Iranian Journal of Mathematical Sciences and Informatics
Volume:18 Issue: 1, May 2023

In this paper, we investigate a Bresse-type system of thermoelasticity of type III in the presence of a distributed delay. We prove the well-posedness of the problem. Furthermore, an exponential stability result will be shown without the usual assumption on the wave speeds. To achieve our goals, we make use of the semigroup method and the energy method.

This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations. In the second part, we use a version of Schlessinger criteria for functors on theArtinian category of nilpotent Lie algebras which is formulated by Pridham, and explore arithmetic deformations using this technique.

The purpose of the present paper is to introduce two new subclasses of the function class ∑m  of bi-univalent functions which both f  and f-1  are m-fold symmetric analytic functions. Furthermore, we obtain estimates on the initial coefficients for functions in each of these new subclasses. Also we explain the relation between our results with earlier known results.

Topological indices are widely used as mathematical tools to analyze different types of graphs emerged in a broad range of applications. The Hyper-Zagreb index (HM) is an important tool because it integrates the first two Zagreb indices. In this paper, we characterize the trees and unicyclic graphs with the first four and first eight greatest HM-value, respectively.

The Haar wavelet collocation with iteration technique is applied for solving a class of time-fractional physical equations. The approximate solutions obtained by two dimensional Haar wavelet with iteration technique are compared with those obtained by analytical methods such as Adomian decomposition method (ADM) and variational iteration method (VIM). The results show that the present scheme is effective and appropriate for obtaining the numerical solution of the timefractional Modified Camassa-Holm equation and Time fractional Modified Degasperis-Procesi equation.

Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through the use of the extended generalized Noor-type integral operator associated with the ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties of this subclass are also studied.

In the present paper, we introduce a new subclass H∑m (λ,β)of the m-fold symmetric bi-univalent functions. Also, we find the estimates of the Taylor-Maclaurin initial coefficients |am+1| , |a2m+1| and general coefficients |amk+1| (k ≥ 2) for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

The numerical approximation methods of the differential problems solution are numerous and various. Their classifications are based on several criteria: Consistency, precision, stability, convergence, dispersion, diffusion, speed and many others. For this reason a great interest must be given to the construction and the study of the associated algorithm: indeed the algorithm must be simple, robust, less expensive and fast. In this paper, after having recalled the δ-ziti method, we reformulat it to obtain an algorithm that does not require as many calculations as many nodes knowing that they are counted by thousands. We have, therefore, managed to optimize the number of iterations by passing for example from 103 at 10 iterations.

In this paper, we show that for any BL-general L-fuzzy automaton (BL-GLFA) there exists a complete deterministic accessible reduced BL-general L-fuzzy automaton that recognizing the behavior of the BL-GLFA. Also, we prove that for any finite realization β, there exists a minimal complete deterministic BL-GLFA recognizing β. We prove any complete deterministic accessible reduced BL-GLFA is a minimal BLGLFA. After that, we show that for any given finite realization β, the minimal complete deterministic BL-GLFA recognizing β is isomorphic to any complete accessible deterministic reduced BL-GLFA recognizing β. Moreover, we give some examples to clarify these notions. Finally, by using these notions, we give some theorems and algorithms and obtain some related results.

In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-Fredholm integral equation. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original equation. The operational matrices of both basic functions are calculated and embeded in the equation to achieve a linear system of equations which give the expansion coefficients of the solution. We prove that the rate of the convergence is O(h2) and O(h4) for these two different bases under some conditions. Two examples are solved and the results are compared with those of block pulse functions method (BPFs) to show the accuracy and reliability of the methods.

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity coindex of some graph products such as lexicographic product, generalized hierarchical product, and strong product. Results are applied to compute the values of this eccentricity-based invariant for some chemical graphs and nanostructures such as hexagonal chain, linear phenylene chain, and zig-zag polyhex nanotube.

Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In particular, we can define analysis, synthesis and frame operators with representation space compatible for (C,C')-Controlled g-fusion frames, which even yield a reconstruction formula. Also, some useful concepts such as Q-dual and perturbation are introduced and investigated.

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (η1,η2)-convex.

In this paper we consider the inverse and reverse network facility location problems with considering the equity on servers. The inverse facility location with equality measure deals with modifying the weights of vertices with minimum cost, such that the difference between the maximum and minimum weights of clients allocated to the given facilities is minimized. On the other hand, the reverse case of facility location problem with equality measure considers modifying the weights of vertices with a given budget constraint, such that the difference between the maximum and minimum weights of vertices allocated to the given facilities is reduced as much as possible. Two algorithms with time complexity O(nlogn) are presented for the inverse and reverse 2-facility location problems with equality measures. Computational results show their superiority with respect to the linear programming models.