Journal of Mathematical Extension
Volume:16 Issue: 8, Aug 2022

In this paper we investigate further properties of the deformable derivative and use the results to study the existence of solutions to the integro-differential equation D α y(t) = h(y(t)) + f(t, y(t)) + R t 0 K(t, s, y(s))ds, t ∈ [0, T], with initial condition y(0) = y0, where D α y(t) is the deformable derivative of y, 0 < α < 1. We use Weissinger’s fixed point theorem and Krasnoselskii’s fixed point theorem to achieve our main results. An example is provided for illustration.

For an edge e = uv in a graph G, MG u (e) is introduced as the set all edges of G that are at shorter distance to u than to v. We say that G is an edge quasi-distance-balanced graph whenever for every arbitrary edge e = uv, there exists a constant λ > 1 such that mG u (e) = λ ±1mG v (e). We investigate that edge quasi-distance-balanced garphs are complete bipartite graphs Km,n with m ̸= n. The aim of this paper is to investigate the notion of cycles in edge quasi-distance-balanced graphs, and expand some techniques generalizing new outcome that every edge quasi-distance-balanced graph is complete bipartite graph. As well as, it is demontrated that connected quasi-distance-balanced graph admitting a bridge is not edge quasi-distance-balanced graph.

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and let M be an R-module. In this paper, we introduce and investigate some properties of the notion of S-2-absorbing second submodules of M as a generalization of S-second submodules and strongly 2-absorbing second submodules of M. Also, we obtain some results concerning S-2-absorbing submodules of M.

By studying and using the quasi-pure part concept, we improve some statements and show that some assumptions in some articles are superfluous. We give some characterizations of Gelfand rings. For example: we prove that R is Gelfand if and only if m (∑ α∈A Iα ) ∑ = α∈A m(Iα), for each family {Iα}α∈A of ideals of R, in addition if R is semiprimitive and Max(R) ⊆ Y ⊆ Spec(R), we show that R is a Gelfand ring if and only if Y is normal. We prove that if R is reduced ring, then R is a von Neumann regular ring if and only if Spec(R) is regular. It has been shown that if R is a Gelfand ring, then Max(R) is a quotient of Spec(R), and sometimes hM(a)’s behave like the zerosets of the space of maximal ideal. Finally, it has been proven that Z ( Max(C(X))) = {hM(f) : f ∈ C(X)} if and only if {hM(f) : f ∈ C(X)} is closed under countable intersection if and only if X is pseudocompact.

In this essay, extensions to the results of Lie symmetry classification of Reynolds equation are proposed. The infinitesimal technique is used to derive symmetry groups of the Reynolds equation. Onedimensional optimal system is constructed for symmetry sub-algebras gained through Lie point symmetry. At the end, the general symmetry group of the non-conservative generalized thin-film equation are determined.

 In this paper, the dynamics of a modified Nicholson-Bailey model as a discrete dynamical system has been studied. Local dynamics in a neighborhood of boundary fixed points are investigated. It is also proved that the model has a unique positive fixed point and a Neimark-Sacker bifurcation emerges at this fixed point. Some numerical simulations are presented to illustrate the analytical results.

Let D be the open unit disc in the complex plane C. A sandwich weighted composition operator Sψ,ϕ takes an analytic map f on the open unit disc D to the map (ψ.f0 oϕ) 0 , where ϕ is an analytic map of D into itself and ψ is an analytic map on D. In this paper, we compute the adjoint of a sandwich weighted composition operator Sψ,ϕ on weighted Hardy spaces.

In this paper, we propose inverse data envelopment analysis (DEA) models in the presence of ratio data. We present the inputs/output estimation process based on ratio based DEA (DEAR) models. We first present a multiple objective linear programming (MOLP) model to determine the level of inputs based on the perturbed outputs, assuming that the relative efficiency of the under evaluation decision making unit (DMU) preserve. We also present the relationship between the Pareto solutions of the proposed MOLP model and the optimal level of inputs and outputs of the new DMU. We presented criterion models to determine the efficiency of the new DMU in the inputs/output estimation process based on inverse DEA-R models in the presence of ratio data. We showed that in the presence of ratio data the selection of criterion model can be important, in order to we provide a new criterion model in the inputs/output estimation process in the presence of ratio data, and so on the amount of calculations is reduced. We have shown that the results for the new criterion model are the same as the existing criterion model presented in the paper. In order to show the validity of the proposed approach in the inputs/output estimation process based on the inverse DEA-R models, we provide an application of our models in a real life for a set of data regarding to medical centers in Taiwan and finally we present the research results.

The insurance industry is one of the important financial institutions that has a significant place in the economic growth and development of the country. Given the industry’s influential role in the financial markets, it is imperative to evaluate the performance and calculate changes in insurance companies’ productivity over time. It is necessary to explain that the internal structure of insurance companies can be considered as a two-stage process involving marketing and investment. The purpose of the current study is to propose a novel approach to calculate the changes in insurance companies’ productivity by considering their two-stage structure as well as the inherent uncertainties in the data. It should be noted that in order to propose of new interval network Malmquist Productivity Index, the network data envelopment analysis approach (NDEA), Malmquist productivity index (MPI), and interval programming are applied. The implementation of the proposed research approach is also evaluated using real data of 10 insurance companies in Iran. According to the obtained results, most of the companies have regressed from the first stage and marketing perspective, but in the second stage and from the investment perspective, the majority of companies have represented an acceptable improvement in their productivity.

This paper considers an inverse eigenvalue problem for bisymmetric nonnegative matrices. We first discuss the specified structure of the bisymmetric matrices. Then for a given set of real numbers of order maximum five with special conditions, we construct a nonnegative bisymmetric matrix such that the given set is its spectrum. Finally, we solve the problem for arbitrary order n in the special case of the spectrum.