Acta Mathematica Vietnamica
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Issue 3, Volume 50, September 2025
2025
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A Dirichlet Type Problem for Non-Pluripolar Complex Monge-Ampère Equations Thai Duong Do , Hoang-Son Do , Van Tu Le , Ngoc Thanh Cong Pham PDF305-328
▸ Abstract
In this paper, we study a Dirichlet type problem for the non-pluripolar complex Monge - Ampère equation with prescribed singularity on a bounded domain of $\mathbb {C}^n$. We provide a local version for an existence and uniqueness theorem proved by Darvas et al. (Math. Ann. 379, 95–132, 2021). Our work also extends a result of Åhag et al. (J. Math. Pures Appl. 92, 613–627, 2009).
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Fundamentals and Stability of Positive Fractional-Order Two-Dimensional (2-D) Systems with Delays Tran Ngoc Nguyen , Phan Thanh Nam PDF329-350
▸ Abstract
In this paper, we address the problem of the fundamentals and stability analysis for a class of positive fractional-order two-dimensional (2-D) systems with time-varying delays. Firstly, based on the Banach fixed point theorem, the fundamentals, including the existence, the uniqueness and the continuous dependence of solution, are studied. Next, by using the continuous dependence of solution, a condition for the positivity is derived. Lastly, by developing a solution comparison method, which is based on the system’s positivity, a sufficient condition for the asymptotic stability of the considered system is established. A numerical example is also provided to illustrate the theoretical results.
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Some Liouville Results for Quasilinear Hamilton-Jacobi Type Problems Phuoc Vinh Dinh , Kim Anh T. Le , Phuong Le PDF351-361
▸ Abstract
We prove a Liouville type theorem for nonnegative solutions of the problem $-\Delta_p u + |\nabla u|^\gamma = u^q$ in $\mathbb {R}^N_+$ with zero Dirichlet boundary condition, where $p>2$ and $q>\gamma > p-1$. Our proof combines a recent monotonicity result with a new Liouville type theorem for nonnegative stable solutions in dimension $N
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A New Polyconvolution Operator with the Weight Function Related to the Hartley Integral Transforms $H_2,H_1$ and Applications N. M. Khoa PDF363-373
▸ Abstract
In this work, we define a novel polyconvolution operator with the trigonometric weight function $\gamma =\cos y$ related to the Hartley integral transforms $H_2,H_1$. We then establish some fashionable algebraic properties for this polyconvolution operator. Finally, we state some applications.
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Powers of the Edge Ideals and Matchings in Hypergraphs Fahimeh Khosh-Ahang Ghasr PDF375-386
▸ Abstract
In this work, some combinatorial lower bound for regularity of powers of the edge ideal of a uniform hypergarph is gained. A family of hypergraphs whose regularity of edge ideal attains this bound and has a significant difference from the lower bounds heretofore obtained have also been introduced.
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A Staggered Cell-centered Finite Element Method with Grad-div Stabilization for the Stokes Problems Ong Thanh Hai PDF387-410
▸ Abstract
This paper introduces a novel approach for efficiently approximating solutions to Stokes problems, combining the staggered cell-centered finite element method (SCCFE) with grad-div stabilization (SCCFE $-\nabla \textrm{div}$). The scheme is implementable on general meshes through the construction of a dual mesh and a triangular dual sub-mesh. The velocity is approximated by piecewise linear $(P_1)$ functions on the dual sub-mesh, and the pressure is approximated by piecewise constant $(P_0)$ functions on the dual mesh. The scheme is cell-centered in the sense that the solution can be computed using cell unknowns of the primal mesh (for the velocity) and of the dual mesh (for the pressure). Its stability is proved using the macroelement technique. The method is presented within a rigorous theoretical framework to show the $[H^1(\varOmega )]^2$ error of the velocity and the $L^2(\varOmega )$ error of the pressure. These error estimates are verified by numerical examples.
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Local Polynomial Convexity of the Union of two Tangential Totally Real Graphs in $\mathbb {C}^3$ Mai The Tan , Kieu Phuong Chi PDF411-418
▸ Abstract
In this note, we consider the local polynomial convexity of the union of totally real graphs in $\mathbb {C}^3$ having the same tangent spaces at the origin. We also construct examples showing that our results are quite sharp in some sense.
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$S$-forms of a Finitely Generated Field Extension EL Hassane Fliouet PDF419-428
▸ Abstract
Let $K$ be a finitely generated extension of a field $k$ of characteristic $p\not =0$. By means of exponents of $K/k$, we introduce the notion of $s$-forms ($s$ being a positive integer less than or equal to $insep(K/k)$ of $K/k$ as a natural generalization of forms of $K/k$. In light of results obtained by James K. Deveney and John N. Mordeson in their investigation on the forms of a finitely generated field extension [Deveney and Mordeson: Can. J. Math. 31(3), 655–662 (1979)], necessary and sufficient conditions characterizing $s$-forms of $K/k$ are given allowing in particular the existence of a unique minimal $s$-form (irreducible $s$-form) of $K/k$ and, accordingly, the development of properties of irreducible $s$-forms of $K/k$. We also seek to identify possible relationships between the structure and invariants of $K/k$ and those of its irreducible $s$-form.
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Asymptotic Regularity Results for Halpern-type Inexact Iterations for Coincidence Problems Alexander J. Zaslavski PDF429-443
▸ Abstract
In our recent work we computed linear rates of asymptotic regularity for a viscosity version of Halpern-type iterations for coincidence problem in a metric space with a hyperbolic structure. In the present paper we extend this result for inexact iterations under the presence of computational errors.