Caspian Journal of Mathematical Sciences
Volume:10 Issue: 2, Summer Autumn 2021

In this paper, the class of strongly PI-lifting modules is introduced and investigated. The connections between strongly PI-lifting modules and the generalizations of lifting modules are presented. We provide that the class of strongly PI-lifting modules is contained in the class of PI-lifting modules. Moreover, it is proved that for an Abelian ring R, R is PI-lifting as a right R-module if and only if R=I has a projective cover for every right ideal I of R.The structural properties of strongly PI-lifting modules are determined, and examples are provided to exhibit and delimit our results.

The object of wreath product of permutation groups is defined the actions on cartesian product of two sets. In this paper we consider S(Γ) and S(Δ) be permutation groups on Γ and Δ respectively, and S(Γ)^{Δ} be the set of all maps of Δ into the permutations group S(Γ). That is S(Γ)^{Δ}={f:Δ→S(Γ)}. S(Γ)^{Δ} is a group with respect to the multiplication defined by for all δ in Δ by (f₁f₂)(δ)=f₁(δ)f₂(δ). After that, we introduce the notion of S(Δ) actions on S(Γ)^{Δ} : S(Δ)×S(Γ)^{Δ}→S(Γ)^{Δ},(s,f)↦s⋅f=f^{s}, wheref^{s}(δ)=(f∘s⁻¹)(δ)=(fs⁻¹)(δ) for all δ∈Δ.Finaly, we give the wreath product W of S(Γ) by S(Δ), and the action of W on Γ×Δ.

‎In this paper‎, ‎we study the ‎prediction problem in the two-sample case for predicting future progressively Type-II censored order statistics based on observed progressively Type-II censored order statistics with random removals from the Rayleigh distribution‎. ‎We consider two important distributions for random removals‎, binomial and discrete uniform distributions‎. ‎In both cases‎, ‎Bayesian point and interval predictors are obtained‎. ‎In the following‎, ‎through a simulation study‎, ‎the results are compared to each other‎. ‎Finally‎, ‎a real data set is given to textcolor{red}{illustrate} the output results‎.

In this paper, we provide examples which show that there exists a type of approximate identity between the class of bounded weak approximate identities and bounded approximate identities.

‎Our aim in this paper is to investigate some geometrical properties of Berger spheres i‎.e.‎,‎ ‎homogeneous‎‎Ricci solitons and harmonicity properties of invariant vector fields‎. ‎We determine all vector fields‎,‎ which are critical points for the energy‎ ‎functional restricted to vector fields of the same length‎. ‎We also see that do‎‎ not exist any vector fields defining harmonic map‎, ‎and the energy of critical points is explicitly calculated.

In this work, we study some spectral properties of one dimensional Dirac system, such as formally self-adjointness, orthogonality of eigenfunctions, Green's function, existence of a countable sequence of eigenvalues. Later, we give an expansion formula in eigenfunctions for Dirac operator on time scales. These results will provide an important contribution to the spectral theory of such operators on time scales.

In this paper, an efficient procedure based on the multiquadric radialbasis functions (RBFs) collocation method is applied for the numerical so-lution of the singularly perturbed differential-difference (SPDDE) equation.The method is coupled with the Residual subsampling algorithm for sup-port adaptivity. The problem considered in this paper shows turning pointbehavior which is added to the complexity in the construction of numericalapproximation to the solution of the problem. The proposed algorithm isvery simple to perform. Some numerical examples are given to validate thecomputational efficacy of the suggested numerical scheme.

In this paper, some basic properties of soft hypervector spaces are studied with respect to some well-known operations such as intersection, union, AND, OR, product and sum. Also, the behavior of them is investigated under linear transformations and b-linear transformations.

In this paper, we prove the existence of at least one non-trivial solution for a discrete nonlinearboundary value problem with $phi_c$-Laplacian. The approach is based on variational methods.

In this article we introduce the sequence spaces $left[chi^{3q}_{fmu },left|left(dleft(x_{1}right),dleft(x_{2}right),cdots, dleft(x_{n-1}right)right)right|_{p}right]^{textit{I}left(Fright)}$ and $left[Lambda^{3q}_{fmu },left|left(dleft(x_{1}right),dleft(x_{2}right),cdots, dleft(x_{n-1}right)right)right|_{p}right]^{textit{I}left(Fright)},$ associated with the differential operator of sequence space defined by Musielak. We study some basic topological and algebraic properties of these spaces. We also investigate some inclusion relations related to these spaces.

This paper is devoted to solve a class of differential equation with simultaneously combining variable coeffcients and variable delays namely variable-delay dierential equations (VDDEs). For this purpose, a numerical method is proposed in which the unknown function and its derivative are approximated with the basis of interpolating Multiquadric radial basis functions (MQRBFs) at arbitrary collocation points. According to the existing mechanism, the synchronization problem is recast to a system of algebraic equations. In the other hand, the proposed method provides a very adjustable framework for approximation according to the discretization and due to a board range of arbitrary nodes. Finally, some illustrative examples are given to verify the validity and applicability of the new technique and also a comparison betweenour results and the existing studies is performed.

The inverse connective eccentricity index of a connected graph G is defined as ξ−1ce (G) =P u∈V(G)ǫG(u)dG(u) , where ǫG(u) and dG(u) are the eccentricity and degree of a vertex u in G,respectively. In this paper, we obtain an upper bounds for inverse connective eccentricity indices for various classes of graphs such as generalized hierarchical product graph and F-sum of graphs.

Singular Spectrum Analysis (SSA) is a non-parametric and rapidly developing method of time series analysis. Recently, this technique receives much attention in a variety of fields. In SSA, a special matrix that is called lag-covariance matrix plays a pivotal role in analyzing stationary time series. The objective of this paper is to examine whether the Empirical Spectral Distribution (ESD) of lag-covariance matrix converges to Marˇcenko{Pastur distribution or not. Such limiting distribution can help us to provide more reliable statistical inference when encountering with high-dimensional data. Moreover, a simulation study is performed and some tools of Random Matrix Theory (RMT) are used.

‎In this paper‎, ‎by making use of q -derivative we introduce a new subclass of meromorphically univalent functions‎. ‎Precisely‎, ‎we give a necessary and sufficient coefficient condition for functions in this class‎. ‎Coefficient estimates‎, ‎extreme points‎, ‎convex linear combination Radii of starlikeness and convexity and finally partial sum property are investigated‎.

 In this paper the author used Salagean differential operator to define a certain subclass of spirallike functions and obtain some convolution results and some upper bounds on the coefficients.

In this work, we have created the four families of memory methods by convergence rates of three, six, twelve, and twenty-four. Every member of the proposed class has a self-accelerator parameter. And, it has approximated by using Newton’s interpolating polynomials. The new iterative with memory methods have a 50% improvement in the order of convergence.