Tassos Bountis

Bio: Tassos Bountis is an academic researcher from Nazarbayev University. The author has contributed to research in topics: Hamiltonian system & Lyapunov exponent. The author has an hindex of 38, co-authored 208 publications receiving 5463 citations. Previous affiliations of Tassos Bountis include California Institute of Technology & Aristotle University of Thessaloniki.

Integrable Hamiltonian Systems and the Painleve Property

Abstract: A direct method is described for obtaining conditions under which certain $N$-degree-of-freedom Hamiltonian systems are integrable, i.e., possess $N$ integrals in involution. This method consists of requiring that the general solutions have the Painlev\'e property, i.e., no movable singularities other than poles. We apply this method to several Hamiltonian systems of physical significance such as the generalized H\'enon-Heiles problem and the Toda lattice with $N=2 \mathrm{and} 3$, and recover all known integrable cases together with a few new ones. For some of these cases the second integral is written down explicitly while for others integrability is confirmed by numerical experiments.

Proton transfer in hydrogen-bonded systems

Abstract: Proceedings of the May 1991 workshop, held in Crete, Greece, within the program of activities of the NATO Special Program on Chaos, Order, and Patterns. Participants were physicists, biologists, and chemists, theoreticians and experimentalists, exchanging perspectives and data on proton transfer, th

Active control and global synchronization of the complex chen and Lü systems

Abstract: Chaos synchronization is a very important nonlinear phenomenon, which has been studied to date extensively on dynamical systems described by real variables. There also exist, however, interesting cases of dynamical systems, where the main variables participating in the dynamics are complex, for example, when amplitudes of electromagnetic fields are involved. Another example is when chaos synchronization is used for communications, where doubling the number of variables may be used to increase the content and security of the transmitted information. It is also well-known that similar generalization of the Lorenz system to one with complex ODEs has been introduced to describe and simulate the physics of a detuned laser and thermal convection of liquid flows. In this paper, we study chaos synchronization by applying active control and Lyapunov function analysis to two such systems introduced by Chen and Lu. First we show that, written in terms of complex variables, these systems can have chaotic dynamics and...

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Convergence of Probability Measures

Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

[서평]「Applied Cryptography」

Abstract: The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind. The emphasis is on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity. Topics covered includes an introduction to the concepts in cryptography, attacks against cryptographic systems, key use and handling, random bit generation, encryption modes, and message authentication codes. Recommendations on algorithms and further reading is given in the end of the paper. This paper should make the reader able to build, understand and evaluate system descriptions and designs based on the cryptographic components described in the paper.