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/274 The paper proposes a novel hybrid cutting-projection method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, the method only requires to solve a strongly convex optimization program at each iteration without the extra-steps as extragradient methods. The strongly convergence theorem is established and some numerical examples are presented to illustrate its convergence. Van Hieu Dang MSc Kim Quy Pham Copyright (c) 2026 Thang Long Journal of Science: Mathematics and Mathematical Sciences 2026-04-25 2026-04-25 5 1 https://science.thanglong.edu.vn/index.php/volc/article/view/295 Differential-algebraic equations (DAEs) play an important role in many applied models, yet their analysis is complicated by algebraic constraints. A central difficulty is the definition of the index. We propose a new index definition for DAEs based on the classical index of a matrix pencil. This approach ensures projection independence and provides explicit solution formulas for DAEs of index at most two, while also clarifying the relation to März’s index. Thi Thanh Nga Ngo Copyright (c) 2026 Thang Long Journal of Science: Mathematics and Mathematical Sciences 2026-04-25 2026-04-25 5 1 https://science.thanglong.edu.vn/index.php/volc/article/view/298 Qi [23] first demonstrated that if an entire function and its shift operator share two distinct periodic functions, then they must coincide. This foundational result has stimulated further research into analogous problems within broader and more generalized framework. In this survey, we systematically develop the theory of periodicity and related topics for various shift operators associated with meromorphic functions, under both normal and partial sharing conditions. This work offers a fresh perspective on the theory of shift operators, streamlining existing results to present them in a compact form. It also includes our own contributions to this specific area of literature with a number illustrative examples. Jhilit Banerjee Doctor Abhijit Banerjee Copyright (c) 2026 Thang Long Journal of Science: Mathematics and Mathematical Sciences 2026-05-25 2026-05-25 5 1 https://science.thanglong.edu.vn/index.php/volc/article/view/332 In this paper, we explore robust duality results between the primal nonsmooth nonconvex single-objective optimization problem with uncertain data (UNMP) and its Mond-Weir-type dual model (DUNMP) in terms of ϵ-upper convexificators: weak ϵ-duality theorem, strong ϵ-duality theorem and converse ϵ-duality theorem, where ϵ ≥ 0. Diệu Hằng Đinh PGS Văn Sự Trần Copyright (c) 2026 Thang Long Journal of Science: Mathematics and Mathematical Sciences 2026-05-23 2026-05-23 5 1 https://science.thanglong.edu.vn/index.php/volc/article/view/339 The purpose of this paper is to investigate a Bregman projection algorithm for solving split feasibility problem with multiple output sets. The proposed algorithm is motivated by the ideas of the Halpern method, the CQ method and the Tseng method. Our proposed algorithm employs the inertial technique and a self-adaptive step size to guarantee a high rate of convergence. The strong convergence theorem is established without prior knowledge of the operator norm and the Lipschitz continuous assumption on the operators involved. A numerical experiments with graphical illustrations are presented to demonstrate the effectiveness and the performance of our proposed algorithm in comparison with some existing ones. Xuân Lý Lê Copyright (c) 2026 Thang Long Journal of Science: Mathematics and Mathematical Sciences 2026-05-23 2026-05-23 5 1 https://science.thanglong.edu.vn/index.php/volc/article/view/344 In this paper, we propose a new self-adaptive inertial and relaxed CQ algorithm for solving the split feasibility problem in real Hilbert spaces. The method incorporates alternated inertial extrapolation, a conjugate-gradient-inspired search direction, and a self-adaptive step-size strategy, which eliminates the need for operator norm evaluations or line search procedures. Under suitable assumptions, we establish strong convergence of the generated sequence to the minimum-norm solution of the problem. To illustrate the practical applicability of the proposed method, we apply it to an elastic net regularization model. The numerical experiment shows that the algorithm converges effectively and is suitable for high-dimensional regression problems. Văn Hưng Nguyễn Copyright (c) 2026 Thang Long Journal of Science: Mathematics and Mathematical Sciences 2025-05-18 2025-05-18 5 1