نشریه مدل سازی پیشرفته ریاضی
سال چهاردهم شماره 2 (پیاپی 34، تابستان 1403)

‎In this paper‎, ‎combining the subgradient extragradient method with‎‎ inertial method‎, ‎we introduce a new iterative algorithm for solving equilibrium problems in real Hilbert spaces‎. ‎Moreover‎, ‎we present a new inertial self-adaptive scheme for solving variational inequalities in real Hilbert spaces‎, ‎which it is not necessary to know the Lipschitz constant of the mapping‎. ‎We prove the weak convergence of the generated iterates by presented algorithms‎. ‎To illustrate the usability of our results and also to show the efficiency of the proposed methods‎, ‎we present some comparative examples with several existing schemes in the literature.

In this paper, by employing the variational method, we show that a boundary value problem of sixth order has infinitely many solutions. In fact, via a critical point theorem, we will present sufficient conditions such that the problem has a sequence of solutions in a suitable function space. Specific cases and an examples of results are also stated.

Rough set theory provides a convenient framework to study and compare algebraic operators in many mathematical structures. In this paper, we establish a connection between the causal structure of space-time in Einstein's theory of relativity and the theory of Rough sets based on coverage, and by means of this, we define the covering approximation operators for the causal structure and show that some of these operators are the same basic and common operators in the causal structure of space-time such as I^± ، J^±، D، ⊥, and some operators like ⊥' and ⊥'⊥' and different operators in the causal structure. Recently, causal logic on space-times has been introduced by a complete orthomodular lattice consisting of all constants of the clouser operator ⊥⊥. Here, through the orthogonal operator ⊥' , we introduce another complete lattice and determine the elements of this lattice in causal space-times. Also, we provide a necessary and sufficient condition for this lattice to be orthomodular in global hyperbolic space-times. Finally, we show that these two lattices are isomorphic in the case of two-dimensional Minkowski space-time, but this is not necessarily true in the general case.

‎In this paper‎, ‎we first study the boundedness of generalized‎ weighted composition operators from minimal Möbius invariant‎ ‎subspace to the $n$th weighted type space‎. ‎Then‎, ‎we obtain‎ ‎equivalence conditions for its boundedness by using the Bell‎ ‎polynomials‎. ‎We also find some estimates for the essential‎ ‎norm of this operator and use them to present equivalence‎ ‎conditions for the compactness of such an operator‎.

Suppose that the random matrix X has a matrix variate normal distribution with the mean matrix Θ and covariance matrix Σ⊗Ψ where Σ and Ψ are known positive definite covariance matrices. This paper studies the soft Bayesian shrinkage wavelet estimation of the mean matrix Θ . Soft Bayesian shrinkage wavelet estimator is proposed based on quadratic balanced loss function and matrix variate normal $N_{p,m}(\mathbf{0}, \mathbf{\Lambda}\otimes \mathbf{\Psi})$ prior distribution. Λ is known positive definite covariance matrix. By using the Bayes estimator as the target estimator in the quadratic balanced loss function and Stien's unbiased risk estimate technique, the soft Bayesian shrinkage wavelet threshold is obtained. Based on the new proposed threshold, we find the soft Bayesian shrinkage wavelet estimator of Θ mean matrix. The simulation study and two real examples to measure the performance of the presented theoretical topics are used. The results show that the soft Bayesian shrinkage wavelet estimator dominates classical shrinkage wavelet estimators.

‎‎‎‎‎Let $H(\mathbb{D})$ be the space of all analytic functions on $\mathbb{D}$‎, ‎$u,v\in H(\mathbb{D})$ and $\varphi,\psi$ be self-map $(\varphi,\psi:\mathbb{D}\rightarrow \mathbb{D})$‎. Difference of weighted composition operator is denoted by $uC_\varphi‎ -‎vC_\psi$ and defined as follows‎ ‎\begin{align*}‎ (uC_\varphi‎ -‎vC_\psi)f(z) = u(z) f{(\varphi(z))}‎- ‎v(z) f(\psi(z))‎ ,‎\quad f\in H(\mathbb{D} )‎, ‎\quad z\in \mathbb{D}‎. ‎\end{align*}‎ ‎In this paper‎, ‎boundedness of difference of weighted composition operator from Cauchy transform into Dirichlet space will be considered and ‎an ‎equivalence condition for boundedness of such operator will be given‎.‎‎ Then the norm of composition operator between the mentioned spaces will be studied and it will be shown ‎that‎‎ $\|C_\varphi\|\geq 1$ ‎and‎ there is no composition isometry from Cauchy transform into Dirichlet ‎space‎.‎

‎In this article‎, ‎we present an $SIR$ model with a general nonlinear incidence rate‎, ‎assuming a $100\%$ effective vaccine‎. ‎This system has a disease-free equilibrium point‎, ‎corresponding to which a basic reproduction number $\mathscr{R}_0$‎​ ‎is obtained‎. ‎For $\mathscr{R}_0 > 1$‎, ‎the system will also have an endemic equilibrium point‎. ‎We study the local and global stability of these equilibrium points‎. ‎Considering the change in the stability status of the equilibrium points with the change of one of the parameters‎, ‎we will examine the existence of a transcritical bifurcation‎. ‎Additionally‎, ‎we calculate the sensitivity index of $\mathscr{R}_0$​‎, ‎which essentially determines the susceptibility of the system to the existing parameters‎. ‎Finally‎, ‎we examine the obtained results with numerical examples‎.

The branch and bound algorithm is a widespread method for global optimization. This algorithm partitions the feasible set of the optimization problem through a branching method and then calculates an upper bound and a lower bound for each member of the partition using a bounding method. Finally, the branch and bound method compares the obtained bounds and the objective function values ​​with each other and removes the members of the partition that do not contain an optimal point. In this paper, the branch and bound algorithm for optimizing increasing co-radiant functions on subsets of $\mathbb{R}_+^n$ which are presented in the form of the intersection of a half-space with a simplex (the purpose of considering such feasible sets is to examine a model of financial mathematics, called the mean-standard deviation model). We use the concept of abstract convexity to increase co-radiant functions for bounding (finding lower bounds). In the end, as an application of this optimization problem, we propose the mean-standard deviation model of portfolio optimization and solve it with the branch and bound method.

‎This paper is devoted to solving cordial Volterra integral equations of the third kind‎. First, ‎generalized log orthogonal functions are introduced and their properties is investigated. ‎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. ‎ ‎The approximation error and convergence analysis of the presented method are investigated‎. In order to verify the efficiency and accuracy of the presented method ‎‎ ‎several numerical examples have been considered‎. ‎A comparison of the obtained results demonstrates that the current method is less expensive and more efficient than some previously proposed methods‎.

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.