https://science.thanglong.edu.vn/index.php/volc/issue/feedThang Long Journal of Science: Mathematics and Mathematical Sciences2025-11-23T00:00:00+00:00Thang Long Journal of Science: Mathematics and Mathematical Sciencestapchikh@thanglong.edu.vnOpen Journal Systems<p>About Mathematics and Mathematical Sciences (Vol. C), published in English language.</p>https://science.thanglong.edu.vn/index.php/volc/article/view/240Convergence in capacity for Cegrell classes on complex varieties in domains of $C^n$2025-10-09T04:37:38+00:00Diệu Nguyễnngquang.dieu@hnue.edu.vnPhuong Chi Kieukieuphuongchi@sgu.edu.vnVan Long Tangtvlong@hnue.edu.vnLet $V$ be a complex variety embedded in a bounded domain $ D \subset C^n.$ Assuming that the singularities of $ V$ are not too severe — for example, if $V$ is locally irreducible — we prove a convergence in capacity for the complex Monge-Ampère operator acting on plurisubharmonic functions in the Cegrell class on $V$.Copyright (c) 2025 Thang Long Journal of Science: Mathematics and Mathematical Scienceshttps://science.thanglong.edu.vn/index.php/volc/article/view/282Global well-posedness of pseudo almost periodic mild solutions for a Keller-Segel system of parabolic-parabolic type2025-09-12T03:52:06+00:00Thi Van Nguyenvan@tlu.edu.vnThi Ngoc Van Damvandn@hvnh.edu.vnWe study the global existence and uniqueness of pseudo almost periodic mild solutions for the parabolic-parabolic Keller-Segel systems on the real hyperbolic spaces Hn(R), where n ⩾ 2. First, we use the dispersive estimates of the scalar heat semigroup to estabilish the well posedness of bounded mild solutions for the corresponding linear systems. Then, we prove the existence and uniquess of pseudo almost periodic mild solutions by proving a Massara-type principle. Finally, the well-posedness of such solutions for semilinear systems are obtained by employing fixed point arguments.2025-11-12T00:00:00+00:00Copyright (c) 2025 Thang Long Journal of Science: Mathematics and Mathematical Scienceshttps://science.thanglong.edu.vn/index.php/volc/article/view/283Adaptive projection-free methods for constrained variational inequalities in machine learning2025-09-24T02:25:35+00:00Thanh Hieu Phamhieupt@ptit.edu.vnWe propose the Penalty-Regularized Adaptive Constrained Gradient Method (PR-A-CGM), a projection-free algorithm for solving variational inequality problems with pseudo-monotone operators and convex functional constraints. Unlike projection-based methods, PR-A-CGM enforces feasibility by introducing a smooth penalty term into the update direction, avoiding costly or intractable projections while retaining convergence guarantees under pseudo-monotonicity and noisy oracles. We prove weak convergence under standard assumptions, establish strong convergence and rates under stronger conditions, and validate our method on machine learning applications such as fairness-constrained classification. Experiments show that PR-A-CGM improves feasibility and robustness over projection-free baselines while narrowing the gap to projection-based methods. These results highlight penalty-regularized primal methods as practical tools for constrained optimization in modern large-scale learning.2025-11-12T00:00:00+00:00Copyright (c) 2025 Thang Long Journal of Science: Mathematics and Mathematical Scienceshttps://science.thanglong.edu.vn/index.php/volc/article/view/287The linear dependency of L−functions and meromorphic functions sharing finite sets2025-09-24T02:15:40+00:00Hoai An Vuvuhoaianlinh@gmail.comProf Duy Phuong Nguyenphuongnd@tnu.edu.vnIn this paper we investigate the linear dependency of L functions and meromorphic functions sharing finite sets. As a consequence, we present some classes of subsets S,T in C such that for a meromorphic function f and an L-function L, the condition that f and L share S and T, respectively (counting multiplicity) implies f = hL for a non-zero constant h. We discuss some applications of main result. The main result obtained in this paper improves and extends a recent result due to the authors in [32]. We extend previous results of Yuan, Li and Yi [32] by considering distinct finite sets S,T and establishing linear dependency between f and L. Our results are inspired by a work of Yuan, Li, and Yi in [32] and Khoai et al. in [11] and [13].2025-11-12T00:00:00+00:00Copyright (c) 2025 Thang Long Journal of Science: Mathematics and Mathematical Scienceshttps://science.thanglong.edu.vn/index.php/volc/article/view/289A Korenblum Maximum Principle for weighted Hilbert spaces of entire Dirichlet series with real frequencies2025-10-03T09:37:10+00:00Hai Khoi Lele-hai.khoi@usth.edu.vnJunJie WeeIn this paper, we study a Korenblum Maximum Principle for weighted Hilbert spaces of entire Dirichlet series with real frequencies. We investigate dominating sets for which the Korenblum Maximum Principle must hold. The results obtained imply that a dominating set, if exists, must be a left half-plane. This provides a new perspective for studying Korenblum Maximum Principle on function spaces containing the entire Dirichlet series.2025-11-12T00:00:00+00:00Copyright (c) 2025 Thang Long Journal of Science: Mathematics and Mathematical Scienceshttps://science.thanglong.edu.vn/index.php/volc/article/view/288Interaction between a single photon and a weak coherent state mediated by a quantum emitter2025-09-25T04:25:35+00:00Dr. Thanh Dat Ledat.le@aqcircuits.comBa An Nguyenannb@thanglong.edu.vnPhoton-photon interaction, an essential ingredient for optical quantum technologies, is indirect actually, i.e., often mediated via a nonlinear medium. In this work, we consider a single photon interacting with a weak coherent state in a one-dimensional waveguide coupled to a two-level quantum emitter. We present a general input-output framework that applies to an arbitrary input Fock state and various types of quantum emitters. We then use this to compute the relevant scattering processes between the single photon and the weak coherent state. We analyse in detail the characteristics of the output state taking into account the continuous-mode nature of the input and output states which are treated as appropriate photon wavepackets.2025-11-12T00:00:00+00:00Copyright (c) 2025 Thang Long Journal of Science: Mathematics and Mathematical Scienceshttps://science.thanglong.edu.vn/index.php/volc/article/view/284An algorithm for minimizing a strongly convex function on the equilibrium set of price equilibrium models2025-09-24T02:16:39+00:00Hải Nguyễn Ngọchainn@dhcd.edu.vnProf Dung Muu Lemuuld@thanglong.edu.vnWe consider a class of equilibrium models including the im plicit Walras supply-demand and competitive models that, in general, is ill posed. We formulate such a model in the form a variational inequality hav ing certain monotonicity property which allows us to describe an algorithm avoiding the ill-posedness by finding the equilibrium point that is nearest to the given guessed or desired equilibrium price for the model. A main difficulty of the problem is that its feasible domain is not given explicitly as in a standard convex programming problem. The proposed algorithm is a combination between the gradient one and the Mann-Krashnoschelskii f ixed point procedure. The obtained computational results with many ran domly generated data show that the proposed algorithm works well for this class of the equilibrium models.2025-11-12T00:00:00+00:00Copyright (c) 2025 Thang Long Journal of Science: Mathematics and Mathematical Sciences