Acta Mathematica Vietnamica
Search within journal
Volumes and issues
Issue 1, Volume 51, March 2026
2026
-
A Local Limit Theorem for Nonlattice Multidimensional Random Walks in Cones D. C. Pham , M. Peigné , D. T. Son PDF1-21
▸ Abstract
We study the asymptotic behavior of a nonlattice random walk in a general cone of $\mathbb {R}^d$. Following the approach initiated by D. Denisov and V. Wachtel in [8], we use a strong approximation of random walks by the Brownian motion and prove local limit theorems, combining integral theorems for random walks in cones with classical theorems for unrestricted random walks.
-
Zassenhaus Filtrations as Intersections Ján Mináč , Duy Tân Nguyễn , Thị Trà Nguyễn PDF23-35
▸ Abstract
Zassenhaus filtrations of profinite groups are an important tool to study profinite groups. In this paper, we describe Zassenhaus filtrations of profinite groups as intersections of kernels of certain representations. In this way we introduce a link between studying profinite groups with methods of Zassenhaus filtrations and representation theory.
-
On the Global Attractor for the 3D Viscous Camassa-Holm Equations with Damping Term in the Whole Space Nguyen Hai Ha Giang , Trinh Dang Duong , Vu Manh Toi PDF37-64
▸ Abstract
We consider the 3D viscous Camassa-Holm equations with damping term in the whole space. Firstly, we prove the existence, uniqueness and regularity of global weak solutions to the equations. Then we prove the existence of a compact global attractor for the associated continuous semigroup. To overcome the essential difficulty when proving the asymptotic compactness of the semigroup, which arises due to the lack of compactness of the Sobolev embeddings, we exploit the energy equation method. Next, by using the regularity of weak solutions and inductive arguments, we study the Sobolev regularity of the global attractor. Finally, we give an explicit upper bound for the fractal dimension of the global attractor.
-
The Depth Formula for Modules Over Quotients of Gorenstein Rings Tran Nguyen An , Pham Hung Quy PDF65-73
▸ Abstract
A foundational result by C. Huneke and V. Trivedi provides a formula for the depth of an ideal in terms of height, computed over a finite set of prime ideals, for rings that are homomorphic images of regular rings. Building on a result by the first author for local quotients of Cohen-Macaulay rings, this paper first gives a new proof for the depth formula and derives a similar formula for the finiteness dimension. Our main result then establishes the depth formula for non-local rings that are homomorphic images of a finite-dimensional Gorenstein ring.
-
An Improvement on Discrete Li–Yau Inequality Bin Shen , Yuhan Zhu PDF75-84
▸ Abstract
In this paper, we study the discrete Li–Yau gradient estimates for the positive solutions u to the heat equation on graphs under $CDE(n,-K)$ condition and derive a sharper estimate than Bauer et al. (J. Differ. Geom. 99(3), 359–405 2015) and Wang and Zhang (Comm. Anal. Geom. 27(4), 969–989 2019).
-
A Priori Error Analysis of a Space-Time Finite Element Method for Advection-Diffusion Equations Thi Thanh Mai Ta PDF85-102
▸ Abstract
We investigate a space-time finite element method for solving a parabolic advection-diffusion problem. We use the Banach-Nečas-Babuška theorem to show the well-posedness of the continuous Petrov-Galerkin variational formulation for this problem. A fully discrete finite-element scheme is analyzed using the standard Galerkin method and unstructured meshes. An optimal error estimate is established in a discrete energy norm under a globally regularity condition. Some numerical results corroborate our theoretical results.
-
Global Error Bounds for Nonmonotone Affine Variational Inequalities Hoang Ngoc Tuan PDF103-122
▸ Abstract
In this paper, we investigate global error bounds for nonmonotone affine variational inequalities in finite-dimensional spaces. We establish a characterization of global error bounds on the feasible sets of these problems. Furthermore, we derive several sufficient conditions and necessary conditions for the existence of global error bounds on the feasible sets. Our results complement existing findings for some classes of monotone affine variational inequalities. Several illustrative examples are presented to demonstrate the applicability of the obtained results.
-
Solution Existence and Stability of the Semi-Affine Variational Inequality Problem on Hilbert Spaces Vu Van Dong , Nguyen Nang Tam PDF123-141
▸ Abstract
This paper investigates the solution existence and stability of the semi-affine variational inequality problem in real separable Hilbert spaces. We demonstrate that, under suitable conditions, the solution set of the semi-affine variational inequality problem is nonempty. Additionally, we consider some related stability analyses of the problem. The obtained results contribute to and complement the existing literature.
-
A Class of Finite $m$-Cyclic Groups Hailin Liu , Zhuhua Shi , Xiangyu Chen PDF143-156
▸ Abstract
A finite group $G$ is called an $m$-cyclic group if it has $m$ cyclic subgroups. In this paper, we classify finite 14-cyclic groups. These results involve a subclass of finite $m$-cyclic groups of order $n$ with $|\pi (n)|\le 3$, where $|\pi (n)|$ is the number of prime divisors of $n$.
-
Erratum to the Article “Maximal Subgroups of Almost Subnormal Subgroups in Division Rings” [Acta Mathematica Vietnamica (2022) 47:197–209] Bui Xuan Hai PDF157-158
▸ Abstract
The aim of this short communication is to say about some mistake in the proof of Theorem 2 in my original article “Maximal subgroups of almost subnormal subgroups in division rings” (Bui Xuan Hai, Acta Mathematica Vietnamica 47, 197–209, 2022). Further, some weaker version of this theorem will be provided.