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Open Access Article
1 - Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method
H. Laeli Dastjerdi M. Nili Ahmadabadi‎In 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 tran More‎In 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. Manuscript profile -
Open Access Article
2 - New three-step iteration process and fixed point approximation in Banach spaces
K. Ullah M. Arshad‎In this paper we propose a new iteration process‎, ‎called the $K^{\ast }$ iteration process‎, ‎for approximation of fixed‎‎points‎. ‎We show that our iteration process is faster than the existing well-known iteration processes using More‎In this paper we propose a new iteration process‎, ‎called the $K^{\ast }$ iteration process‎, ‎for approximation of fixed‎‎points‎. ‎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 in‎‎fixed point theory‎. Manuscript profile -
Open Access Article
3 - A note on the new basis in the mod 2 Steenrod algebra
T. Vergili I. Karaca‎The 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 spac More‎The 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 $s\geq 0$ and $t\geq 1$‎. Manuscript profile -
Open Access Article
4 - Stability and hyperstability of orthogonally ring $*$-$n$-derivations and orthogonally ring $*$-$n$-homomorphisms on $C^*$-algebras
R. Gholami Gh. Askari M. Eshaghi GordjiIn 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 hyper MoreIn 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. Manuscript profile -
Open Access Article
5 - On Laplacian energy of non-commuting graphs of finite groups
P. Dutta R. K. Nath‎Let $G$ 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 $G\setminus Z(G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy \ne yx$‎. ‎In this paper‎, More‎Let $G$ 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 $G\setminus Z(G)$ 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.. Manuscript profile -
Open Access Article
6 - On the powers of fuzzy neutrosophic soft matrices
M. Kavitha P. Murugadas S. SriramIn 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 fuzz MoreIn 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. Manuscript profile -
Open Access Article
7 - A representation for some groups, a geometric approach
A. Parsian‎In the present paper‎, ‎we are going to use geometric and topological concepts‎, ‎entities and properties of the‎‎integral curves of linear vector fields‎, ‎and the theory of differential equations‎,‎to establish a representa More‎In the present paper‎, ‎we are going to use geometric and topological concepts‎, ‎entities and properties of the‎‎integral curves of linear vector fields‎, ‎and the theory of differential equations‎,‎to establish a representation for some groups on $R^{n} (n\geq 1)$‎. ‎Among other things‎, ‎we investigate the surjectivity and faithfulness of the representation‎.At the end‎, ‎we give some applications‎. . Manuscript profile
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