Abstract: In our paper we describe the corresponding dynamic mathematical models to perform a comparative analysis of the reliability of two types of networks: serial-parallel and parallel-serial when the number of subnetworks is constant and the numbers of units in each sub-network are Power Series Distributed (PSD) random variables (r.v.), but also when the lifetimes are independent, identically distributed r.v. We shows that the lifetime distributions of such kind of networks leads us to two new families of distributions called Min(Max-PSD) and Max(Min-PSD) distributions. The formulas for calculating the reliability of the related networks it was deduced too. Su cient conditions have been formulated for the serial-parallel network to always be more reliable than the parallel-serial network. Some graphically illustrated examples have been provided. PubDate: Sat, 08 Oct 2022 00:00:00 GMT

Abstract: In this paper, we consider the partition function Q(n) counting the partitions of n into distinct parts and investigate congruence identities of the formQ(p⋅n+p2-124)≡0 (mod4),Q\left( {p \cdot n + {{{p^2} - 1} \over {24}}} \right) \equiv 0\,\,\,\left( {\bmod 4} \right),where p ⩾ 5 is a prime. PubDate: Sat, 08 Oct 2022 00:00:00 GMT

Abstract: We inquire whether there are some fundamental interpretations of elementary inequalities in terms of curvature of a three-dimensional smooth hypersurface in the four-dimensional real ambient space. The main outcome of our exploration is a perspective of regarding the natural substance of some mathematical inequalities, which represent important physical quantities. PubDate: Sat, 08 Oct 2022 00:00:00 GMT

Abstract: The advantage of various fuzzy normed spaces is to analyse impreciseness and ambiguity that arise in modelling problems. In this paper, various classical stabilities of a new hexic functional equation in di erent fuzzy spaces like fuzzy Banach space, Felbin’s fuzzy Banach space and intuitionistic fuzzy Banach space are presented, concerning the Ulam’s theory of stabilities of equations. To validate the stability results, experimental results are presented. Also, a comparative study of the results obtained in this investigation are provided. PubDate: Sat, 08 Oct 2022 00:00:00 GMT

Abstract: To model statistical data coming from two di erent distributions, Cooray and Ananda [1] introduced a composite (two-spliced) Lognormal-Pareto model, that was further extended by Scollnik [9] and fitted to insurance data. Inspired by these studies, more general three-spliced composite models are considered in this work, built by joining three di erent distributions. In particular, the study is focused on the three-spliced Exponential-Lognormal-Pareto distribution. The main characteristics of this model, as well as statistical inference are discussed. The parameters estimation is illustrated on random generated data. PubDate: Sat, 08 Oct 2022 00:00:00 GMT

Abstract: In this paper, we study the link between finite-dimensional Zinbiel algebras and combinatorial structures or (pseudo)digraphs determining which configurations are associated with those algebras. Some properties of Zinbiel algebras that can be read from their associated combinatorial structures are studied. We also analyze the isomorphism classes for each configuration associated with these algebras providing a new method to classify them and we compare our results with the current classifications of 2- and 3-dimensional Zinbiel algebras. We also obtain the 3-vertices combinatorial structures associated with such algebras. In order to complement the theoretical study, we have designed and performed the implementation of an algorithm which constructs and draws the (pseudo)digraph associated with a given Zinbiel algebra and, conversely, another procedure to test if a given combinatorial structure is associated with some Zinbiel algebra. PubDate: Sat, 08 Oct 2022 00:00:00 GMT

Abstract: Life expectancy models are highly important, as they indicate the populations health. The present models consider several types of factors, and by analyzing them we extend the formulae to new, mixed types in order to create particular representations that are beneficial for creating future results and estimations. PubDate: Sat, 08 Oct 2022 00:00:00 GMT

Abstract: In this paper we deal with the discretization of the second order wave equation by the implicit Euler scheme for the time and the spectral method for the space. We prove that the time semi discrete and the full discrete problems are well posed. We show an optimal error estimates related to both variables time and space. PubDate: Sat, 08 Oct 2022 00:00:00 GMT

Abstract: In the present paper, a numerical scheme is discussed to solve one-dimensional nonlinear diffusion equation of fractional order in which collocation is performed using the Lucas operational matrix. Since the spectral collocation method is used in the proposed method, therefore the residual, initial and boundary conditions of the presented problem are collocated at fixed collocation points. The result is a system of nonlinear equations that can be solved by using Newton’s method. Through error analysis and application to some existing problems, the accuracy of the method is confirmed. The obtained results are presented in tabular forms, which clearly show the higher accuracy of the proposed method. The variations of the solute profile of the proposed model are shown graphically due to the presence or absence of advection and reaction terms for different particular cases. PubDate: Sat, 08 Oct 2022 00:00:00 GMT

Abstract: Using the technique of enriching contractive type mappings, we introduce a more general concept of enriched Ćirić-Reich-Rus contraction than the one studied in [Berinde, V.; Păcurar, M. Fixed point theorems for enriched Ćirić-Reich-Rus contractions in Banach spaces and convex metric spaces. Carpathian J. Math. 37 (2021), no. 2, 173–184.] and provide convergence results for the Krasnoselskij iterative algorithm used to approximate their fixed points. Examples to illustrate the effectiveness of the new results as well as comparison to other classes of contractive type mappings existing in literature are also presented. In this context, we also conclude that Ćirić-Reich-Rus contractions form a class of unsaturated mappings. PubDate: Sat, 08 Oct 2022 00:00:00 GMT

Abstract: Many curve evolutions have been determined which are integrable in recent times. The motion of curves can be defined by certain integrable equations including the modified Korteweg-de Vries. In this study, the quaternionic curves in 3 and 4-dimensional Euclidean spaces have been considered and the motions of inextensible quaternionic curves have been characterized by the modified Korteweg-de Vries (mKdV) equations. For this purpose, the basic concepts of the quaternions and quaternionic curves have been summarized. Then the evolutions of inextensible quaternionic curves with reference to the Frenet formulae have been obtained. Finally, the mKdV equations have been generated with the help of their evolutions PubDate: Thu, 02 Jun 2022 00:00:00 GMT

Abstract: Since the Bin Packing Problem (BPP) has application to industry and supply chain management problems (to mention only the most important ones), it attracted attention from its formulation. The Single Nesting Problem treated here is a particular case of this optimization problem, which different methods, mainly combinatorial, can solve. In this article, we propose using a genetic algorithm for solving the single nesting problem formulated in a previous article by the authors. The results comparisons prove that this approach is an excellent alternative to the combinatorial ones. PubDate: Thu, 02 Jun 2022 00:00:00 GMT

Abstract: A ring is called negative clean if the negative (i.e., the additive inverse) of each clean element is also clean. Clean rings are negative clean.In this paper, we develop the theory of the negative rings, with special emphasis on finding the clean matrices which have (or have not) clean negatives. Many explicit results are proved for 2 × 2 matrices and some hard to solve quadratic Diophantive equations are displayed. PubDate: Thu, 02 Jun 2022 00:00:00 GMT

Abstract: Using a similar approach as Korteweg and de Vries, [19], we obtain periodic solutions expressed in terms of the Jacobi elliptic function cn, [3], for the self-focusing and defocusing one-dimensional cubic nonlinear Schrödinger equations. We will show that solitary wave solutions are recovered through a limiting process after the elliptic modulus of the Jacobi elliptic function cn that describes the periodic solutions for the self-focusing nonlinear Schrödinger model. PubDate: Thu, 02 Jun 2022 00:00:00 GMT

Abstract: In our study we consider a generalized thermoelasticity theory based on a heat conduction equation in micropolar bodies. Specifically, the heat conduction depends on two distinct temperatures, the conductive temperature and the thermodynamic temperature. In our analysis, the difference between the two temperatures is clear and is highlighted by the heat supply. After we formulate the mixed initial boundary value problem defined in this context, we prove the uniqueness of a solution corresponding some specific initial data and boundary conditions. Also, if the initial energy is negative or null, we prove that the solutions of the mixed problem are exponentially instable. PubDate: Thu, 02 Jun 2022 00:00:00 GMT

Abstract: The set Si,n = {0, 1, 2, …, i − 1, i + 1, …, n − 1, n}, 1 ⩽ i ⩽ n, is called Laplacian realizable if there exists a simple connected undirected graph whose Laplacian spectrum is Si,n. The existence of such graphs was established by S. Fallat et all. In the present paper, we find the Laplacian energy and first Zagreb index of graphs whose Laplacian spectrum is Si,n. PubDate: Thu, 02 Jun 2022 00:00:00 GMT

Abstract: Our work adds to the picture of second order differential operators with a full set of algebraic solutions, which we will call algebraic. We see algebraic Heun operators as pull-backs of algebraic hypergeometric operators via Belyi functions. We focus on the case when the hypergeometric one has a tetrahedral monodromy group. We find arithmetic conditions for the pull-back functions to exist. For each distribution of the singular points in the ramified fibers, we identify the minimal values of the exponent differences and we explicitly construct the dessin d’enfant corresponding to the pull-back function in the minimal cases. Then by allowing some parameters to vary, we find infinite families of such graphs, hence of Heun operators with tetrahedral monodromy. PubDate: Thu, 02 Jun 2022 00:00:00 GMT

Abstract: In this research we generalize our result for numbers satisfying the Delannoy triangle. We obtain a central limit theorem and a local limit theorem for weighted numbers of the triangle and establish the rate of convergence to the limiting (normal) distribution. PubDate: Thu, 02 Jun 2022 00:00:00 GMT

Abstract: We present collectively fixed point results for multivalued maps which automatically generate analytic alternatives and minimax inequalities. As an application we consider equilbrium type problems for generalized games. PubDate: Thu, 02 Jun 2022 00:00:00 GMT

Abstract: In this paper, we investigate the Sombor index of the zero-divisor graph of ℤn which is denoted by Γ(ℤn) for n ∈ {pα, pq, p2q, pqr} where p, q and r are distinct prime numbers. Moreover, we introduce an algorithm which calculates the Sombor index of Γ(ℤn). Finally, we give Sombor index of product of rings of integers modulo n. PubDate: Thu, 02 Jun 2022 00:00:00 GMT