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Bài báo/Newspaper Second-order optimality conditions for strict local Pareto minima of cosntrained nonsmooth multiobjective optimization problems Authors: Do Van Luu (2024) This paper presents primal and dual Fritz John secondorder necessary conditions for strict local Pareto minima of order two of nonsmooth vector optimization problems in terms of the P´ales–Zeidan second-order directional derivatives without constraint qualifications. Dual second-order Karush–Kuhn–Tucker necessary and sufficient conditions for strict local Pareto minima of order two are established under a suitable constraint qualification.

Bài báo/Newspaper A proximal point algorithm for solving a class of implicit equilibrium models Authors: Dung Muu Le (2024) We apply the proximal point algorithm to solve a class of implicit price equilibrium models including the Walras supply-demand and competitive equilibrium ones, where both supply and demand are given implicitly as the solution-sets of mathematical programs depending on the price. Such models are formulated as complementarity or variational inequality forms. We employ a monotonicity property of the cost operator to develop proximal point based algorithms to approximate an equilibrium point of the model. Convergence of the algorithm is proved and some computational results with many randomly generated data are reported to show that the proposed algorithms work well for this class of eq...

Bài báo/Newspaper Differentiably nondegenerate Meromorphic mappings on K\"{a}hler manifolds weakly sharing hyperplanes Authors: Si Duc Quang (2024) In this paper, we study the uniqueness problem for differentiably nondegenerate meromorphic mappings from a K\"{a}hler manifold into $\P^n(\C)$ satisfying a condition $(C_\rho)$ and sharing hyperplanes in general position, where the condition that two meromorphic mappings $f,g$ have the same inverse image for some hyperplanes $H$ is replaced by a weaker one that $f^{-1}(H)\subset g^{-1}(H)$. An improvement on the algebraic dependence problem of differentiably nondegenerate meromorphic mappings also is given. Moreover, in this case, the condition $f^{-1}(H)\subset g^{-1}(H)$ is even omitted for some hyperplanes.

Bài báo/Newspaper On certain classes of mild solutions of the scalar Liénard equation revisited Authors: Tran Minh Nguyet (2024) In this work we revisit the existence, uniqueness and expo- nential decay of some classes of mild solutions which are almost periodic (AP-), asymptotically almost periodic (AAP-) and pseudo almost peri- odic (PAP-) of the scalar Lin ́eard equation by employing the notion of Green function and Massera-type principle. First, by changing variable we convert this equation to a system of first order differential equations. Then, we transform the problem into a framework of an abstract parabolic evolution equation which associates with an evolution family equipped an exponential dichtonomy and the corresponding Green function is exponen- tially almost periodic.

Bài báo/Newspaper A self-adaptive step size algorithm for solving the split feasibility problem with multiple output sets in Hilbert spaces Authors: Viet Anh Tran (2024) The purpose of this manuscript is to introduce a new self- adaptive algorithm for solving the split feasibility problem with multiple output sets in real Hilbert spaces. Our algorithm leverages information from previous steps to guide its execution, thereby removing the need to compute or estimate the norm of the given operator. Lastly, we present a simple numerical example to illustrate the performance of our proposed algorithm.

Bài báo/Newspaper Multi-dimensional Poisson transform and applications Authors: Marko Kostic (2024) In this paper, we consider several new types of multi-dimensional Poisson transforms for the functions with values in complex Banach spaces. We also prove some new properties of multidimensional vector-valued Laplace transform and analyze certain connections between the solutions of the abstract fractional partial differential equations and the abstract fractional partial difference equations.

Bài báo/Newspaper Upper bound of multiplicity in Cohen-Macaulay rings of prime characteristic Authors: Huong Duong (2024) Let (R,m) be a local ring of prime characteristic p and of dimension d with the embedding dimension v, type s and the Frobenius test exponent for parameter ideals Fte(R). We will give an upper bound for the multiplicity of Cohen-Macaulay rings in prime characteristic in terms of Fte(R), d, v and s. Our result extends the main results for Gorenstein rings due to Huneke and Watanabe

Bài báo/Newspaper Uniqueness of L-functions sharing finite sets with meromorphic functions having Deficient Poles Authors: Hoai An Vu (2024) n this paper we investigate the uniqueness of L-functions sharing finite sets with meromorphic functions having deficient poles. Asa consequence, we have exhibited a extended version of a recent result of A. Banerjee and A. Kundu [1]. The results obtained in this paper improve and extend a recent result due to Khoai-An-Phuong [10] and a some result in [18].