‎In 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 More
‎In 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.
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‎In 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 More
‎In 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.
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‎The 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 More
‎The 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 $t\geq 1$‎.
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In 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 More
In 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.
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‎Let $G$ 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, More
‎Let $G$ 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..
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In 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 More
In 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.
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‎In 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 More
‎In 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. .
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