https://science.thanglong.edu.vn/index.php/volc/issue/feed 2023-10-10T07:42:18+00:00 Open 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/112 2023-10-10T07:42:18+00:00 Prof Baez John C. Baez@math.ucr.edu

During what Vietnamese call the American War, Alexander Grothendieck spent three weeks teaching mathematics in and near Hanoi. Hoàng Xuân Sính took notes on his lectures and later did her thesis work with him by correspondence. In her thesis she developed the theory of ‘Gr-categories’, which are monoidal categories in which all objects and morphisms have inverses. Now often called ‘2-groups’, these structures allow the study of symmetries that themselves have symmetries. After a brief account of how Hoàng Xuân Sính wrote her thesis, we explain some of its main results, and its context in the history of mathematics.

2023-09-10T00:00:00+00:00 Copyright (c) 2023 Thang Long Journal of Science: Mathematics and Mathematical Sciences https://science.thanglong.edu.vn/index.php/volc/article/view/87 2023-05-04T05:55:14+00:00 Muu Le Dung ldmuu@math.ac.vn Jean Jacques Strodiot jean-jacques.strodiot@unamur.be Xuan Thanh Le lxthanh@math.ac.vn

We provide a brief survey on basic solution approaches for solving the equilibirum problem defined by the Nikaido-Isoda-Fan inequality. Namely, first we state the problem and consider its most important special cases including the optimization, inverse optimization, Kakutani fixed point, variational inequality, Nash equilibrium problems. Next, we present some basic solution approaches for the problem. Finally, as an application, we consider the famous Cournot-Nash oligopolistic equilibrium model and discuss algorithms for solving it.

2023-09-10T00:00:00+00:00 Copyright (c) 2023 Journal of Mathematics and Mathematical Sciences https://science.thanglong.edu.vn/index.php/volc/article/view/88 2023-05-04T06:33:19+00:00 vietdung@math.ac.vn nguyenninhsp@gmail.com

In [4] M. Farber defined the topological complexity TC(X) of a path-connected space X. Generalizing this notion, ten years later, Yu. Rudyak introduced a sequence of invariants, called the higher topological complexities TCn(X), for any path-connected space X in [7]. These invariants have their origin in the notion of the Schwarz genus of a fibration defined in [8]. One of the tools used to calculate these invariants is the product inequality for the Schwarz genus. In this paper, we will give a generalization of the product inequality of the higher topological complexity.

2023-09-10T00:00:00+00:00 Copyright (c) 2023 Journal of Mathematics and Mathematical Sciences https://science.thanglong.edu.vn/index.php/volc/article/view/90 2023-05-19T03:15:26+00:00 Quang Duy Tran trqduy@gmail.com Minh Hoang Trong minhht.ptit@gmail.com

In recent years, blockchain technology, with its outstanding advantages in terms of security and decentralized data storage, has quickly been applied in education, especially in managing educational certificates. The traditional paper certificate management process has many limitations on security, storage, verification, ownership, and prevention of certificate fraud and tampering. With emerging blockchain technology, the traditional paper certificate management process has changed to a new stage with massive benefits and opportunities to overcome the above challenges. Following this approach, many blockchain-based applications have been proposed, and several universities worldwide have adopted various solutions based on blockchain technology. This paper presents implementing an educational certificate management system based on blockchain technology using the Hyperledger Fabric platform. Our proposed solution can be solved in almost storage and security aspects of certificate management problems, such as confidence, verification, ownership, and tamper avoid.

2023-09-10T00:00:00+00:00 Copyright (c) 2023 Journal of Mathematics and Mathematical Sciences https://science.thanglong.edu.vn/index.php/volc/article/view/89 2023-05-04T07:06:56+00:00 JunJie Wee weej0016@e.ntu.edu.sg Hai Khoi Le le-hai.khoi@usth.edu.vn

In this paper, we survey the results on the Korenblum Maximum Principle for some weighted function spaces. Progress and results discussed include the upper bounds and lower bounds of Korenblum constants, as well as the failure of the principle for weighted Bergman spaces, weighted Hardy spaces, weighted Bloch spaces, weighted Fock spaces, and mixed norm spaces. Existing and new open questions are provided.

2023-09-10T00:00:00+00:00 Copyright (c) 2023 Journal of Mathematics and Mathematical Sciences https://science.thanglong.edu.vn/index.php/volc/article/view/93 2023-06-02T09:26:55+00:00 quangsd@hnue.edu.vn

Let F be an algebraically closed field of characteristic p ≥ 0, which is complete with respect to a non-Archimedean absolute value. Let V be a projective subvariety of PM(F). In this paper, we will prove some second main theorems for non-Archimedean meromorphic maps of Fm into V intersecting a family of hypersurfaces in N-subgeneral position with truncated counting functions.

2023-09-10T00:00:00+00:00 Copyright (c) 2023 Journal of Mathematics and Mathematical Sciences