https://science.thanglong.edu.vn/index.php/volc <p>About Mathematics and Mathematical Sciences (Vol. C), published in English language.</p> en-US tapchikh@thanglong.edu.vn (Thang Long Journal of Science: Mathematics and Mathematical Sciences) hotro@vojs.vn (VOJS) Thu, 29 Sep 2022 00:00:00 +0700 OJS 3.2.1.1 http://blogs.law.harvard.edu/tech/rss 60 https://science.thanglong.edu.vn/index.php/volc/article/view/39 The paper extends author’s method of modular distributions (2002, [75]) to arithmetic automorphic L functions on general classical groups. Main resultat gives a p-adic interpolation of their critical L values in the form of integrals of distributions constructed from a given eigen function of Hecke algebras by applying BGG modules, (see also preprints [78] and [79]. In particular, algebraic differential operators are described acting on auto-morphic forms ' on unitary groups U(n; n) over an imaginary quadratic field K=ℚ-DK⊂ℂ. Applications are given to Shimura’s zeta functions L(s,f) [90] attached special L-values L(s,φ) attached to φ. and normalized in accordance with Deligne’s Gamma factors rule [21]. An explicit description of Shimura’s Γ-factors is used. Alexei Pantchichkine Copyright (c) 2023 https://science.thanglong.edu.vn/index.php/volc/article/view/39 Tue, 27 Sep 2022 00:00:00 +0700 https://science.thanglong.edu.vn/index.php/volc/article/view/41 In this article, we propose to present several recent results: a new proof of the p-adic Hermite-Lindemann Theorem, a new proof of the p-adic Gel'fond-Schneider Theorem, exceptional values of meromorphic functions and derivatives and the p-adic Nevanlinna theory applied to small functions. We first have to recall the definitions of the p-adic logarithm and exponential. Alain Escassut Copyright (c) 2023 https://science.thanglong.edu.vn/index.php/volc/article/view/41 Tue, 20 Sep 2022 00:00:00 +0700 https://science.thanglong.edu.vn/index.php/volc/article/view/50 We explain a new idea of how to use the high probability interval thresholds for neurons in quantum neural networks. Some basic quantum neural networks were analyzed and constructed in a recent work of the author. In particular the Least Square Error Problem (LSEP) and the Linear Regression Problem (LRP) was discussed. In this paper we an- alyze a new look on the threshold rules for neurons, taking the intervals of high probability in place of classical sigmoid half-line threshold and then we construct the least-square quantum neural network (LS-QNN), the poly- nomial interpolation quantum neural network (PI-QNN), the polynomial regression quantum neural network (PR-QNN) and chi-squared quantum neural network (X2-QNN). We use the corresponding solutions or statistical tests as the threshold for the corresponding training rules. Ngoc Diep Do Copyright (c) 2023 https://science.thanglong.edu.vn/index.php/volc/article/view/50 Tue, 20 Sep 2022 00:00:00 +0700 https://science.thanglong.edu.vn/index.php/volc/article/view/49 Fritz John necessary conditions for local Henig and global efficient solutions of vector equilibrium problems involving equality, inequality and set constraints with nonsmooth functions are established via convexificators. Under suitable constraint qualications, Kuhn-Tucker necessary conditions for local Henig and gobally efficient solutions are derived. Note that Henig and global efficient solutions of (VEP) are studied with respect to a closed convex cone. Sufficient condition for Henig and globally efficient solutions are derived under some assumptions on asymptotic semiinvexityinfne of the problem. Some illustrative examples are also given. Van Luu Do, Thi Mai Tran Copyright (c) 2023 https://science.thanglong.edu.vn/index.php/volc/article/view/49 Tue, 20 Sep 2022 00:00:00 +0700 https://science.thanglong.edu.vn/index.php/volc/article/view/51 Secure communication in general and secure dialogue in particular are highly demanded, especially in the current information exploding era. Here we are concerned with secure dialogue. Because any dialogue conducted merely by classical means is fully eavesdropped without traces left behind, quantum version of dialogue, the so-called quantum dialogue, offers a promising solution to the security problem. The security desired does not simply focus on the exchanged information but also on their classical correlations, i.e., a quantum dialogue protocol should be protected from both information theft and information leakage. Such a secure quantum dialogue protocol is proposed in this paper employing Greenberger-Horne-Zeilinger states as the quantum channel. The above-mentioned requirement for security is achieved in message rounds by using extra random bits for the encoding/decoding processes combined with two kinds of control rounds which are designed to detect eavesdropping, if any. Ba An Nguyen Copyright (c) 2023 https://science.thanglong.edu.vn/index.php/volc/article/view/51 Tue, 20 Sep 2022 00:00:00 +0700 https://science.thanglong.edu.vn/index.php/volc/article/view/52 In this paper, we give a new class of unique range sets for meromorphic functions ignoring multiplicity with 15 elements. Hoai An Vu Copyright (c) 2023 https://science.thanglong.edu.vn/index.php/volc/article/view/52 Sun, 11 Sep 2022 00:00:00 +0700 https://science.thanglong.edu.vn/index.php/volc/article/view/53 We prove the existence of the pullback attractor of the generated ow by a dissipative nonautonomous diferential equations driven by unbounded variation paths under the condition of smallness of nonlinear term. In case perturbed term is linear we prove that the attractor is singleton and also is forward one. Thanh Hong Phan Copyright (c) 2023 https://science.thanglong.edu.vn/index.php/volc/article/view/53 Sun, 11 Sep 2022 00:00:00 +0700 https://science.thanglong.edu.vn/index.php/volc/article/view/54 We give all solutions of the equation F(n2 + m2 + k) = H(n) + H(m) + K (∀n;m ∈ N), where k ∈ N is the sum of two xed squares, K ∈ C and F, H are completely multiplicative functions. Imre Kátai, B. M. M. Khanh, B. M. Phong Copyright (c) 2023 https://science.thanglong.edu.vn/index.php/volc/article/view/54 Tue, 20 Sep 2022 00:00:00 +0700