Vietnam Journal of Mathematics
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Exponential Stability of Linear Delay Difference Equations with Continuous Time
Vietnam Journal of Mathematics - Tập 43 - Trang 195-205 - 2014
Linear time-varying delay difference equations with continuous time are considered. New criteria for exponential stability are given. Furthermore, an explicit stability bound for equations subject to time-varying perturbations is presented. Some examples are given to illustrate the obtained results.
Extragradient Algorithms with Linesearches for Solving Nonmonotone Equilibrium Problems in Banach Spaces
Vietnam Journal of Mathematics - - Trang 1-21 - 2023
In this paper, we introduce a new extragradient algorithm with linesearches for solving equilibrium problems in a real Banach space where the bifunction is not required to satisfy any monotone property. Under assumptions on the continuity, convexity of the bifunction, and the nonemptyness of the solution set of the Minty equilibrium problem, we show that the iterative sequences generated by this a......
Overdetermined Strata for Degree 5 Hyperbolic Polynomials
Vietnam Journal of Mathematics - Tập 43 Số 1 - Trang 139-150 - 2015
In the present paper, we consider degree 5 hyperbolic polynomials (HPs) in one variable (i.e., real and with all roots real). We are interested in such HPs whose number of equalities between roots of the polynomial and its derivatives is greater or equal to 4. We give a new method, based on resultants and subresultants, to calculate the overdetermined strata for degree 5 hyperbolic polynomials.
On Mathematical and Numerical Modelling of Multiphysics Wave Propagation with Polytopal Discontinuous Galerkin Methods: a Review
Vietnam Journal of Mathematics - Tập 50 - Trang 997-1028 - 2022
In this work we review discontinuous Galerkin finite element methods on polytopal grids (PolydG) for the numerical simulation of multiphysics wave propagation phenomena in heterogeneous media. In particular, we address wave phenomena in elastic, poro-elastic, and poro-elasto-acoustic materials. Wave propagation is modeled by using either the elastodynamics equation in the elastic domain, the acous......
Structure Exploitation in an Interior-Point Method for Fully Discretized, State Constrained Optimal Control Problems
Vietnam Journal of Mathematics - Tập 46 - Trang 1089-1113 - 2018
We discuss a direct discretization method for state-constrained optimal control problems and an interior-point method, which is used to solve the resulting large-scale and sparse nonlinear optimization problems. The main focus of the paper is on the investigation of an efficient method to solve the occurring linear equations with saddle-point structure. To this end, we exploit the particular struc......
Tunneling for the $$\overline{\partial }$$ -Operator
Vietnam Journal of Mathematics - - 2024
We study the small singular values of the 2-dimensional semiclassical differential operator
$$P = 2\textrm{e}^{-\phi /h}\circ hD_{\overline{z}}\circ \textrm{e}^{\phi /h}$$
on
$$S^1+iS^1$$
and on
......
Consensus Convergence with Stochastic Effects
Vietnam Journal of Mathematics - Tập 45 - Trang 51-75 - 2016
We consider a stochastic, continuous state and time opinion model where each agent’s opinion locally interacts with other agents’ opinions in the system, and there is also exogenous randomness. The interaction tends to create clusters of common opinion. By using linear stability analysis of the associated nonlinear Fokker–Planck equation that governs the empirical density of opinions in the limit ......
Ashtekar Variables: Structures in Bundles
Vietnam Journal of Mathematics - Tập 44 - Trang 203-214 - 2016
Canonical gravity can be formulated by means of a densitized dreibein field together with an SU(2) connection. These so-called Ashtekar variables are the fundamental quantities, loop quantum gravity is resting on. In this paper, we review these variables from the perspective of fibre bundles. This is straightforward for the dreibein field as this is simply a frame field. The Ashtekar connection, h......
The Second-Order Riesz Transforms Related to Schrödinger Operators Acting on BMO Type Spaces on the Stratified Lie Group
Vietnam Journal of Mathematics - Tập 46 - Trang 629-651 - 2018
Let
$\mathcal {L}=-{\Delta } + V$
be a Schrödinger operator on stratified Lie group G, where V is a nonnegative potential satisfying the suitable reverse Hölder’s inequality. In this paper, we study the boundedness of the second-order Riesz trans......
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