Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070220180601Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method7585540893ENH. Laeli DastjerdiDepartment of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, IranM. Nili AhmadabadiDepartment of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, IranJournal Article20161227In this paper, a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method. In this method, a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution. Error analysis of this method is also presented. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.http://jlta.iauctb.ac.ir/article_540893_15536c980ac1f2c9de9e47e56f86264e.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070220180601New three-step iteration process and fixed point approximation in Banach spaces87100540894ENK. UllahDepartment of Mathematics, International Islamic University H-10, 44000- Islamabad, PakistanM. ArshadDepartment of Mathematics, International Islamic University H-10, 44000- Islamabad, PakistanJournal Article20171025In this paper we propose a new iteration process, called the $K^{ast }$ iteration process, for approximation of fixed points. We show that our iteration process is faster than the existing well-known iteration processes using numerical examples. Stability of the $K^{ast}$ iteration process is also discussed. Finally we prove some weak and strong convergence theorems for Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results are the extension, improvement and generalization of many well-known results in the literature of iterations in fixed point theory.http://jlta.iauctb.ac.ir/article_540894_7f56deb6bb491b42eb6aade3302b2847.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070220180601A note on the new basis in the mod 2 Steenrod algebra101107540968ENT. VergiliDepartment of Mathematics, Faculty of Science, Ege University, Turkey0000-0003-1821-6697I. KaracaDepartment of Mathematics, Faculty of Science, Ege University, TurkeyJournal Article20180111The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations, denoted by $Sq^n$, between the cohomology groups with $mathbb{Z}_2$ coefficients of any topological space. Regarding to its vector space structure over $mathbb{Z}_2$, it has many base systems and some of the base systems can also be restricted to its sub algebras. On the contrary, in addition to the work of Wood, in this paper we define a new base system for the Hopf subalgebras $mathcal{A}(n)$ of the mod $2$ Steenrod algebra which can be extended to the entire algebra. The new base system is obtained by defining a new linear ordering on the pairs $(s+t,s)$ of exponents of the atomic squares $Sq^{2^s(2^t-1)}$ for the integers $sgeq 0$ and $tgeq 1$.http://jlta.iauctb.ac.ir/article_540968_7c5b6f76f4c87e519e2a83399b80eb9e.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070220180601Stability and hyperstability of orthogonally ring $*$-$n$-derivations and orthogonally ring $*$-$n$-homomorphisms on $C^*$-algebras109119541008ENR. GholamiDepartment of Mathematics, Islamic Azad University Dehloran Branch, Dehloran, IranGh. AskariDepartment of Mathematics, Semnan University, P.O.Box 35195-363, Semnan, IranM. Eshaghi GordjiDepartment of Mathematics, Semnan University, P.O.Box 35195-363, Semnan, IranJournal Article20180212In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.http://jlta.iauctb.ac.ir/article_541008_79e4735f4e3444e5b380eb6cc3001154.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070220180601On Laplacian energy of non-commuting graphs of finite groups121132541040ENP. DuttaDepartment of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, IndiaR. K. NathDepartment of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, IndiaJournal Article20171213Let $G$ be a finite non-abelian group with center $Z(G)$. The non-commuting graph of $G$ is a simple undirected graph whose vertex set is $Gsetminus Z(G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy ne yx$. In this paper, we compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups..http://jlta.iauctb.ac.ir/article_541040_8cd3233041da38453ff594f7a7132513.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070220180601On the powers of fuzzy neutrosophic soft matrices133147541177ENM. KavithaDepartment of Mathematics, Annamalai University, Annamalainagar-608002, IndiaP. MurugadasDepartment of Mathematics, Government Arts college (Autonomous), Karur, IndiaS. SriramMathematics Wing, Directorate of Distance Education, Annamalai University, Annamalainagar-608002, IndiaJournal Article20180312In this paper, The powers of fuzzy neutrosophic soft square matrices (FNSSMs) under the operations $oplus(=max)$ and $otimes(=min)$ are studied. We show that the powers of a given FNSM stabilize if and only if its orbits stabilize for each starting fuzzy neutrosophic soft vector (FNSV) and prove a necessary and sufficient condition for this property using the associated graphs of the FNSM. Applications of the obtained results to several spacial classes of FNSMs (including circulants) are given.http://jlta.iauctb.ac.ir/article_541177_7b0d65f25cb0de011b4d53a11dda7950.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070220180601A representation for some groups, a geometric approach149153541178ENA. ParsianDepartment of Mathematics, Tafresh Universiy, 39518-79611 Tafresh, IranJournal Article20180223In the present paper, we are going to use geometric and topological concepts, entities and properties of the integral curves of linear vector fields, and the theory of differential equations, to establish a representation for some groups on $R^{n} (ngeq 1)$. Among other things, we investigate the surjectivity and faithfulness of the representation. At the end, we give some applications.<br /> .http://jlta.iauctb.ac.ir/article_541178_6c204215936e1623e23d670e5d87eccc.pdf