Ismail Naci CANGÜL, Veli KURT, Yilmaz SIMSEK, Hong Kyung PAK, Seog-Hoon RIM
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...
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...
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),...
In this paper, by using q-Volkenborn integral, the first author 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...
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...
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....
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...
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
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  we argued for the advantages of an extension of this approach based on
considering a chain of double pendulums with...
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...