Volume 14, Issue 1, February 2007

Pages: 1 - 7

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.

Pages: 8 - 14

The purpose of this paper is to consider q-Euler numbers and polynomials which are
q-extensions of ordinary Euler numbers and polynomials by the computations of the
p-adic q-integrals due to T. Kim, cf. [1, 3, 6, 12], and to derive the "complete sums
for q-Euler polynomials" which are evaluated by...

Pages: 15 - 27

The main purpose of this paper is to present a systemic study of some families of
multiple q-Euler numbers and polynomials. In particular, by using the q-Volkenborn
integration on Zp, we construct p-adic q-Euler numbers and polynomials of higher
order. We also define new generating functions of multiple...

Pages: 28 - 43

The paper deals with a problem of developing an inverse-scattering transform for
solving the initial-boundary value problem (IBVP) for the Korteweg-de Vries equation
on the positive quarter-plane:
pt - 6ppx + pxxx = 0, x 0, t 0, (a)
with the given initial and boundary conditions:
p(x, 0) = p(x),...

Pages: 44 - 56

In this paper, by using q-Volkenborn integral[10], the first author[25] constructed new
generating functions of the new twisted (h, q)-Bernoulli polynomials and numbers. We
define higher-order twisted (h, q)-Bernoulli polynomials and numbers. Using these
numbers and polynomials, we obtain new approach...

Pages: 57 - 81

The Yakushevich model provides a very simple pictures of DNA torsion dynamics,
yet yields remarkably correct predictions on certain physical characteristics of the dynamics. In the standard Yakushevich model, the interaction between bases of a pair
is modelled by a harmonic potential, which becomes...

Pages: 82 - 94

Legendre transformations provide a natural symmetry on the space of solutions to the
WDVV equations, and more specifically, between different Frobenius manifolds. In
this paper a twisted Legendre transformation is constructed between solutions which
define the corresponding dual Frobenius manifolds....

Pages: 95 - 111

We study the complex Riccati tensor equation DcG + GCG - R = 0 on a geodesic c on a Riemannian 3-manifold. This non-linear equation appears in
the study of Gaussian beams. Gaussian beams are asymptotic solutions to hyperbolic
equations that at each time instant are concentrated around one point in...

Pages: 112 - 127

Let Vect(R) be the Lie algebra of smooth vector fields on R. The space of symbols Pol(T
R) admits a non-trivial deformation (given by differential operators on
weighted densities) as a Vect(R)-module that becomes trivial once the action is restricted to sl(2) Vect(R). The deformations of Pol(T
R),...

Pages: 128 - 146

It was first suggested by Englander et al to model the nonlinear dynamics of DNA
relevant to the transcription process in terms of a chain of coupled pendulums. In a
related paper [4] we argued for the advantages of an extension of this approach based on
considering a chain of double pendulums with...

Pages: 147 - 156

It is shown how pseudoconstants of the Liouville-type equations can be exploited as a
tool for construction of the Bäcklund transformations. Several new examples of such
transformations are found. In particular we obtained the Bäcklund transformations
for a pair of three-component analogs of the dispersive...