Existence of homoclinic solution for the second order Hamiltonian systems

An existence theorem of homoclinic solution is obtained for a class of the nonautonomous second order Hamiltonian systems , ∀t∈R, by the minimax methods in the critical point theory, specially, the generalized mountain pass theorem, where L(t) is unnecessary uniformly positively definite for all t∈R, and W(t,x) satisfies the superquadratic condition W(t,x)/|x|²→+∞ as |x|→∞ uniformly in t, and need not satisfy the global Ambrosetti-Rabinowitz condition.     

Boundedness of solutions for semilinear reversible systems

In this paper we will study the boundedness of all solutions for second-order differential equations

where and satisfies the sublinear growth condition. Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible mappings. Under some suitable conditions we then obtain the existence of invariant tori and thus the boundedness of all solutions.

     

Real bounds, ergodicity and negative Schwarzian for multimodal maps

We consider smooth multimodal maps which have finitely many non-flat critical points. We prove the existence of real bounds. From this we obtain a new proof for the non-existence of wandering intervals, derive extremely useful improved Koebe principles, show that high iterates have `negative Schwarzian derivative' and give results on ergodic properties of the map. One of the main complications in the proofs is that we allow to have inflection points.

     

A new approximation technique for div-curl systems

In this paper, we describe an approximation technique for div-curl systems based in where is a domain in . We formulate this problem as a general variational problem with different test and trial spaces. The analysis requires the verification of an appropriate inf-sup condition. This results in a very weak formulation where the solution space is and the data reside in various negative norm spaces. Subsequently, we consider finite element approximations based on this weak formulation. The main approach of this paper involves the development of ``stable pairs" of discrete test and trial spaces. With this approach, we enlarge the test space so that the discrete inf-sup condition holds and we use a negative-norm least-squares formulation to reduce to a uniquely solvable linear system. This leads to optimal order estimates for problems with minimal regularity which is important since it is possible to construct magnetostatic field problems whose solutions have low Sobolev regularity (e.g., with ). The resulting algebraic equations are symmetric, positive definite and well conditioned. A second approach using a smaller test space which adds terms to the form for stabilization will also be mentioned. Some numerical results are also presented.

     

Semilinear parabolic equations involving measures and low regularity data

A detailed study of abstract semilinear evolution equations of the form is undertaken, where generates an analytic semigroup and is a Banach space valued measure depending on the solution. Then it is shown that the general theorems apply to a variety of semilinear parabolic boundary value problems involving measures in the interior and on the boundary of the domain. These results extend far beyond the known results in this field. A particularly new feature is the fact that the measures may depend nonlinearly and possibly nonlocally on the solution.

     

Performance of run-length limited (4, 18) code for optical storage systems

In this paper, the authors investigate the performance of recently presented run-length limited (4, 18) code for high density optical storage systems. The construction of the code is described simply. The code has code rate R = 1/3 and density ratio (DR) = 1.67. The bit error rate (BER) performance for decision feedback equalizer (DFE) and partial response maximum likelihood (PRML) detector are simulated, considering signal-to-noise ratio (SNR) and optical channel jitter. The result shows that the performance of the code is acceptable. The encoder and decoder of the code are implemented by complex programmable logic device (CPLD) chip and the hardware resources required for encoder and decoder arelow.     

Absolute Continuity in Periodic Thin Tubes and Strongly Coupled Leaky Wires

Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube is sufficiently thin. In a similar way we demonstrate absolute continuity at the bottom of the spectrum for generalized Schrödinger operators with a sufficiently strongly attractive interaction supported by a periodic curve in R^d = 2, 3.     

Equations in Dual Variables for Whittaker Functions

It is known that the Whittaker functions w(q) associated with the group GL(N) are eigenfunctions of the Hamiltonians of the open Toda chain, hence satisfy a set of differential equations in the Toda variables q _i . Using the expression of the q _i for the closed Toda chain in terms of Sklyanin variables _i , and the known relations between the open and the closed Toda chains, we show that Whittaker functions also satisfy a set of new difference equations in _i .     

Embedding optimisation algorithms with Mosel

Algebraic modelling languages allow models to be implemented in such a way that they can easily be understood and modified. They are therefore a working environment commonly used by practitioners in Operations Research. Having once developed models, they need to be integrated inside the company information system. This step often involves embedding a model into a programming language environment: many existing algebraic modelling languages make possible to run parameterised models and subsequently retrieve their results, but without any facility for interacting with the model during the model generation or solution process.In this paper we show how to use the Mosel environment to implement complex algorithms directly in the modelling language.The Office cleaning problem is solved by a branch-and-cut algorithm, implemented entirely in the modelling language (including the definition of the callback function for the solver). Secondly, a cutting stock problem is solved by column generation, also implemented in the modelling language.AMS classification: 90Cxx, 65K05, 68N15     

Elliptic Linear Problem for Painlevé VI Equation with Spectral Parameter

We introduce a linear problem with a spectral parameter for the elliptic form of the Painlevé VI equation. The corresponding nonautonomous version produces the Lax pair with spectral parameter for the Calogero-Inozemtsev model with a single degree of freedom.