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Hoàng Xuân Sính’s thesis: Categorifying Group Theory
Tập 2 Số 8 - 2023
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
str...
#2-group #Gr-category #Picard category #monoidal category #symmetric monoidal category #crossed module
A STUDY OF PROPERTY INHERITANCE IN THE NINETEENTH CENTURY RED RIVER DELTA
Tập 1 Số 2 - Trang 86-105 - 2021
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 wi...
#Early Modern Vietnam #Lineage #Multi-household compound #Confucianism #Village documents
A NEW CLASS OF UNIQUE RANGE SETS FOR MEROMORPHIC FUNCTIONS IGNORING MULTIPLICITY WITH 15 ELEMENTS
Tập 1 Số 4 - Trang 103-115 - 2022
In this paper, we give a new class of unique range sets for meromorphic
functions ignoring multiplicity with 15 elements.
#Meromorphic Function #uniqueness #ignoring multiplicity.
A blockchain-based Certificate Management System using the Hyperledger Fabric Platform
Tập 2 Số 8 - Trang - 2023
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 b...
A survey on solution approaches for the equilibrium problem defined by the nikaido-isoda-fan inequality
Tập 2 Số 8 - 2023
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 prob...
#Nikaido-Isoda-Fan equilibrium problem #variational inequality #Cournot-Nash equilibrium model
A SURVEY ON A FEW RECENT PAPERS IN 𝙋-ADIC VALUE DISTRIBUTION
Tập 1 Số 4 - Trang 27-56 - 2022
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.
ALGEBRAIC DIFFERENTIAL OPERATORS ON ARITHMETIC AUTOMORPHIC FORMS, MODULAR DISTRIBUTIONS, 𝙋-ADIC INTERPOLATION OF THEIR CRITICAL 𝙇 VALUES VIA BGG MODULES AND HECKE ALGEBRAS
Tập 1 Số 4 - Trang 1-26 - 2023
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
differen...
#Automorphic forms #classical groups #p-adic L-functions #differential operators #non-archimedean weight spaces #quasi-modular forms #Fourier coefficients
INFORMATION-LEAKAGE-FREE QUANTUM DIALOGUE VIA GREENBERGER-HORNE-ZEILINGER STATES
Tập 1 Số 4 - Trang 87-102 - 2023
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 prob...
#Quantum dialogue #GHZ states #information leakage
ON THE EQUATION F(n² + m² + k) = H(n) + H(m) + K
Tập 1 Số 4 - Trang 135-151 - 2022
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.
#Arithmetical function #equation of functions
OPTIMALITY CONDITIONS FOR EFFICIENCY OF CONSTRAINED VECTOR EQUILIBRIUM PROBLEMS
Tập 1 Số 4 - Trang 67-85 - 2023
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 soluti...
#Local Henig efficient solution #local global solution #vector equilibrium problems #Fritz John and Kuhn-Tucker necessary conditions #convexificators