Acta Mathematica Vietnamica最新文献

Let K be a finitely generated extension of a field k of characteristic (pnot =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.

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.

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.

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.

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.

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.

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).

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.