Nguyen Xuan Minh - Academia.edu (original) (raw)

Papers by Nguyen Xuan Minh

Research paper thumbnail of Samr Model: Clarification of Ambiguous Terms

In the rising trend of applying Information Communication Technology (ICT) into teaching, ICT int... more In the rising trend of applying Information Communication Technology (ICT) into teaching, ICT integration means much more than simply using Power Point slides, software like Hot Potatoes, or platforms like Facebook or Moodle in teaching and learning. Therefore, many scales have been designed to guide teachers in the evaluation of their ICT integration, and one of which is the<br> increasing popular model of SAMR. Interesting as it seems, but the SAMR model proves to be a weak framework to base on for this evaluation. This study points out how inconsistent the interpretation of the SAMR is in the literature and point out what should be done to improve the model for measuring the levels of ICT use of language teachers. The study proposes an understanding of tasks which include textbook tasks, teaching tasks, and learning tasks, and attempts to modify the terms of "functional changes", and "task redesign" to help distinguish different levels of ICT integration...

Research paper thumbnail of Local models of the greatest characteristic exponent of differential equations depending on parameters

Banach Center Publications, 1989

Research paper thumbnail of On the proof of characterizations of the exponential dichotomy

Proceedings of the American Mathematical Society, 1999

We describe explicitly the generator of the evolutionary semigroup associated with the evolutiona... more We describe explicitly the generator of the evolutionary semigroup associated with the evolutionary operator generated by the linear differential equation x ′ ( t ) = A ( t ) x ( t ) x’(t)=A(t)x(t) . From this we give a short proof of some known characterizations of the exponential dichotomy of the above mentioned equation.

Research paper thumbnail of A Topological Classification of Differential Equations with Impulse Effect

Tamkang Journal of Mathematics, 1994

The present paper is concerned with the problem of topological clas- sification of differential e... more The present paper is concerned with the problem of topological clas- sification of differential equations with impulse effect. Under the assumption that the linear part of the right-hand side of the equation considered has an exponential dichotomy and the nonlinear perturbation is small enough it is proved that for the underlying equations there exist N+1N + 1N+1 types topologicall'y,,different from one another.

Research paper thumbnail of Spectral analysis of an operator associated with linear functional differential equations and its applications

Proceedings of The 6'th Colloquium on the Qualitative Theory of Differential Equations (August 10--14, 1999, Szeged, Hungary) edited by: Géza Makay and László Hatvani, 1999

Research paper thumbnail of Semigroups and Exponential Stability of Nonautonomous Linear Differential Equations on the Half-Line

Dynamical Systems and Applications, 1995

WSSIAA 4 (1995) pp. 45-61 © World Scientific Publishing Company 45 SEMIGROUPS AND EXPONENTIAL STA... more WSSIAA 4 (1995) pp. 45-61 © World Scientific Publishing Company 45 SEMIGROUPS AND EXPONENTIAL STABILITY OF NONAUTONOMOUS LINEAR DIFFERENTIAL EQUATIONS ON THE HALF-LINE BERND AULBACH Department of Mathematics, University of Augsburg ...

Research paper thumbnail of Topics on Stability and Periodicity in Abstract Differential Equations

Series on Concrete and Applicable Mathematics, 2008

Research paper thumbnail of Seafood-exporter logistics activities and services - an international cooperation between Taiwan and Vietnam

2010 The 2nd International Conference on Computer and Automation Engineering (ICCAE), 2010

Wei-Shuo Lo Department of Public Finance and Graduate Institute of Business and Management Meiho ... more Wei-Shuo Lo Department of Public Finance and Graduate Institute of Business and Management Meiho Institute of Technology Ping Tung, Taiwan x2134@meiho.edu.tw ... Nguyen Xuan Minh Foreign Trade University Ho Chi Minh City, Vietnam minhftu2@yahoo.com

Research paper thumbnail of Semigroups and differential equations with almost periodic coefficients

Nonlinear Analysis: Theory, Methods & Applications, 1998

Google, Inc. (search). ...

Research paper thumbnail of A Massera type theorem for almost automorphic solutions of differential equations

Journal of Mathematical Analysis and Applications, 2004

In this note, we present a Massera type theorem for the existence of almost automorphic solutions... more In this note, we present a Massera type theorem for the existence of almost automorphic solutions of periodic linear evolution equations of the form x (t) = A(t)x(t) + f (t), where A(t) is unbounded linear operator depending on t periodically and generates a τ-periodic evolutionary process, f is almost automorphic. The main results are stated in terms of the almost automorphy of solutions and their Carleman spectra.

Research paper thumbnail of Evolution Semigroups and Sums of Commuting Operators: A New Approach to the Admissibility Theory of Function Spaces

Journal of Differential Equations, 2000

This paper is concerned with conditions for the admissibility of a translation invariant function... more This paper is concerned with conditions for the admissibility of a translation invariant function space M with respect to a well posed linear evolution equation duÂdt=Au+ f (t), t # R (V). We propose a new approach to this problem by considering the sum of two commuting operators &dÂdt := &D M and the operator of multiplication by A on M. On the one hand, the closure of this operator is the infinitesimal generator of the so-called evolution semigroup associated with (V). On the other hand, the generator G of this semigroup relates a mild solution u of (V) to the forcing term f by the rule Gu=&f. Consequently, various spectral criteria of the type _(D M) & _(A)=< for the admissibility of the function space M with respect to (V) can be proved in an elegant manner. Moreover, they can be naturally extended to general classes of differential equations, including higher order and abstract functional differential equations. Applications and examples are provided to illustrate the obtained results.

Research paper thumbnail of Evolution Semigroups and Spectral Criteria for Almost Periodic Solutions of Periodic Evolution Equations

Journal of Differential Equations, 1999

We investigate spectral criteria for the existence of (almost) periodic solutions to linear 1-per... more We investigate spectral criteria for the existence of (almost) periodic solutions to linear 1-periodic evolution equations of the formdx/dt=A(t)x+f(t) with (in general, unbounded)A(t) and (almost) periodicf. Using the evolution semigroup associated with the evolutionary process generated by the equation under consideration we show that if the spectrum of the monodromy operator does not intersect the seteisp(f), then the above equation

Research paper thumbnail of The concept of spectral dichotomy for linear difference equations II

Journal of Difference Equations and Applications, 1996

This paper is a continuation of a previous one (J. Math. Anal. Appl. 185 (1994), 275–287) in whic... more This paper is a continuation of a previous one (J. Math. Anal. Appl. 185 (1994), 275–287) in which the concept of spectral dichotomy has been introduced. This new notion of dichotomy has proved to be useful since it allows to apply the well known theory of linear operators to study dynamic properties of nonautonomous linear difference equations. In the present paper we extend our result on the equivalence of the spectral dichotomy and the well known exponential dichotomy to the class of linear differenc equations whose right-hand sides are not necessarily invertible. We furthermore investigate equations on the set of positive integers for which we establish necessary and sufficient conditions for exponential and unifrom stability.

Research paper thumbnail of Integral manifolds of impulsive differential equations

Journal of Applied Mathematics and Stochastic Analysis, 1992

The present paper is concerned with the existence of integral manifolds of impulsive differential... more The present paper is concerned with the existence of integral manifolds of impulsive differential equations as t→+∞. Under the assumption of exponential trichotomy on the linear part of the right-hand side of the equation, it is proved that if the nonlinear perturbation is small enough, then there exist integral manifolds as t→+∞ for the perturbed equations.

Research paper thumbnail of Existence of exponential dichotomy of a class of impulsive differential equations

International Journal of Theoretical Physics, 1995

ABSTRACT

Research paper thumbnail of Topological classification of impulsive differential equations

International Journal of Theoretical Physics, 1995

The present paper is concerned with the topological classification of impulsive differential equa... more The present paper is concerned with the topological classification of impulsive differential equations. Under the assumption that the linear part of the right-hand side of the equation considered has an exponential dichotomy and the nonlinear perturbation is small enough, it is proved that for the underlying equations there exist N + 1 types topologically different from one another.

Research paper thumbnail of Continuous dependence on a parameter of the solutions of impulsive differential equations in a Banach space

International Journal of Theoretical Physics, 1993

We prove that the solutions of an impulsive differential equation depend continuously on a small ... more We prove that the solutions of an impulsive differential equation depend continuously on a small parameter under the assumption that the right-hand side of the equation and the impulse operators satisfy conditions of Lipschitz type.

Research paper thumbnail of Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line

Integral Equations and Operator Theory, 1998

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Research paper thumbnail of Structural stability of linear difference equations in Hilbert space

Computers & Mathematics with Applications, 1998

In this note, we prove that linear difference equations in Hilbert space are structurally stable ... more In this note, we prove that linear difference equations in Hilbert space are structurally stable if and only if they have an exponential dichotomy.

Research paper thumbnail of Lectures on the Asymptotic Behavior of Solutions of Differential Equations

Preface An Introduction and Preliminaries Evolution Equations and Semigroups of Linear Operators ... more Preface An Introduction and Preliminaries Evolution Equations and Semigroups of Linear Operators Almost Periodic Functions Asymptotic Behavior of Solutions Exponential Dichotomy Spectrum of a Bonded Function Evolution of Semigroups Method Sums of Commuting Operators Method Decomposition Technique and Massera Theorem for Almost Periodic Solutions Bibliography Index.

Research paper thumbnail of Samr Model: Clarification of Ambiguous Terms

In the rising trend of applying Information Communication Technology (ICT) into teaching, ICT int... more In the rising trend of applying Information Communication Technology (ICT) into teaching, ICT integration means much more than simply using Power Point slides, software like Hot Potatoes, or platforms like Facebook or Moodle in teaching and learning. Therefore, many scales have been designed to guide teachers in the evaluation of their ICT integration, and one of which is the<br> increasing popular model of SAMR. Interesting as it seems, but the SAMR model proves to be a weak framework to base on for this evaluation. This study points out how inconsistent the interpretation of the SAMR is in the literature and point out what should be done to improve the model for measuring the levels of ICT use of language teachers. The study proposes an understanding of tasks which include textbook tasks, teaching tasks, and learning tasks, and attempts to modify the terms of "functional changes", and "task redesign" to help distinguish different levels of ICT integration...

Research paper thumbnail of Local models of the greatest characteristic exponent of differential equations depending on parameters

Banach Center Publications, 1989

Research paper thumbnail of On the proof of characterizations of the exponential dichotomy

Proceedings of the American Mathematical Society, 1999

We describe explicitly the generator of the evolutionary semigroup associated with the evolutiona... more We describe explicitly the generator of the evolutionary semigroup associated with the evolutionary operator generated by the linear differential equation x ′ ( t ) = A ( t ) x ( t ) x’(t)=A(t)x(t) . From this we give a short proof of some known characterizations of the exponential dichotomy of the above mentioned equation.

Research paper thumbnail of A Topological Classification of Differential Equations with Impulse Effect

Tamkang Journal of Mathematics, 1994

The present paper is concerned with the problem of topological clas- sification of differential e... more The present paper is concerned with the problem of topological clas- sification of differential equations with impulse effect. Under the assumption that the linear part of the right-hand side of the equation considered has an exponential dichotomy and the nonlinear perturbation is small enough it is proved that for the underlying equations there exist N+1N + 1N+1 types topologicall'y,,different from one another.

Research paper thumbnail of Spectral analysis of an operator associated with linear functional differential equations and its applications

Proceedings of The 6'th Colloquium on the Qualitative Theory of Differential Equations (August 10--14, 1999, Szeged, Hungary) edited by: Géza Makay and László Hatvani, 1999

Research paper thumbnail of Semigroups and Exponential Stability of Nonautonomous Linear Differential Equations on the Half-Line

Dynamical Systems and Applications, 1995

WSSIAA 4 (1995) pp. 45-61 © World Scientific Publishing Company 45 SEMIGROUPS AND EXPONENTIAL STA... more WSSIAA 4 (1995) pp. 45-61 © World Scientific Publishing Company 45 SEMIGROUPS AND EXPONENTIAL STABILITY OF NONAUTONOMOUS LINEAR DIFFERENTIAL EQUATIONS ON THE HALF-LINE BERND AULBACH Department of Mathematics, University of Augsburg ...

Research paper thumbnail of Topics on Stability and Periodicity in Abstract Differential Equations

Series on Concrete and Applicable Mathematics, 2008

Research paper thumbnail of Seafood-exporter logistics activities and services - an international cooperation between Taiwan and Vietnam

2010 The 2nd International Conference on Computer and Automation Engineering (ICCAE), 2010

Wei-Shuo Lo Department of Public Finance and Graduate Institute of Business and Management Meiho ... more Wei-Shuo Lo Department of Public Finance and Graduate Institute of Business and Management Meiho Institute of Technology Ping Tung, Taiwan x2134@meiho.edu.tw ... Nguyen Xuan Minh Foreign Trade University Ho Chi Minh City, Vietnam minhftu2@yahoo.com

Research paper thumbnail of Semigroups and differential equations with almost periodic coefficients

Nonlinear Analysis: Theory, Methods & Applications, 1998

Google, Inc. (search). ...

Research paper thumbnail of A Massera type theorem for almost automorphic solutions of differential equations

Journal of Mathematical Analysis and Applications, 2004

In this note, we present a Massera type theorem for the existence of almost automorphic solutions... more In this note, we present a Massera type theorem for the existence of almost automorphic solutions of periodic linear evolution equations of the form x (t) = A(t)x(t) + f (t), where A(t) is unbounded linear operator depending on t periodically and generates a τ-periodic evolutionary process, f is almost automorphic. The main results are stated in terms of the almost automorphy of solutions and their Carleman spectra.

Research paper thumbnail of Evolution Semigroups and Sums of Commuting Operators: A New Approach to the Admissibility Theory of Function Spaces

Journal of Differential Equations, 2000

This paper is concerned with conditions for the admissibility of a translation invariant function... more This paper is concerned with conditions for the admissibility of a translation invariant function space M with respect to a well posed linear evolution equation duÂdt=Au+ f (t), t # R (V). We propose a new approach to this problem by considering the sum of two commuting operators &dÂdt := &D M and the operator of multiplication by A on M. On the one hand, the closure of this operator is the infinitesimal generator of the so-called evolution semigroup associated with (V). On the other hand, the generator G of this semigroup relates a mild solution u of (V) to the forcing term f by the rule Gu=&f. Consequently, various spectral criteria of the type _(D M) & _(A)=< for the admissibility of the function space M with respect to (V) can be proved in an elegant manner. Moreover, they can be naturally extended to general classes of differential equations, including higher order and abstract functional differential equations. Applications and examples are provided to illustrate the obtained results.

Research paper thumbnail of Evolution Semigroups and Spectral Criteria for Almost Periodic Solutions of Periodic Evolution Equations

Journal of Differential Equations, 1999

We investigate spectral criteria for the existence of (almost) periodic solutions to linear 1-per... more We investigate spectral criteria for the existence of (almost) periodic solutions to linear 1-periodic evolution equations of the formdx/dt=A(t)x+f(t) with (in general, unbounded)A(t) and (almost) periodicf. Using the evolution semigroup associated with the evolutionary process generated by the equation under consideration we show that if the spectrum of the monodromy operator does not intersect the seteisp(f), then the above equation

Research paper thumbnail of The concept of spectral dichotomy for linear difference equations II

Journal of Difference Equations and Applications, 1996

This paper is a continuation of a previous one (J. Math. Anal. Appl. 185 (1994), 275–287) in whic... more This paper is a continuation of a previous one (J. Math. Anal. Appl. 185 (1994), 275–287) in which the concept of spectral dichotomy has been introduced. This new notion of dichotomy has proved to be useful since it allows to apply the well known theory of linear operators to study dynamic properties of nonautonomous linear difference equations. In the present paper we extend our result on the equivalence of the spectral dichotomy and the well known exponential dichotomy to the class of linear differenc equations whose right-hand sides are not necessarily invertible. We furthermore investigate equations on the set of positive integers for which we establish necessary and sufficient conditions for exponential and unifrom stability.

Research paper thumbnail of Integral manifolds of impulsive differential equations

Journal of Applied Mathematics and Stochastic Analysis, 1992

The present paper is concerned with the existence of integral manifolds of impulsive differential... more The present paper is concerned with the existence of integral manifolds of impulsive differential equations as t→+∞. Under the assumption of exponential trichotomy on the linear part of the right-hand side of the equation, it is proved that if the nonlinear perturbation is small enough, then there exist integral manifolds as t→+∞ for the perturbed equations.

Research paper thumbnail of Existence of exponential dichotomy of a class of impulsive differential equations

International Journal of Theoretical Physics, 1995

ABSTRACT

Research paper thumbnail of Topological classification of impulsive differential equations

International Journal of Theoretical Physics, 1995

The present paper is concerned with the topological classification of impulsive differential equa... more The present paper is concerned with the topological classification of impulsive differential equations. Under the assumption that the linear part of the right-hand side of the equation considered has an exponential dichotomy and the nonlinear perturbation is small enough, it is proved that for the underlying equations there exist N + 1 types topologically different from one another.

Research paper thumbnail of Continuous dependence on a parameter of the solutions of impulsive differential equations in a Banach space

International Journal of Theoretical Physics, 1993

We prove that the solutions of an impulsive differential equation depend continuously on a small ... more We prove that the solutions of an impulsive differential equation depend continuously on a small parameter under the assumption that the right-hand side of the equation and the impulse operators satisfy conditions of Lipschitz type.

Research paper thumbnail of Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line

Integral Equations and Operator Theory, 1998

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Research paper thumbnail of Structural stability of linear difference equations in Hilbert space

Computers & Mathematics with Applications, 1998

In this note, we prove that linear difference equations in Hilbert space are structurally stable ... more In this note, we prove that linear difference equations in Hilbert space are structurally stable if and only if they have an exponential dichotomy.

Research paper thumbnail of Lectures on the Asymptotic Behavior of Solutions of Differential Equations

Preface An Introduction and Preliminaries Evolution Equations and Semigroups of Linear Operators ... more Preface An Introduction and Preliminaries Evolution Equations and Semigroups of Linear Operators Almost Periodic Functions Asymptotic Behavior of Solutions Exponential Dichotomy Spectrum of a Bonded Function Evolution of Semigroups Method Sums of Commuting Operators Method Decomposition Technique and Massera Theorem for Almost Periodic Solutions Bibliography Index.