, we introduce and study the concept of almost graded comultiplication modules as a generalization of graded comultiplication modules; a graded R-module M is said to be almost graded comultiplication if whenever $a∈h(R)$ satisfies $AnnR(aM)=AnnR(M)$, then $aM=M$. We investigate several properties of these classes of graded modules.

## Abstract

In this paper, the notion of an operator $γ$ on a supra topological space $(X,μ)$ is studied and then utilized to analyze supra $γ$-open sets. The notions of $μγ$-g.closed sets on the subspace are introduced and investigated. Furthermore, some new $μγ$-separation axioms are formulated and the relationships between them are shown. Moreover, some characterizations of the new functions via operator $γ$ on $μ$ are presented and investigated. Finally, we give some properties of $S(γ,β)$-closed graph and strongly $S(γ,β)$-closed graph.

## Abstract

In this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.

## Abstract

Properties of linear regression of order statistics and their functions are usually utilized for the characterization of distributions. In this paper, based on such statistics, the concept of Pearson covariance and the pseudo-covariance measure of dependence is used to characterize the exponential, Pearson and Pareto distributions.

## Abstract

In this work, we study Hasimoto surfaces for the second and third classes of curve evolution corresponding to a Frenet frame in Minkowski 3-space. Later, we derive two formulas for the differentials of the second and third Hasimoto-like transformations associated with the repulsive-type nonlinear Schrödinger equation.

## Abstract

Given Hilbert space operators $T,S∈B(ℋ)$, let $Δ$ and $δ∈B(B(ℋ))$ denote the elementary operators $ΔT,S(X)=(LTRS−I)(X)=TXS−X$ and $δT,S(X)=(LT−RS)(X)=TX−XS$. Let $d=Δ$ or $δ$. Assuming T commutes with $S∗$, and choosing X to be the positive operator $S∗nSn$ for some positive integer n, this paper exploits properties of elementary operators to study the structure of n-quasi $[m,d]$-operators $dT,Sm(X)=0$ to bring together, and improve upon, extant results for a number of classes of operators, such as n-quasi left m-invertible operators, n-quasi m-isometric operators, n-quasi m-self-adjoint operators and n-quasi $(m,C)$ symmetric operators (for some conjugation C of $ℋ$). It is proved that $Sn$ is the perturbation by a nilpotent of the direct sum of an operator $S1n=S|Sn(ℋ)¯n$ satisfying $dT1,S1m(I1)=0$, $T1=TSn(ℋ)¯$, with the 0 operator; if S is also left invertible, then $Sn$ is similar to an operator B such that $dB∗,Bm(I)=0$. For power bounded S and T such that $ST∗−T∗S=0$ and $ΔT,S(S∗nSn)=0$, S is polaroid (i.e., isolated points of the spectrum are poles). The product property, and the perturbation by a commuting nilpotent property, of operators $T,S$ satisfying $dT,Sm(I)=0$, given certain commutativity properties, transfers to operators satisfying $S∗ndT,Sm(I)Sn=0$.

## Abstract

In this paper, we study the Hyers-Ulam stability of a nonautonomous semilinear reaction-diffusion equation. More precisely, we consider a nonautonomous parabolic equation with a diffusion given by the fractional Laplacian. We see that such a stability is a consequence of a Gronwall-type inequality.

## Abstract

The combined systems of integral equations have become of great importance in various fields of sciences such as electromagnetic and nuclear physics. New classes of the merged type of Urysohn Volterra-Chandrasekhar quadratic integral equations are proposed in this paper. This proposed system involves fractional Urysohn Volterra kernels and also Chandrasekhar kernels. The solvability of a coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type is studied. To realize the existence of a solution of those mixed systems, we use the Perov’s fixed point combined with the Leray-Schauder fixed point approach in generalized Banach algebra spaces.

## Abstract

This paper is concerned with a system governed by nonsingular delay differential equations. We study the β-Ulam-type stability of the mentioned system. The investigations are carried out over compact and unbounded intervals. Before proceeding to the main results, we convert the system into an equivalent integral equation and then establish an existence theorem for the addressed system. To justify the application of the reported results, an example along with graphical representation is illustrated at the end of the paper.