The aim of this article is to extend the applicability of a multi-point iterative method for solving equations involving Banach space valued operators. The method uses evaluations of : two vector values, two linear operators, one inverse of a linear operator and one frozen inverse of a linear operator per iteration. The ball convergence was established in earlier works on the m-dimensional space and requiring very high order derivatives. We only use hypotheses on the first derivative. Hence, we extend the applicability of this method. Moreover, estimations are given on a radius of convergence and the error distances based on generalized Lipschitz conditions not given before. Numerical examples are used to complete this article.

We introduce Rokhlin properties for certain discrete group actions on $C^*$- correspondences as well as on Hilbert bimodules and analyze them. It turns out that the group actions on any $C^*$- correspondence $E$ with Rokhlin property induces group actions on the associated $C^*$-algebra $\m O_E$ with Rokhlin property and the group actions on any Hilbert bimodule with Rokhlin property induces group actions on the linking algebra with Rokhlin property. Permanence properties of several notions such as the nuclear dimension and the $\m D$-absorbing property with respect to the crossed product of Hilbert $C^*$-modules with groups, where group actions have Rokhlin property, are studied.

A well known generalization of the extending concept is projection invariant-extending property. In this trend, a module is called $\pi$-extending if every projection invariant submodule is essential in a direct summand of the module. Based on an annihilator condition, dominant submodules are introduced in the literature. In this paper, we introduce and investigate projection invariant-extending property on dominant submodules of a module.

The object of the present paper is to study a three dimensional normal almost contact metric manifold. First we study three dimensional normal almost contact metric manifolds with $Q\phi =\phi Q$ and prove some equivalent conditions. Beside this locally $\phi $-Ricci symmetry is studied here. Among others we prove that the $\xi $-sectional curvature of this manifold is constant. All the above results are verified by non-trivial examples. Finally we study isometric immersion of a three dimensional normal almost contact metric manifold in a four dimensional Riemannian manifold of constant curvature $1.$

Quantum mechanics is known as matrix mechanics, in contrast with an alternative alias, wave mechanics. In this article, we briefly review the historic motivation of introducing matrix mechanics in physics and demonstrate more mathematically that matrix mechanics requires Hermitian operators on and state-vectors in Hilbert space, as a physical variables and quantum states. Implication of non-Hermiticity of a quantum system is noted in connection with nontrivial boundaries of the systems.

In this paper, we study the curvature difference flow about two smooth strictly convex closed plane curves. The two initial curves have the same length, one of them is fixed and another is evolving. We show that, the flow is length-preserving and exists for a short time $[0,T]$. From the analysis of the solutions to the flow, we can't get any information about keeping convexity and explosion.

In this paper, a structural description of a quasi rectangular skew-ring is obtained. Also spined products of quasi rectangular skew-rings are investigated and described.

The concept of $\ast$-$0$-distributive almost lattice ($\ast$-$0$-DAL) is introduced. Some necessary and sufficient conditions for a $0$-distributive almost lattice to become $\ast$-$0$-distributive almost lattice in topological and algebraic terms are proved.

In this paper, we introduce the semiring of quotients of a $H-$ semimodule semialgebra $A$ with respect to the filter $\mathfrak{F}$ of $H-$stable ideals $I$ of $A$ with right and left annihilators of $I$ are zero. We establish a connection between semiring of quotients of a semialgebra $A$ and the ring of quotients of the algebra of differences $A^{\triangle}.$ We also introduce the Hopf algebra action of the semiring of quotients and study the connection between the smash product of semialgebra of quotients and the smash product of algebra of quotients.

The notion of regular ternary partial semiring is introduced. Also, the concepts of left ideal, right ideal, lateral ideal, two-sided ideal and ideal in a ternary partial semiring are introduced and are used to characterize regular ternary partial semirings.

Let $G$ be a finite group. A subgroup $H$ of $G$ is called nearly $S$-permutable in $G$ if for every prime $p$ with $(p,|H|)=1$ and for every subgroup $K$ of $G$ containing $H$ the normalizer $N_K(H)$ contains some Sylow $p$-subgroup of $K$. A subgroup $H$ of $G$ is said to be weakly $NS^*$-supplemented subroup of $G$ if there exists a subgroup $T$ of $G$ such that $G=HT$, and $H\cap T\le H_{nG}$, where $H_{nG}$ is the subgroup of $H$ generated by all those subgroups of $H$ which are nearly $S$-permutable in $G$. In this article, we investigate the structure of $G$ under the assumption that every subgroups of prime order are weakly $NS^*$-permutable subgroups of $G$. Some recent results are generalized.