فهرست مطالب
Journal of Mathematical Extension
Volume:15 Issue: 2, Spring 2021
 تاریخ انتشار: 1400/01/10
 تعداد عناوین: 18


Page 1
The BirnbaumSaunders (BS) distribution is one of the most considered rightskewed distributions to model failure times for materials subjectto lifetime data. In this paper, a new extension of the BS model is initiallyproposed based on the family of meanmixtures of normal distributions. Then,we present a new probabilistic mixture model based on the new extended BSdistribution for modeling and clustering rightskewed and heavytailed data.The maximum likelihood (ML) parameter estimates of the model in questionare estimated by employing an expectationmaximization (EM) type algorithm.Moreover, the empirical information matrix is derived by using an informationbased approach. Simulations and real data analysis illustrate the performanceof the proposed methodology.
Keywords: BirnbaumSaunders distribution, Meanmixtures of normal distributions, Finite mixture model, ECM algorithm 
Page 2
This paper deals with the study of relaxed conditions for semilocal convergence for a general iterative method, kstep Newton's method, using majorizing sequences. Dynamical behavior of the mentioned method is also analyzed via Julia set and basins of attraction. Numerical examples of nonlinear systems of equations will be examined to clarify the given theory.
Keywords: Majorizing sequence, High order of convergence, Semilocal convergence, Julia set, Basin of attraction 
Page 3
In the present paper, by using the variational methods incritical point theory, the existence and multiplicity of periodic solutionsfor a class of pHamiltonian systems is established. In fact, using twofundamental theorems that are attributed to Bonanno, we get someimportant results. Are presented the results were extention of someexisting results.

Page 4
In this paper, we investigate conditions under which the numerical range of a composition operator, acting on a Hilbert space, contains zero as an interior point and we investigate extreme points of the numerical range of an operator acting on an arbitrary Banach space. Also, we give necessary and suﬃcient conditions under which the numerical range of an operator on some Banach spaces, to be closed. Finally, we characterize the structure of the numerical range of an operator acting on Banach weighted Hardy spaces.
Keywords: Banach weighted Hardy spaces, bounded point evaluation, composition operator, numerical range, extreme point 
Page 5
In this paper, we introduce the concepts of strongly 2absorbing primary ideals (resp., submodules) and strongly 2absorbing ideals (resp., submodules) as generalizations of strongly prime ideals. Furthermore, we investigate some basic properties of these classes of ideals.
Keywords: Strongly prime ideal, strongly 2absorbing primary ideal, strongly 2absorbing primary submodule, strongly 2absorbing ideal, strongly 2absorbing submodule 
Page 6
We study the properties of the existence and uniqueness of solutions of a class of evolution quantum stochastic differential equations(QSDEs) dened on a locally convex space whose topology is generated by a family of seminorms dened via the norm of the rangespace of the operator processes. These solutions are called strong solutions in comparison with the solutions of similar equations denedon the space of operator processes where the topology is generated bythe family of seminorms dened via the inner product of the rangespace. The evolution operator generates a bounded semigroup. Weshow that under some more general conditions, the unique solutionis stable. These results extend some existing results in the literatureconcerning strong solutions of quantum stochastic differential equations.
Keywords: Strong solutions, Stability, Bounded semigroup, General Lipschitz condition 
Page 7
In this investigation, we solve the Caputo's fractional parabolic partial integrodifferential equations (FPPIDEs) by Gaussianradial basis functions (GRBFs) method. The main idea for solving these equations is based on RBF which also provides approaches to higher dimensional spaces.In the suggested method, FPPIDEs are reduced to nonlinear algebraic systems. We propose to apply the collocation scheme using GRBFs to approximate the solutions of FPPIDEs. Error analysis of the proposed method is investigated. Numerical examples are provided to show the convenience of the numerical schemes based on the GRBFs. The results reveal that the method is very efficient and convenient for solving such equations.
Keywords: Fractional parabolic partial integrodifferential equations, Radial basis functions, Collocation method, Quadrature methods 
Page 8
. In the current work, we present some innovative solutions for the attractivity of fractional functional qdifferential equations involving Caputo fractional qderivative in a kdimensional system, by using some fixed point principle and the standard Schauder’s fixed point theorem. Likewise, we look into the global attractivity of fractional qdifferential equations involving classical RiemannLiouville fractional qderivative in a kdimensional system, by employing the famous fixed point theorem of Krasnoselskii. Also, we must note that, this paper is mainly on the analysis of the model, with numerics used only to verify the analysis for checking the attractivity and global attractivity of solutions in the system. Lastly, we give two examples to illustrate our main results.
Keywords: Positive attractivity, fractional qdifferentialequations, fractional Caputo type qderivative, RiemannLiouville fractional qderivative 
Page 9
Let £ be the category of all locally compact abelian (LCA) groups. Let G ∈ £ and H ⊆ G. The maximal torsion subgroup of G is denoted by tG and the closure of H by H. A proper short exact sequence 0 → A ϕ→ B ψ→ C → 0 in £ is said to be a generalized textension if 0 → tA ϕ→ tB ψ→ tC → 0 is a proper short exact sequence. We show that the set of all generalized textensions of a torsion group A ∈ £ by a compact group C ∈ £ is a subgroup of Ext(C, A). We establish conditions under which the generalized textensions split.
Keywords: : Generalized textensions, textensions, locally compact abelian groups 
Page 10
This paper is about, the detailed analysis of soft ditopological space theory (SDT  space theory) is ameliorated by introducing new soft sets called ˜δbunclosed sets, ˜δbclosed sets and ˜δbdense sets, which are needed for the definition of extremally disconnected spaces and submaximal spaces in soft ditopological spaces. Moreover, ˜δregular unclosed, ˜δpreunclosed, ˜δsemi unclosed, ˜δ αunclosed and ˜δβ unclosed sets in SDTspace are determined and studied relations between these sets in detail. A new idea is introduced in order to prove relations, which gives an affirmative answer to understand the structure of SDTspaces. It is demonstrated that separately these frameworks can in any case be very confounded, a perhaps increasingly tractable errand is to portray their conceivable joint dispersions by using recently characterized ˜δsets.
Keywords: ˜δbunclosed set, ˜δbclosed set, ˜δbdenseset, ˜δregular unclosed set, ˜δpreunclosed set, ˜δsemi unclosed set, ˜δαunclosed set, ˜δβ unclosed set, ˜δbextremally disconnected space, ˜δbsubmaximal space 
Page 11
In this paper, we introduce the concept of primary submodules over S which is a generalization of the concept of Sprime submodules. Suppose S is a multiplicatively closed subset of a commutative ring R and let M be a unital Rmodule. A proper submodule Q of M with (Q :R M) ∩ S = ∅ is called primary over S if there is an s ∈ S such that, for all a ∈ R, m ∈ M, am ∈ Q implies that sm ∈ Q or san ∈ (Q :R M), for some positive integer n. We get some new results on primary submodules over S. Furtheremore, we compare the concept of primary submodules over S with primary ones. In particular, we show that a submodule Q is primary over S if and only if (Q :M s) is primary, for some s ∈ S.
Keywords: Multiplicatively closed subset, Multiplication module, Primary module, primary module over S 
Page 12
In this paper, we introduce a new trigonometric family of continuous distributions called the sine KumaraswamyG family of distributions. It can be presented as a natural extension of the wellestablished sineG family of distributions, with new perspectives in terms of applicability. We investigate the main mathematical properties of the sine KumaraswamyG family of distributions, including asymptotes, quantile function, linear representations of the cumulative distribution and probability density functions, moments, skewness, kurtosis, incomplete moments, probability weighted moments and order statistics. Then, we focus our attention on a special member of this family called the sine Kumaraswamy exponential distribution. The statistical inference for the related parametric model is explored by using the maximum likelihood method. Among others, asymptotic confidence intervals and likelihood ratio tests for the parameters are discussed. A simulation study is performed under varying sample sizes to assess the performance of the model. Finally, applications to two practical data sets are presented to illustrate its potentiality and robustness.
Keywords: SineG family of distributions, Kumaraswamydistribution, moments, practical data sets 
Page 13
Dominions have been studied from different perspectives however their major application lies to study the closure property for monoids. The most useful characterization of semigroup domonions is provided by the famous Isbell’s Zigzag Theorem. In this paper, we introduce the dominion of a $\Gamma$semigroups and give the analogue of Isbell's zigzag theorem in $\Gamma$semigroups.
Keywords: Dominions, Zigzag equations, $, Gamma$semigroups 
Page 14
In this work, we introduce and investigate an interesting operator Q ν λ based on fractional derivative which is introduced by Owa and Srivastava in [10]. We consider a new technique to prove our results and then, we introduce two subclasses of analytic functions in the open unit disk U concerning with this operator. Some results such as inclusion relations, subordination properties, integral preserving properties and argument estimate are investigated.
Keywords: Analytic function, subordination, integraloperator, fractional derivative, argument 
Page 15
This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex) functions have been proved. Several special cases are discussed as well.
Keywords: Operator order, Jensen’s inequality, convexfunctions, selfadjoint operators, positive operators 
Page 16
In traditional data envelopment analysis (DEA), the efficiency and productivity changes computations are based on an optimistic perspective and an efficient unit may perform rather poorly when the realist weights are assigned to inputs and outputs. Hence, the results of productivity change of decision making units (DMUs) between two time periods may change from progress to regress or vice versa when the weights are modified. Because of the cross efficiency merits, we use it to obtain a common set of weights so called common set of cross weights. On the other hand, we need a base for comparing the productivity change of DMUs. To this end, the common set of cross weights are used to approximate the cross efficient frontier as a base for determining cross Malmquist (CM) index for evaluating the productivity change. This leads to introduce a new efficiency, weight efficiency, and the decomposition of the cross efficiency. Some DEA and cross efficiency models are modified to find the value of the proposed CM index and its components. An empirical example is used to compare the proposed method and the technical Malmquist index.
Keywords: Data envelopment analysis (DEA), Cross efficiency, Malmquist index, Productivity, Common set of weights (CSW) 
Page 17
Let H be a separable infinite dimensional complex Hilbert space and SA(H) be the real Jordan algebra of all bounded selfadjoint operators acting on H. In this paper, we study the general form of surjective nonlinear maps ξ : SA(H) → SA(H), that preserve the difference of minimum and surjectivity moduli of selfadjoint operators in both directions. It turns out that ξ(PLet H be a separable infinite dimensional complex Hilbert space and SA(H) be the real Jordan algebra of all bounded selfadjoint operators acting on H. In this paper, we study the general form of surjective nonlinear maps ξ : SA(H) → SA(H), that preserve the difference of minimum and surjectivity moduli of selfadjoint operators in both directions. It turns out that ξ(P) = EP E∗ + R, (P, R ∈ SLet H be a separable infinite dimensional complex Hilbert space and SA(H) be the real Jordan algebra of all bounded selfadjoint operators acting on H. In this paper, we study the general form of surjective nonlinear maps ξ : SA(H) → SA(H), that preserve the difference of minimum and surjectivity moduli of selfadjoint operators in both directions. It turns out that ξ(P) = EP E∗ + R, (P, R ∈ SA(H)) where E : H → H, is either a bounded unitary or an antiunitary operator.A(H)) where E : H → H, is either a bounded unitary or an antiunitary operator.) = EP E∗ + R, (P, R ∈ SA(H)) where E : H → H, is either a bounded unitary or an antiunitary operator.
Keywords: Nonlinear preserver problems, algebraicoperators, algebraic singularity 
Page 18
In this paper, we show that every $(n,m)$Jordan homomorphism between two commutative algebras is an $(n,m)$homomorphism. For the noncommutative case, we prove that every surjective $(2,m)$Jordan homomorphism from an algebra $\mathcal{A}$ to a semiprime commutative algebra $\mathcal{B}$ is $(2,m)$homomorphism.
Keywords: $n$homomorphism, $n$Jordan homomorphism, mixed $n$Jordan homomorphism, automatic continuity, semisimple