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

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.

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.

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.

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.

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.

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.

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.