Acta Mathematica Vietnamica最新文献

In this paper, we present strategies for determining the error indicator threshold value at each refinement step. The error indicator threshold is not directly computed from the maximum error indicator, improving refinement efficiency. Moreover, to enhance refinement efficiency, we propose three new candidate center structures, which include a greater number of centers and may double the distribution density. Additionally, we improve the variable support size algorithm for making it more flexible. Moreover, we introduce a measure to evaluate the average recursive preprocessing cost per new center generated by the adaptive RBF-FD (Radial Basis Function-Finite Difference) meshless method. This metric is used to assess the preprocessing cost efficiency of the adaptive RBF-FD meshless method and to compare it with our previously published adaptive RBF-FD methods for solving 2D elliptic equations. The results demonstrate that the numerical solutions obtained using the methods proposed in this paper are significantly more accurate, more stable, and more effective in terms of refinement than those from our earlier studies and the adaptive FEM (Finite Element Method), while achieving the lowest computational cost.

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<N^sharp ), where ( N^sharp ) is explicitly computed.

Addressing the intricate challenges in plane elasticity, especially with non-vanishing traction and complex geometries, requires innovative methods. This paper offers a novel approach, drawing inspiration from the Neumann problem for the inhomogeneous Cauchy-Riemann equations. Our method applies to domains conformally equivalent to a unit disk or an annulus, focusing on deriving explicit solutions for the displacement field rather than the stress tensor, which distinguishes it from most traditional approaches. We explore solutions for specific classical cases to demonstrate its efficacy, such as a cardioid domain, a ring domain with a shifted hole, and a gear-like structure. This work enhances the toolkit for researchers and practitioners tackling isotropic planar elastostatic challenges with a unified and flexible approach.

Our aim in this paper is to study the linear heat equation on a Riemannian manifold evolving by the Ricci-harmonic flow. We first show a Hamilton type gradient estimate for the positive solution of the heat equation, which allows us to derive a Harnack inequality. It is worthy to note that comparing with the Li-Yau type estimate by Bailesteanu [1], our gradient estimate can be obtained without any assumption on the harmonic quantity in the flow.

This paper is devoted to the Dirichlet problem associated to operators defined on the nuclear algebra of entire functions. Firstly, we give a probabilistic representation of the solution of the Dirichlet problem associated to the extended K-Gross Laplacian in terms of K-Wiener process. Secondly, we prove that the Dirichlet problem associated to the operator (mathcal {F}_{t(-K),I})-transform has an explicit solution. Finally, an application to the large deviation principle is given.

Let T be a tree. A vertex of degree one is a leaf of T and a vertex of degree at least three is a branch vertex of T. A graph is said to be (K_{1,4})-free if it does not contain (K_{1,4}) as an induced subgraph. In this paper, we study the spanning trees with a bounded number of leaves and branch vertices of (K_ {1,4})-free graphs. Applying the main results, we also give some improvements of previous results on the spanning tree with few branch vertices for the case of (K_{1,4})-free graphs.

In this paper, we consider a class of stochastic Volterra integral equations with general singular kernels, driven by a Brownian motion and a pure jump Lévy process. We first show that these equations have a unique strong solution under certain regular conditions on their coefficients. Furthermore, the solutions of this equation depend continuously on the initial value and on the kernels k, (k_B), and (k_Z). We will then show the regularity of solutions for these equations. Finally, we propose a (theta )-Euler-Maruyama approximation scheme for these equations and demonstrate its convergence at a certain rate in the (L^2)-norm. Some numerical simulations is also presented to support for the theoretical results.

This paper establishes a large deviation principle for a stochastic 2D Cahn-Hilliard-Oldroyd model of order one under random influences. The model used in the analysis consists of the stochastic Oldroyd model of order one, coupled with a Cahn-Hilliard equation for the order parameter. The approach used is the weak convergence method with the main idea laid on a variational representation formula for the Laplace transform of continuous and bounded functionals.

A measure-theoretic pressure was defined by [L. He, J. Lv and L. Zhou: Definition of measure-theoretic pressure using spanning sets, Acta Math. Sinica (English Series) 20, 709–718 (2004)] based on the Katok entropy formula. For a measure preserving map f, we generalized this definition to define a measure-theoretic pressure by using both ((n,epsilon ))-spanning and ((n,epsilon ))-separated sets. A variational principle for this pressure is established. Furthermore, we investigate an upper bound for the measure theoretic pressure of a (C^{2}) endomorphism preserving a hyperbolic measure.

We characterize boundedness and compactness of the differences of products of Volterra integral operators (V_g) (Volterra companion operators (J_g)) and composition operators (C_{varphi }) between different Fock spaces (mathcal {F}^p(mathbb {C})) and (mathcal {F}^q(mathbb {C})) for every (p, q in (0, infty ]).