Tạp chí Khoa học Thăng Long

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

In this article, family structure and land ownership in Vietnam during the first half of the nineteenth century are considered by analyzing two testaments and the land cadastre of the Nguyễn Dynasty.From these, it seems probable that the nineteenth-century Vietnamese village had multi-household compounds that were biased toward patrilocal residence. These compounds share certain characteristics with Southeast Asian multi-household compounds and indicate that paternal kinship groups (dòng họ) were formed from cohabitation groups based on bilateral descent owing to the spread of patrilocal marriage with the popularization of Confucianism in the early modern period.Although abundant village documents still exist in Vietnam, they have not been fully utilized as historical materials owing to a lack of cooperation with anthropologists. The analysis in this article incorporates anthropological as well as historical perspectives and offers new possibilities for the utilization of village documents.

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.

In this paper, we give a new class of unique range sets for meromorphic functions ignoring multiplicity with 15 elements.

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.

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.

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.

Thiên Y A Na is a special female deity in the system of Vietnamese goddesses. On the one hand, historical ups and downs are reflected in the transition of her story; from a story about a Chăm goddess (Po Ina Nagar) to a story about a Vietnamese goddess (Thiên Y A Na). On the other hand, cultural changes, which mask discourses of power, and the cultural symbiosis phenomenon, which represents the vitality of ancient beliefs in spite of the deepening and spreading roots of new beliefs, can be observed from an analysis of performing practices of the Po Ina Nagar/Thiên Y A Na cult.Using theories on folklore genres, including myths and legends, and cultural symbiosis theory as well as the concepts of “discourse” and “invented tradition,” this paper critically analyzes the use of myths and legends in the creation of discourse, identifies the impact of discourses of power on the formation and transformation in the tangible and intangible heritage complex of Tháp Bà Po Ina Nagar (Nha Trang, Khánh Hòa), and confirms that cultural symbiosis has brought about heritage cohesion and encouraged the enduring vitality of the religious life of local communities.

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.

The purpose of this paper is to study uniqueness problem of meromorphic mapping from Cm into the complex space Pn(C) sharing partial fixed and moving hypersurfaces. Using the second main theorems due to S. D. Quang and D. P. An [12, 13], we obtain some uniqueness results. Our results are improved some before results in this trend. In our best knowledge, there are not any uniqueness results of meromorphic mapping partially shared hypersurfaces up to now.