فهرست مطالب
Journal of Mathematical Extension
Volume:15 Issue: 3, Summer 2021
 تاریخ انتشار: 1400/01/24
 تعداد عناوین: 18


Page 1
In this research an analytic method is used to solve fuzzy heat equation with fuzzy initial values, which is based on ogeneralized Hukuhara differentiability. At rst, we dene fuzzy laplace transform in t considering x as a parameter on fuzzy functions u(x; t) and their derivatives by using generalized Hukuhara differentiability. The fuzzy laplace transform is used in an analytic method for solving the fuzzy partial differential equation with generalized Hukuhara differantiation.finally, the method is explained by presenting examples.ش
Keywords: Fuzzynumber, Fuzzyvalued function, Generalized differentiability, Fuzzy partial differential equation, Fuzzy Laplace transform 
Page 2
Abstract. The concept of 2normed spaces and 2Banach spacesare considerd as generalization of normed and Banach spaces. Inthe present paper we have studied the existence of square rootsand quasi square roots of some elements of a 2Banach algebra.Also relation between nth roots and quasi nth root of elements of2Banach algebras are considered.
Keywords: 2normed algebras, square root, quasi square root, 2normed spaces 
Page 3
In this paper, we discuss the periodicity problems in the finitely generated algebraic structures and exhibit their natural sources in the theory of invariants of finite groups and it forms an interesting and relatively selfcontained nook in the imposing edifice of group theory. One of the deepest and important results of the related theory of finite groups is a complete classification of all periodic groups, that is, the finite groups with periodic properties. If an integer be $k\geq 2$, let $S$ will be a finite $k$generated as well as nonassociative algebraic structure $S=$, where $A=\lbrace a_{1}, a_{2},\dots, a_{k}\rbrace$, and the sequence $$x_{i}=\left\{ \begin{array}{ll} a_{i}, & 1\leq i\leq k, \\ x_{ik}(x_{ik+1}(\ldots(x_{i3}(x_{i2}x_{i1}))\ldots)), & i>k, \end{array} \right. $$ is called the $k$nacci sequence of $S$ with respect to the generating set $A$, as denoted in $k_{A}(S)$. When $k_{A}(S)$ is periodic, we will use the length of the period of the periodicity length of $S$ proportional to $A$ in $LEN_{A}(S)$ and the minimum of the positive integers of $LEN_A(S)$ will be mentioned as periodicity invariant of $S$, denoted in $\lambda_k(S)$. However, this invariant has been studied for groups and semigroups during the years as well as the associative property of $S$ where above sequence was reduced to $x_i=x_{ik}x_{ik+1}\dots x_{i3}x_{i2}x_{i1}$, for every $i\geq k+1$. Thus, we attempt to give explicit upper bounds for the periodicity invariant of two infinite classes of finite nonassociative $3$generated algebraic structures. Moreover, two classes of nonisomorphic Moufang loops of the same periodicity length were obtained in the study.
Keywords: Nonassociativity, Loops, Periodic sequences, Finitely generated structures 
Page 4
Recently, absolute value equations (AVEs) are lied in theconsideration center of some researchers since they are very suitable alternatives for many frequently occurring optimization problems. Therefore, nding a fast solution method for these type of problems is verysignicant. In this paper, based on the mixedtype splitting (MTS) ideafor solving linear system of equations, a new fast algorithm for solvingAVEs is presented. This algorithm has two auxiliary matrices whichare limited to be nonnegative strictly lower triangular and nonnegative diagonal matrices. The convergence of the algorithm is discussedvia some theorems. In addition, it is shown that by suitable choice ofthe auxiliary matrices, the convergence rate of this algorithm is fasterthan that of the SOR, AOR, Generalized Newton, Picard and SORlike methods. Eventually, some numerical results for dierent size ofproblem dimensionality are presented which admit the credibility of theproposed algorithm.
Keywords: Absolute value equations, M−splitting, Mixedtype splitting method, Unique solution, Spectral radius 
Page 5
We first introduce a novel notion named $C^{*}$algebravalued $b_{v}(s)$metric spaces. Then, we give proofs of the Banach contraction principle, the expansion mapping theorem, and Jungck's theorem in $C^{*}$algebravalued $b_{v}(s)$metric spaces. As an application of our results, we establish a result for an integral equation in a $C^{*}$algebravalued $b_{v}(s)$metric space. Finally, a numerical method is presented to solve the proposed integral equation, and the convergence of this method is also studied. Moreover, a numerical example is given to show applicability and accuracy of the numerical method and guarantee the theoretical results.
Keywords: $C^{*}$algebra, $b, {v}(s)$metric space, Fixed point theorem, Integral equation, Contractive mapping 
Page 6
In this paper, we generalize the concepts of para and quasi topological MV algebras, which was first introduced by Najafi et al. in 2017, to BLalgebras as para and quasi topological BLalgebras and elaborate these concepts via some examples. We further derive and prove some theorems by employing prefilters and a fundamental system of neighborhoods.
Keywords: BLalgebra, Para, QuasiTopological BLalgebra, Ideal, Prefilter, Filter 
Page 7
This paper deals with the spatial behavior of solutions for aviscoelastic wave equations with nonlinear dissipative terms in asemiinfinite $n$dimensional cylindrical domain. An alternativeof Phragm\'{e}nLindel\"{o}f type theorems is obtained in theresult. In the case of decay, an upper bound will be derived forthe total energy by means of the boundary data. The main point ofthe contribution is the use of energy method.
Keywords: Spatial estimates, hyprbolic equations, viscoelasticity 
Page 8
In this paper, we give a complete classification of the translation hypersurfaces in the (n+1)dimensional LorentzMinkowski space whose Gauss map G satisfies the condition Ln−1G = AG where Ln−1 is the linearized operator of the first variation of the the GaussKronecker curvature of the hypersurface and A ∈ R (n+1)×(n+1) is a constant matrix.
Keywords: GaussKronecker curvature, LorentzMinkowskispace, Linearized operator Ln−1, Translation hypersurface 
Page 9
The theory of algebraic frames for a Hilbert space $H$ is a generalization of the theory of frames and generalized frames. The paper applies the theory of unbounded operators to define the dual of algebraic frames with densely defined unbounded analysis operators. It is shown that every algebraic frame has an algebraic dual frame, and if an algebraic frame has a nonzero redundancy, then it is not Riesztype. An example of an algebraic frame with finite redundancy is constructed which is not a Riesztype algebraic frame. Finally, for a lower bounded analytic frame, the discreteness of its indexing measure space and the uniqueness of its algebraic dual are studied and shown to be interrelated.
Keywords: Unbounded operators, algebraic frames, algebraic dual frame, dual frame, generalized frames 
Page 10
In this paper, we study $N(k)$contact metric manifolds endowed with a torseforming vector field and give some characterizations for such manifolds. Then, we deal with $N(k)$contact metric manifolds admitting a Ricci soliton and find that the potential vector field $V$ of the Ricci soliton is a constant multiple of $\xi$. Also, we obtain a necessary condition for a torseforming vector field to be recurrent and Killing on $M$.
Keywords: N(k)−contact metric manifold, Recurrenttensor field, Ricci Soliton, Sasakian manifold, Torseforming vector field 
Page 11
The concept of a $w$distance on a metric space has been introduced by Kada et al. \cite{Kst}. They generalized Caristi fixed point theorem, Ekeland variational principle and the nonconvex minimization theorem according to Takahashi. In the present paper, we first introduce the notion of quasi $w$distances in quasimetric spaces and then we will prove some fixed point theorems for $\mathcal{L}$contractive mappings in the class of quasimetric spaces with $w$distances via a control function introduced by Jleli and Samet \cite{JL}. These results generalize many fixed point theorems by Kada et al. \cite{Kst}, Suzuki \cite{S}, Ciri\'{c} \cite{ciric}, Aydi et al. \cite{Aydbarlak}, Abbas and Rhoades \cite{Ar}, Kannan \cite{Kannan}, Hicks and Rhoades \cite{H}, Du \cite{D}, Lakzian et al. \cite{LAR}, Lakzian and Rhoades \cite{LR} and others. Some examples in support of the given concepts and presented results.
Keywords: Quasimetric space, Fixed point, $, mathcal{L}$contraction 
Page 12
The main objective of this paper is to propose a new analytical method called the inverse fractional Aboodh transform method for solving fractional differential equations. Fractional derivatives are taken in the RiemannLiouville and Caputo sense. The main advantages of this method it that it is direct and concise. Various examples are given to shows that the proposed method is very efficient and accurate.
Keywords: Fractional differential equations, RiemannLiouville derivative, Caputo derivative, Aboodh transform method 
Page 13
Nonlocal functional fractional differential inclusions with impulses effect in Banach spaces are studied. This paper deals with the case when the multivalued function is lower semicontinuous and nonconvex as well as the linear term generates a semigroup which is not,in general, compact. Our results are obtained by using NCHM (noncompactness Hausdorff measure), multivalued properties and theorems of fixed point. We finally present an example to lighten our results.
Keywords: Semilinear impulsive differential inclusions, Nonlocal conditions, Fixed point theorems, Mild solutions 
Page 14
Let (R, m) be a ddimensional Noetherian local ring and T be a commutative strict algebra with unit element 1T over R such that mT 6= T. We define almost exact sequences of Tmodules and characterize almost flat Tmodules. Moreover, we define almost (faithfully) flat homomorphisms between Ralgebras T and W, where W has similar properties that T has as an Ralgebra. By almost (faithfully) flat homomorphisms and almost flat modules, we investigate Cousin complexes of T and Wmodules. Finally, for a finite filtration F = (Fi)i≥0 of length less than d of Spec(T) such that it admits a Tmodule X, we show that IE 2 p,q := TorT p M, H d−q (CT (F, X)) p⇒ Hp+q(Tot(T )) and IIE 2 p,q := Hd−p TorT q (M, CT (F, X)) p⇒ Hp+q(Tot(T )), where M is an any flat Tmodule and as a result we show that IE 2 p,q and IIE 2 p,q are almost zero, when M is almost flat
Keywords: Almost flat, almost flat homomorphism, Cousin complex, filtration, spectral sequence 
Page 15
Let G be a group and AutΦ(G) denote the group of all automorphisms of G centralizing G/Φ(G) elementwise. In this paper, we give a necessary and sufficient condition on a finite pgroup G for the group AutΦ(G) to be elementary abelian.
Keywords: Automorphism group, Finite pgroup, Frattini subgroup 
Page 16
An efficient family of the recursive methods of adaptive is proposed for solving nonlinear equations, is developed such that all previous information are applied. These methods have reached the maximum degree of convergence improvement of 100%, and also have an efficiency index of 2. Three families have been examined from SteffensenLike single, two, and threestep methods that have used 2, 3 and 4 parameters respectively. Numerical comparisons are made with other existing methods one, two, three, and fourpoint to show the performance of the convergence speed of the proposed method and confirm theoretical results.
Keywords: Adaptive method with memory, Accelerator parameter, Nonlinear equations, Newton's interpolatory polynomial, Order convergence 
Page 17
The agricultural sector ensures food security in every country.Optimal agricultural practices presuppose the optimal allocationof resources, including water, soil, etc., by official authorities in everycountry because excessive use of natural resources would have harmfulconsequences for posterity despite meeting ad hoc needs. Therefore,sustainable agricultural practices in different regions should be basedon environmental, social, and economic criteria in the decisionmakingprocess for the future. This study investigated the agricultural practicesin two stages: environmental stage (planting and maintaining)and economic stage (harvesting), which use shared resources. A networkDEA model was proposed for developing sustainable agriculturalpractices based on the proposed process. The development of sustainableagricultural practices in different regions presupposes the optimal allocation of water and human resources, which is realized by the improvementof irrigation methods and the quality of life of farmers. Innetwork DEA models, weight restrictions are used to determine sustainabledevelopment. The proposed model was analyzed with and withoutweight restrictions to determine the sustainable development of agriculturein Sistan and Baluchestan Province, Iran, between 2013 and 2017.On the other hand, given the important role human resources play inthe development of sustainable agricultural practices, some models weresuggested for determining the maximum required human resources foreach stage according to the obtained performance levels.
Keywords: Sustainability, Resource Allocation, Agricultural Practices, Network DEA 
Page 18
The main purpose of this note is to define an analogues of the numerical radius related to the matricial range. However, we will find relations between the numerical radius and matricial range of an operator. The tone of the paper is mostly expository.
Keywords: Numerical range, matricial range, completely positive mapping, numerical radius