https://science.thanglong.edu.vn/index.php/volc <p>About Mathematics and Mathematical Sciences (Vol. C), published in English language.</p> Thang Long University en-US Thang Long Journal of Science: Mathematics and Mathematical Sciences 3030-4911 https://science.thanglong.edu.vn/index.php/volc/article/view/167 In this paper we investigate the uniqueness of L-functions sharing finite sets with meromorphic functions having deficient poles. As a 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]. Hoai An Vu Chanthaphone Phommavong Copyright (c) 2024 Thang Long Journal of Science: Mathematics and Mathematical Sciences 3 2 https://science.thanglong.edu.vn/index.php/volc/article/view/117 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 [8]. Huong Duong Quy Pham Hung Copyright (c) 2024 Thang Long Journal of Science: Mathematics and Mathematical Sciences 3 2 https://science.thanglong.edu.vn/index.php/volc/article/view/159 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. Marko Kostic Copyright (c) 2024 Thang Long Journal of Science: Mathematics and Mathematical Sciences 2024-11-21 2024-11-21 3 2 https://science.thanglong.edu.vn/index.php/volc/article/view/208 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. Viet Anh Tran Copyright (c) 2024 Thang Long Journal of Science: Mathematics and Mathematical Sciences 3 2 https://science.thanglong.edu.vn/index.php/volc/article/view/166 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. After that, we prove a Massera-type principle that the corresponding linear equation has a unique AP-, AAP- and PAP- mild solution if the right hand side and the coefficient functions are AP-, AAP- and PAP- functions, respectively. The well-posedness of semilinear equa- tion is proved by using fixed point arguments and the exponential decay of mild solutions is established by using Gronwall’s inequality. Although our works revisits some previous works on well-posedness of these types of mild solutions for the Lin ́eard equation but provide a difference view by using Green function and go further on the aspects of asymptotic behaviour of solutions and the construction of abstract theory. Our abstract results can be also applied to other parabolic evolution equations. Doctor Minh Nguyet Tran Doctor Thi Loan Nguyen Doctor Thi Van Nguyen Doctor Truong Xuan Pham Copyright (c) 2024 Thang Long Journal of Science: Mathematics and Mathematical Sciences 3 2 https://science.thanglong.edu.vn/index.php/volc/article/view/160 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. Duc Quang Si Mr. Duc Ngoc Tran Ms. Thi Thuy Hang Do Copyright (c) 2024 Thang Long Journal of Science: Mathematics and Mathematical Sciences 3 2 https://science.thanglong.edu.vn/index.php/volc/article/view/187 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 equilibrium models. Dung Muu Le Ngoc Hai Nguyen Copyright (c) 2024 Thang Long Journal of Science: Mathematics and Mathematical Sciences 3 2 https://science.thanglong.edu.vn/index.php/volc/article/view/169 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. Van Luu Do Lam Tung Nguyen Copyright (c) 2024 Thang Long Journal of Science: Mathematics and Mathematical Sciences 3 2