http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/5708 JAEM 2023, Vol 13, No 4 koleksiyonunu içerir. 2026-04-08T22:26:03Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7203 On a regularized solution of the cauchy problem for matrix factorizations of the Helmholtz equation Juraev, Davron Aslonqulovich; Noeiaghdam, Samad; Agarwal, Praveen In this paper, we consider the problem of recovering solutions for matrix factorizations of the Helmholtz equation in a multidimensional bounded domain from their values on a part of the boundary of this domain, i.e., the Cauchy problem. An approximate solution to this problem is constructed based on the Carleman matrix method. 2023-10-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/5745 A multi criteria group decision making approach based on fuzzy measure theory to assess the different gene regions used in rodent species Olgun Karacan, Gül; Ünver, Mehmet; Inostroza Ponta, Mario Many mitochondrial and nuclear gene regions are used in phylogenetic and taxonomic studies to investigate the historical background of the species and to present the hierarchy of the species. In this paper, we consider the problem of proposing a favorable gene region that determines the diversification of rodent species as a multi criteria group decision making problem. We use fuzzy measure theory and fuzzy integrals to get the results. We conclude with different fuzzy measures and fuzzy integral techniques that COI gene region which is preferred in animal barcoding studies is more favorable. 2023-10-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/5744 Congruent dominating sets in a graph - a new concept Vaidya, Samir K.; Vadhel, Harshadkumar D. A dominating set D ? V (G) is said to be a congruent dominating set of G if ?v?V (G) d(v) ? 0 ( mod ?v?D d(v) ). The minimum cardinality of a minimal congruent dominating set of G is called the congruent domination number of G which is denoted by ?cd(G). Some characterizations are established and congruent domination number for various graphs have been investigated. 2023-10-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/5743 Shifted Legendre polynomial solutions of nonlinear stochastic Itô - Volterra integral equations Balachandar, S. Raja; D., Uma; Venkatesh, Sivaramakrishnan Gopalakrishnan In this article, we propose the shifted Legendre polynomial-based solution for solving a stochastic integral equation. The properties of shifted Legendre polynomials are discussed. Also, the stochastic operational matrix required for our proposed methodology is derived. This operational matrix is capable of reducing the given stochastic integral equation into simultaneous equations with N+1 coefficients, where N is the number of terms in the truncated series of function approximation. These unknowns can be found by using any well-known numerical method. In addition to the capability of the operational matrices, an essential advantage of the proposed technique is that it does not require any integration to compute the constant coefficients. This approach may also be used to solve stochastic differential equations, both linear and nonlinear, as well as stochastic partial differential equations. We also prove the convergence of the solution obtained through the proposed method in terms of the expectation of the error function. The upper bound of the error in L² norm between exact and approximate solutions is also elaborately discussed. The applicability of this methodology is tested with a few numerical examples, and the quality of the solution is validated by comparing it with other methods with the help of tables and figures. 2023-10-01T00:00:00Z