Journal of Advanced Mathematical Modeling
https://jamm.scu.ac.ir/
Journal of Advanced Mathematical Modelingendaily1Thu, 22 Aug 2024 00:00:00 +0330Thu, 22 Aug 2024 00:00:00 +0330A Finite Difference Method for Smooth Solution of a System of Linear Volterra Integral Equations
https://jamm.scu.ac.ir/article_19462.html
In this paper, we propose a finite difference numerical method for the smooth solution of a system of linear Volterra integral equations. This method is a generalization of the finite difference method proposed in [11] and [12] for scalar linear Volterra integral equations. Error analysis of this method is presented via asymptotic expansion of the absolute error, and verification of accuracy is examined by two illustrative test problems.A seasonal Integer-Valued AR(1) model with delaporte marginal distribution
https://jamm.scu.ac.ir/article_19403.html
Real-count data time series often show the phenomenon of over-dispersion. In this paper, we introduce the first-order integer-valued autoregressive process with seasonal structure. The univariate marginal distribution is derived from the Delaporte distribution and the innovations are convolution of Poisson with &alpha;-fold zero modified geometric distribution, based on binomial thinning operator, for modeling integer-valued time series with over-dispersion. Some properties of the model are derived. The methods of Yule-Walker, conditional least squares, and conditional maximum likelihood are used to estimate the parameters. The Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. At the end, this model is illustrated using a real data set and is compared to some INAR(1) models.α-TYPE SHORT MODULES
https://jamm.scu.ac.ir/article_19540.html
In this paper, we first consider the concept of type Noetherian dimension of a module such as $M$, which is dual of the type Krull dimension, denoted by $\tndim\, (M)$, and defined to be the codeviation of the poset of the type submodules of $M$, then we dualize some basic results of type Krull dimension for type Noetherian dimension. In the following, we introduce the concept of $\alpha$-type short modules (i.e., for each type submodule $A$ of $M$, either $\ndim\, (\frac{M}{A})\leq \alpha$ or $\tndim\, (A)\leq \alpha$ and $\alpha$ is the least ordinal number with this property), and extend some basic results of $\alpha$-short modules to $\alpha$-type short modules. In particular, it is proved that if $M$ is an $\alpha$-type short module, then it has type Noetherian dimension and $\tndim\, (M)=\alpha$ or $\tndim\, (M)=\alpha+1$.A numerical method based on generalized log orthogonal functions for solving cordial Volterra integral equations of the third kind
https://jamm.scu.ac.ir/article_19478.html
&lrm;This paper is devoted to solving cordial Volterra integral equations of the third kind&lrm;. First, &lrm;generalized log orthogonal functions are introduced and their properties is investigated. &lrm;Then by using this kind of orthogonal functions as basis function in spectral collocation method, a numerical method is proposed to solve this kind of integral equations. &lrm; &lrm;The approximation error and convergence analysis of the presented method are investigated&lrm;. In order to verify the efficiency and accuracy of the presented method &lrm;&lrm; &lrm;several numerical examples have been considered&lrm;. &lrm;A comparison of the obtained results demonstrates that the current method is less expensive and more efficient than some previously proposed methods&lrm;.On λ-pure exact structure
https://jamm.scu.ac.ir/article_19544.html
Let &lambda; be an infinite regular cardinal and A be a locally &lambda;-presentable additive category. It is shown that the class of all &lambda;-pure short sequences in A induces an exact structure on A. Furthermore, we will show that any &lambda;-pure short sequence is a &lambda;-directed colimit of split sequences. In the case in which C is a class of objects in A which is closed under isomorphisms, we prove that C is closed under &lambda;-directed colimits if and only if it is closed under &lambda;-pure homomorphic images.Conditional Weighted Operators in $L^{2}(\Sigma)$-Semi-Hilbertian space
https://jamm.scu.ac.ir/article_19601.html
In this paper, we discuss matrix theoretic characterization for weighted conditional operators by properties of conditional expectation operator in some operator classes on $L^{2}(\Sigma)$-semi-Hilbertian space such as self-adjoint, isometry and normal classes of these type operators on this space. Also, we consider the matrix representation of the Moore-Penrose inverse for these types of operators. We also gave examples to show our results.Positive solutions for semilinear elliptic problem with nonlinear boundary condition on conical Sobolev spaces
https://jamm.scu.ac.ir/article_19629.html
In this paper, a system of elliptic equations with a perturbation in the system and also the nonlinear Neumann boundary conditions near a conical singular point are studied. By introducing the conical Sobolv space and using variational methods and Nehari manifold method, we will prove the existence of at least two positive solutions for this problem on the conical Sobolev space.Ideals, grills, primals and filters from the categorical viewpoint
https://jamm.scu.ac.ir/article_19657.html
In this paper, we study the categorical structures of the concepts of ideal, grill, primal, and filter, which play a fundamental and important role in the study of topology spaces. Some researchers have shown that all these concepts are equivalent, regardless of the categorical viewpoint. Here, we define the homomorphisms and so the category of each of these concepts and then show that all of them are isomorphic, except for the category of filters. As an important result, it has been shown that these categories are topological, except for the category of filters. Consequently, they are complete and cocomplete, but they are not algebraic. Thus, many topological properties can be easily expressed and analyzed in terms of each of these concepts. Finally, some categorical structures of ideals are described.