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In this paper, a discrete version of the Eckhaus equation is introduced. The discretiztion is obtained by considering a discrete analog of the transformation taking the cotinuous Eckhaus equation to the continuous linear, free Schrödinger equation. The resulting discrete Eckhaus equation is a nonlinear...

An overview of the lectures at the 2002 Bialowiea Workshop is presented. The symbol* after a proper name indicates that a copy of the corresponding contribution to the proceedings was communicated to the author of this summary.

In two previous papers the quantization was discussed of three one-degree-of-freedom Hamiltonians featuring a constant c, the value of which does not influence at all the corresponding classical dynamics (which is characterized by isochronous solutions, all of them periodic with period 2: "nonlinear...

In this paper, we compare the degrees and the orders of approximation of vector and matrix Padé approximants for series with matrix coefficients. It is shown that, in this respect, vector Padé approximants have better properties. Then, matrix­vector Padé approximants are defined and constructed. Finally,...

We discuss the solvability of the time-dependent incompressible Navier­Stokes equtions with nonhomogeneous Dirichlet data in spaces of low regularity.

A two cocycle is associated to any action of a Lie group on a symplectic manifold. This allows to enlarge the concept of anomaly in classical dynamical systems considered by F Toppan in [J. Nonlinear Math. Phys. 8, Nr. 3 (2001), 518­533] so as to encompass some extensions of Lie algebras related to noncanonical...

The reduction of nonlinear ordinary differential equations by a combination of first integrals and Lie group symmetries is investigated. The retention, loss or even gain in symmetries in the integration of a nonlinear ordinary differential equation to a first integral are studied for several examples....

Separability theory of one-Casimir Poisson pencils, written down in arbitrary coordnates, is presented. Separation of variables for stationary Harry-Dym and the KdV dressing chain illustrates the theory.

Qualitative approach to homogeneous anisotropic Bianchi class A models in terms of dynamical systems reveals a hierarchy of invariant manifolds. By calculating the Kovalevski Exponents according to Adler - van Moerbecke method we discuss how algebraic integrability property is distributed in this class...

We propose Dirac formalism for constraint Hamiltonian systems as an useful tool for the algebro-geometrical and dynamical characterizations of a class of integrable systems, the so called hyperelliptically separable systems. As a model example, we apply it to the classical geodesic flow on an ellipsoid.

The 2n dimensional manifold with two mutually commutative operators of differetiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general solution of them is presented in explicit form.

We prove the existence of a Lax pair for the Calogero Korteweg-de Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2 + 1)-dimensional case and thereby propose a new equation in (2+1) dimensions. We named this the (2+1)-dimensional...

We present a complete proof that solutions of the WDVV equations in Seiberg-Witten theory may be constructed from root systems. A generalization to weight systems is proposed.

Quantization of BKP type equations are done through the Moyal bracket and the formalism of pseudo-differential operators. It is shown that a variant of the dressing operator can also be constructed for such quantized systems.

As an example of how to deal with nonintegrable systems, the nonlinear partial differential equation which describes the evolution of long surface waves in a convecting fluid ut + (uxxx + 6uux) + 5uux + (uxxx + 6uux)x = 0, is fully analyzed, including symmetries (nonclassical and contact transformatons),...

We show that within the framework of linear theory the particle paths in a periodic gravity-capillary or pure capillary deep-water wave are not closed.

SOME MEASURES RELATING PARTITIONS USEFUL FOR COMPUTATIONAL INTELLIGENCE We investigate a number of measures relating partitions. One class of measures we consider are congru- ence measures. These measures are used to calculate the similarity between two partitionings. We provide a number of examples...

The Camassa-Holm (CH) and Hunter-Saxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H 1 and H 1 right-invariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a...

Similarity methods include the calculation and use of symmetries and conservation laws for a given partial differential equation (PDE). There exists a variety of software to calculate and use local symmetries and local conservation laws. However, it is often the case that a given PDE admits no useful...

We study the dynamics of a particle moving on the SU(2) group manifold. An exact quantization of this system is accomplished by finding the unitary and irreducible representations of a finite-dimensional Lie subalgebra of the whole Poisson algebra in phase space. In fact, the basic position and momentum...

This paper considers the robust stability analysis problem for a class of uncertain stochastic neural net- works with time-varying delay. Based on the Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the stochastic derivative of Lyapunov functionals,...

High-stakes (dangerous, catastrophic) risks take on a wider profile as progress unfolds. What are the impacts of technological and social change on the risk landscape? Due to the complexities and dynamics involved, we can only answer these questions approximately. By using the concept of fuzziness, we...

A new clonal selection immune algorithm with perturbation guiding search and non-uniform hypermutation (nCSIA) is proposed based on the idea of perturbed particle swarm algorithm and non-uniform mutation. The proposed algorithm proportional clones antibody based on the affinity, adaptively adjusts the...

Rough set theory has witnessed great success in data mining and knowledge discovery, which provides a good support for decision making on a certain data. However, a practical decision problem always shows diversity under the same circumstance according to different personality of the decision makers....

The production of biogas is positioned as energy which can not only generate a source of energy known as "green" but also which can recycle waste. In the context of sustainable development, the place of biogas is therefore essential. The risks corresponding to the production processes and uses of are...

This paper describes in the broad terms, the field of supply chain management and then, in particular, its application to agriculture. Modern supply chain management technologies have a lot to offer in the development of agriculture in developing countries.

After several years of growth, E-commerce has become mainstream and matured. However, the new challenges require that tomorrow’s E-commerce system move beyond the basic functions such as a static website with electronic catalogue and/or a shopping cart towards an intelligent, dynamic, and secure commerce...

True information about rainfall is crucial for human activities such as the use and the management of water resources, hydroelectric power projects, warning to impend droughts or floods, urban areas sewer systems and many others. This paper investigates the development of an efficient model to forecast...

This study examines how technology orientation interacts with innovation to affect business performance in small and medium-sized enterprises (SMEs) in an emerging market, namely Dubai in the United Arab Emirates. Survey data from 200 Dubai SMEs demonstrated, firstly, that technology orientation influenced...

In this paper we consider some widely utilized classes of discrete distributions and aim to provide a systematic overview about their preservation under convolution. This paper will serve as a detailed reference for the study and applications of the preservation of the discrete NBU(2), NBUCA classes...

The microvasculature of retinal ganglion cell layer, which is the part of central nervous system, can be investigated non-invasively in human. For clinical routine the fluorescence angiography is used to test patency and leak of retinal or choroid vessels, and to determine the blood passage time through...

Several applications of an explicitly invertible transformation are reported. This transformation is elementary and therefore all the results obtained via it might be considered trivial; yet the findings highlighted in this paper are generally far from appearing trivial until the way they are obtained...

A boson-fermion correspondence allows an analytic definition of functional super derivative, in particular, and a bosonic functional calculus, in general, on Bargmann Gelfand triples for the second super quantization. A Feynman integral for the super transformation matrix elements in terms of bosonic...

We study the solitary wave solutions of a non-integrable generalized KdV equation proposed by Fokas [A. S. Fokas, Physica D87, 145 (1995)], aiming to describe unidirectional waves in shallow water with greater accuracy than the standard KdV equation. This generalized equation includes higher-order terms...

We consider the two-dimensional irrotational water-wave problem with a free surface and a flat bottom. In the shallow-water regime and without smallness assumption on the wave amplitude we derive, by a variational approach in the Lagrangian formalism, the Green–Naghdi equations (1.1). The second equation...