Combinatorics
1. On the commuting graph of non-commutative rings of order $p^nq$

E. Vatandoost; F. Ramezani; A. Bahraini

Volume 03, Issue 01 , Winter 2014, , Pages 1-6

Abstract
Let $R$ be a non-commutative ring with unity. The commuting graph of $R$ denoted by $\Gamma(R)$, is a graph with vertex set $R\Z(R)$ and two vertices $a$ and $b$ are adjacent iff $ab=ba$. In this paper, we consider the commuting graph of non-commutative rings of order pq and $p^2q$ with ...  Read More

2. $n$-Jordan homomorphisms on C-algebras

A. Bodaghi; B. Shojaee

Volume 01, Issue 01 , Winter 2012, , Pages 1-7

Abstract
Let $n\in \mathbb{N}$. An additive map $h:A\to B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $a\in A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$. For these cases, every ...  Read More

Functional analysis
3. Upper and lower $\alpha(\mu_{X},\mu_{Y})$-continuous multifunctions

M. Akdag; F. Erol

Volume 04, Issue 01 , Winter 2015, , Pages 1-9

Abstract
In this paper, a new class of multifunctions, called generalized $\alpha(\mu_{X},\mu_{Y})$-continuous multifunctions, has been de ned and studied. Some characterizations and several properties concerning generalized $\alpha(\mu_{X},\mu_{Y})$-continuous multifunctions are obtained. The relationships ...  Read More

4. Solved and unsolved problems in generalized notions of Connes amenability

A. Mahmoodi Kebriya

Volume 02, Issue 01 , Winter 2013, , Pages 1-7

Abstract
We survey the recent investigations on (bounded, sequential) approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We will discuss the core problems concerning these notions and address the signi cance of any solutions to them to the development of the ...  Read More

Calculus of variations and optimal control; optimization
5. Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

F. M. Yaghoobi; J. Shamshiri

Volume 05, Issue 01 , Winter 2016, , Pages 1-13

Abstract
This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using ...  Read More

Combinatorics
6. Normalized laplacian spectrum of two new types of join graphs

Volume 06, Issue 01 , Winter 2017, , Pages 1-9

Abstract
‎Let $G$ be a graph without an isolated vertex‎, ‎the normalized Laplacian matrix $\tilde{\mathcal{L}}(G)$‎ ‎is defined as $\tilde{\mathcal{L}}(G)=\mathcal{D}^{-\frac{1}{2}}\mathcal{L}(G)\mathcal{D}^{-\frac{1}{2}}$‎, where ‎$\mathcal{D}$ ‎is a‎ diagonal matrix ...  Read More

General topology
7. Preclosure operator and its applications in general topology

A. A. Nasef; S. Jafari; M. Caldas; R. M. Latif; A. A. Azzam

Volume 07, Issue 01 , Winter 2018, , Pages 1-9

Abstract
In this paper, we show that a pointwise symmetric pre-isotonic preclosure function is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric, functions ...  Read More

Linear and multilinear algebra; matrix theory
8. *-frames in Hilbert modules over pro-C*-algebras

M. Naroei Irani; A. Nazari

Volume 08, Issue 01 , Winter 2019, , Pages 1-10

Abstract
‎In this paper‎, ‎by using the sequence of multipliers‎, ‎we introduce frames with algebraic bounds in Hilbert pro-$C^*$-modules‎. ‎We investigate the relations between frames and $\ast$-frames‎. ‎Some properties of $\ast$-frames in Hilbert pro-$C^*$-modules ...  Read More

Difference and functional equations
9. Approximate solutions of homomorphisms and derivations of the generalized Cauchy-Jensen functional equation in $C^*$-ternary algebras

Volume 09, Issue 01 , Winter 2020, , Pages 1-15

Abstract
In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$\eta \mu f\left(\frac{x+y}{\eta}+z\right) = f(\mu x) + f(\mu y) +\eta f(\mu z)$$ for all $\mu \in \mathbb{S}:= \{ \lambda \in \mathbb{C} : |\lambda | =1\}$ ...  Read More

10. Weak amenability of (2N)-th dual of a Banach algebra

M. Ettefagh; S. Houdfar

Volume 01, Issue 02 , Spring 2012, , Pages 55-65

Abstract
In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $n\geq 1$ implies the weak amenability of A.  Read More

Linear and multilinear algebra; matrix theory
11. On the construction of symmetric nonnegative matrix with prescribed Ritz values

A. M. Nazaria; E. Afshari

Volume 03, Issue 02 , Spring 2014, , Pages 61-66

Abstract
In this paper for a given prescribed Ritz values that satisfy in the some special conditions, we find a symmetric nonnegative matrix, such that the given set be its Ritz values.  Read More

Associative rings and algebras
12. Commuting $\pi$-regular rings

Volume 02, Issue 02 , Spring 2013, , Pages 67-70

Abstract
R is called commuting regular ring (resp. semigroup) if for each x,y $\in$ R there exists a $\in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $\pi$-regular rings (resp. semigroups) and study various properties of them.  Read More

Difference and functional equations
13. Asymptotic aspect of quadratic functional equations and super stability of higher derivations in multi-fuzzy normed spaces

M. khanehgir; F. Hasanvand

Volume 05, Issue 02 , Spring 2016, , Pages 67-81

Abstract
In this paper, we introduce the notion of multi-fuzzy normed spaces and establish an asymptotic behavior of the quadratic functional equations in the setup of such spaces. We then investigate the superstability of strongly higher derivations in the framework of multi-fuzzy Banach ...  Read More

Integral equations
14. Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method

Volume 07, Issue 02 , Spring 2018, , Pages 75-85

Abstract
‎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 ...  Read More

Functional analysis
15. Operator frame for $End_{\mathcal{A}}^{\ast}(\mathcal{H})$

M. Rossafi; S. Kabbaj

Volume 08, Issue 02 , Spring 2019, , Pages 85-95

Abstract
‎Frames generalize orthonormal bases and allow representation of all the elements of the space‎. ‎Frames play significant role in signal and image processing‎, ‎which leads to many applications in informatics‎, ‎engineering‎, ‎medicine‎, ‎and probability‎. ...  Read More

Partial differential equations
16. On the convergence of the homotopy analysis method to solve the system of partial differential equations

Volume 04, Issue 02 , Spring 2015, , Pages 87-100

Abstract
One of the efficient and powerful schemes to solve linear and nonlinear equations is homotopy analysis method (HAM). In this work, we obtain the approximate solution of a system of partial differential equations (PDEs) by means of HAM. For this purpose, we develop the concept of HAM for ...  Read More

Approximations and expansions
17. New three-step iteration process and fixed point approximation in Banach spaces

Volume 07, Issue 02 , Spring 2018, , Pages 87-100

Abstract
‎In 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. ...  Read More

Approximations and expansions
18. Smooth biproximity spaces and P-smooth quasi-proximity spaces

O. A. Tantawy; S. A. El-Sheikh; R. A. Majeed

Volume 06, Issue 02 , Spring 2017, , Pages 91-107

Abstract
The notion of smooth biproximity space  where $\delta_1,\delta_2$ are gradation proximities defined by Ghanim et al. [10]. In this paper, we show every smooth biproximity space $(X,\delta_1,\delta_2)$ induces a supra smooth proximity space $\delta_{12}$ finer than $\delta_1$ and $\delta_2$. We ...  Read More

Algebraic topology
19. A note on the new basis in the mod 2 Steenrod algebra

T. Vergili; I. Karaca

Volume 07, Issue 02 , Spring 2018, , Pages 101-107

Abstract
‎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 $\mathbb{Z}_2$‎, ...  Read More

Integral equations
20. An efficient method for the numerical solution of functional integral equations

Volume 09, Issue 02 , Spring 2020, , Pages 105-111

Abstract
We propose an efficient mesh-less method for functional integral equations. Its convergence analysis has been provided. It is tested via a few numerical experiments which show the efficiency and applicability of the proposed method. Attractive numerical results have been obtained.  Read More

Difference and functional equations
21. Stability and hyperstability of orthogonally ring $*$-$n$-derivations and orthogonally ring $*$-$n$-homomorphisms on $C^*$-algebras

R. Gholami; Gh. Askari; M. Eshaghi Gordji

Volume 07, Issue 02 , Spring 2018, , Pages 109-119

Abstract
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 ...  Read More

Global analysis, analysis on manifolds
22. Signature submanifolds for some equivalence problems

M. Nadja khah; Z. Pahlevani Tehrani

Volume 03, Issue 03 , Summer 2014, , Pages 121-130

Abstract
This article concerned on the study of signature submanifolds for curves under Lie group actions SE(2), SA(2) and for surfaces under SE(3). Signature submanifold is a regular submanifold which its coordinate components are differential invariants of an associated manifold under Lie group ...  Read More

Associative rings and algebras
23. Derivations in semiprime rings and Banach algebras

Sh. Sahebi; V. Rahmani

Volume 02, Issue 03 , Summer 2013, , Pages 129-135

Abstract
Let $R$ be a 2-torsion free semiprime ring with extended centroid $C$, $U$ the Utumi quotient ring of $R$ and $m,n>0$ are fixed integers. We show that if $R$ admits derivation $d$ such that $b[[d(x), x]_n,[y,d(y)]_m]=0$ for all $x,y\in R$ where $0\neq b\in R$, then there exists a central idempotent ...  Read More

General topology
24. On weakly eR-open functions

M. Ozkoc; B. S. Ayhan

Volume 05, Issue 03 , Summer 2016, , Pages 145-153

Abstract
The main goal of this paper is to introduce and study a new class of function via the notions of $e$-$\theta$-open sets and $e$-$\theta$-closure operator which are defined by Özkoç and Aslım [10] called weakly $eR$-open functions and $e$-$\theta$-open functions. Moreover, we investigate ...  Read More

Fixed point theory
25. Existence of best proximity and fixed points in $G_p$-metric spaces

S. Rathee; K. Dhingra

Volume 07, Issue 03 , Summer 2018, , Pages 155-168

Abstract
In this paper, we establish some best proximity point theorems using new proximal contractive mappings in asymmetric $G_{p}$-metric spaces. Our motive is to find an optimal approximate solution of a fixed point equation. We provide best proximity points for cyclic contractive mappings in $G_{p}$-metric ...  Read More