Journal of Mahani Mathematical Research
Volume:10 Issue: 2, Summer and Autumn 2021

Let R and R0 be two unital rings such that R contains a non-trivial idempotent P1. If R is a prime ring, we characterize the form of bijective map ϕ : R → R0 which satisfies ϕ(ABP) = ϕ(A)ϕ(B)ϕ(P), for every A, B ∈ R and P ∈ {P1, P2}, where P2 := I − P1 and I is the unit member of R. It is shown that ϕ is an isomorphism multiplied by a central element. Finally, we characterize the form of ϕ : R → R which satisfies ϕ(P)ϕ(A)ϕ(P) = P AP, for every A ∈ R and P ∈ {P1, P2}.

The aim of this paper is introduce an approach to convert the topology of a topological space to another topology(in fact, a coarser topology). For this purpose, considering a closed set P of subsets of a topological space (X, τ) and a grill G on the space, we use the closure operator cl associated with τ, to define a new Kuratowski closure operator cl∗ P on X. The operator cl∗ P induces the desired topology. We then characterize the form of this resulting topology and also determine its relationship to the initial topology of the space. Some examples are given. Also, using a suitable grill in the method, we convert each topological space to corresponding D-space.

Recently, Zhang et al. [Applied Mathematics Letters 104 (2020) 106287] proposed a preconditioner to improve the convergence speed of three types of Jacobi iterative methods for solving multi-linear systems. In this paper, we consider the Jacobi-type method which works better than the other two ones and apply a new preconditioner. The convergence of proposed preconditioned iterative method is studied. It is shown that the new approach is superior to the recently examined one in the literature. Numerical experiments illustrate the validity of theoretical results and the efficiency of the proposed preconditioner.

Analysis of variance (ANOVA) is an important method in exploratory and confirmatory data analysis when explanatory variables are discrete and response variables are continues and independent from each other. The simplest type of ANOVA is one-way analysis of variance for comparison among means of several populations. In this paper, we extend one-way analysis of variance to a case where observed data are non-symmetric triangular or normal fuzzy observations rather than real numbers. Meanwhile, a case study on the car battery length-life is provided on the basis on the proposed method.

We present an extension of Perron-Frobenius theory to the higher-rank numerical range of real matrices. We define a new type of the rank-k numerical radius for real matrices, i.e., the sign-real rankk numerical radius, and derive some properties of it. In addition, we extend Issos’ results on the higher-rank numerical range of nonnegative matrices to real matrices. Finally, we give some examples that are used to illustrate our theoretical results.

In this paper, we study the eigenvalues of real tridiagonal 3-Toeplitz matrices of different order. When the order of a tridiagonal 3- Toeplitz matrix is n = 3k+ 2, the eigenvalues were found explicitly. Here, we consider the distribution of eigenvalues for a tridiagonal 3-Toeplitz matrix of orders n = 3k and n = 3k + 1. We explain our method by finding roots of a combination of Chebyshev polynomials of the second kind. This distribution solves the eigenproblem for integer powers of such matrices.

This presentation outlines from a quantitative point of view, the relationships between probability theory, possibility theory, and generalized uncertainty theory, and the role that fuzzy set theory plays in the context of these theories. Fuzzy sets, possibility, and probability entities are de…ned in terms of a function. In each case, these three functions map the real numbers to the interval [0,1]. However, each of these functions are de…ned with di¤erent properties. There are generalizations associated with these three theories that lead to intervals (sets of connected real numbers bounded by two points) and interval functions (sets of functions that are bounded by known upper and lower functions). An interval or interval function encodes the fact that it is unknown which of the points or functions is the point or function in questions, that is, the numerical value or real-valued function is unknown, it is uncertain. For generalizations given by pairs of numbers or functions, a case is made for a particular type of generalized uncertainty theory, interval-valued probability measures, as a way to unify the generalizations of probability, possibility theory, as well as other generalized probability theories via fuzzy intervals and fuzzy interval functions. This presentation brings a new understanding of quantitative fuzzy set theory, possibility theory, probability theory, and generalized uncertainty and gleans from existing research with the intent to organize and further clarify existing approaches.

In this work we carry out a multiple imputation technique for handling missing observations. We propose an algorithm, which performs a hierarchical multiple imputation using edition rules to impute missing values. We assess our algorithm using a simulation study and a numerical application of our algorithm in dataset of Kerman Chamber of Commerce, Industries, Mines and Agriculture is presented for more illustration.

Using fixed point methods, we prove the stability of orthogonally ring homomorphism and orthogonally ring derivation in Banach
algebras.

The contribution of generl fuzzy automata to neural networks has been considerable, and dynamical fuzzy systems are becoming more and more popular and useful. Basic logic, or BL for short, has been introduced by Hájek [5] in order to provide a general framework for formalizing statements of fuzzy nature. In this note, some of the closure properties of the BL-general fuzzy automaton based on lattice valued such as union, intersection, connection and a serial connection are considered, after that, the behavior of them are discussed. Moreover, for a given BL-general fuzzy automaton on the basis of lattice valued, a complete BL-general fuzzy automaton on the basis of lattice valued is presented. Afterward, we may test the Pumping Lemma for the BL-general fuzzy automaton based on lattice valued. In particular, a connection between the behavior of BL-general fuzzy automaton based on lattice valued and its language is presented. Also, it is proven that L is a recognizable set if and only if L is rational. Also, it is driven that Kleen’s Theorem is valid for the BL-general fuzzy automaton on the basis of lattice valued. Finally, we give some examples to clarify these notions.

This paper studies the dynamics of a non-smooth vibrating system of the Filippov type. The main focus is on investigating the stability and bifurcation of a simple harmonic oscillator subjected to a non-smooth velocity-dependent damping force. In this way, we can analyze the effects of damping on the system's vibrations. For this purpose, we will find a parametric region for the existence of generalized Hopf bifurcation, in order to compute a branch of periodic orbits for the system. The tool for our purpose is the theoretical results about generalized Hopf bifurcation for planar Filippov systems. Some numerical simulations as examples are given to illustrate our theoretical results. Our theoretical and numerical findings indicate that the harmonic oscillator can experience different kinds of vibrations, in the presence of a non-smooth damping.

In this paper, we first study the non-positive decreasing and inverse co-radiant functions defined on a real locally convex topological vector space X. Next, we characterize non-positive increasing, co-radiant and quasi-concave functions over X. In fact, we examine abstract concavity, upper support set and superdifferential of this class of functions by applying a type of duality. Finally, we present abstract concavity of extended real valued increasing, co-radiant and quasi-concave functions.