Vietnam Journal of Mathematics
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A Simple Proof for a More Generalized Form of the AZ-identity
Vietnam Journal of Mathematics - Tập 43 - Trang 771-775 - 2015
This paper gives a simple proof for a generalized form of the AZ-identity of one or two set systems. We also extend the results further and establish some new identities related to the AZ-identity. Our method uses some properties of rational functions.
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......
Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis
Vietnam Journal of Mathematics - Tập 48 - Trang 633-659 - 2020
In this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solution set of the LMI. It is shown that the analytic center is described by closely related matrix equa......
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......
Asymptotic Stability and Strict Boundedness for Non-autonomous Nonlinear Difference Equations with Time-varying Delay
Vietnam Journal of Mathematics - Tập 44 - Trang 789-800 - 2016
In this paper, we derive some new results on the asymptotic stability and strict boundedness for a new class of non-autonomous nonlinear difference equations with time-varying delay. We employ fixed point theory and compute some difference inequalities to derive the new results. We apply these results to determine the extinction condition and the persistence condition for some discrete population ......
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
......
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