234,021 research outputs found
A note on the values of the weighted q-Bernstein polynomials and modified q-Genocchi numbers with weight alpha and beta via the p-adic q-integral on Zp
The rapid development of q-calculus has led to the discovery of new
generalizations of Bernstein polynomials and Genocchi polynomials involving
q-integers. The present paper deals with weighted q-Bernstein polynomials and
q-Genocchi numbers with weight alpha and beta. We apply the method of
generating function and p-adic q-integral representation on Zp, which are
exploited to derive further classes of Bernstein polynomials and q-Genocchi
numbers and polynomials. To be more precise we summarize our results as
follows, we obtain some combinatorial relations between q-Genocchi numbers and
polynomials with weight alpha and beta. Furthermore, we derive an integral
representation of weighted q-Bernstein polynomials of degree n on Zp. Also we
deduce a fermionic p-adic q-integral representation of product weighted
q-Bernstein polynomials of different degrees n1,n2,...on Zp and show that it
can be written with q-Genocchi numbers with weight alpha and beta which yields
a deeper insight into the effectiveness of this type of generalizations. Our
new generating function possess a number of interesting properties which we
state in this paper.Comment: 10 page
A note on q-Bernstein polynomials
In this paper we constructed new q-extension of Bernstein polynomials. Fron
those q-Berstein polynomials, we give some interesting properties and we
investigate some applications related this q-Bernstein polynomials.Comment: 13 page
Extended Optical Model Analyses of Elastic Scattering and Fusion Cross Section Data for the 7Li+208Pb System at Near-Coulomb-Barrier Energies using the Folding Potential
Simultaneous analyses previously made for elastic scattering and
fusion cross section data for the Li+Pb system is extended to the
Li+Pb system at near-Coulomb-barrier energies based on the
extended optical model approach, in which the polarization potential is
decomposed into direct reaction (DR) and fusion parts. Use is made of the
double folding potential as a bare potential. It is found that the experimental
elastic scattering and fusion data are well reproduced without introducing any
normalization factor for the double folding potential and that both the DR and
fusion parts of the polarization potential determined from the
analyses satisfy separately the dispersion relation. Further, we find that the
real part of the fusion portion of the polarization potential is attractive
while that of the DR part is repulsive except at energies far below the Coulomb
barrier energy. A comparison is made of the present results with those obtained
from the Continuum Discretized Coupled Channel (CDCC) calculations and a
previous study based on the conventional optical model with a double folding
potential. We also compare the present results for the Li+Pb system
with the analysis previously made for the Li+Pb system.Comment: 7 figures, submitted to PR
Multivariate p-dic L-function
We construct multivariate p-adic L-function in the p-adic number fild by
using Washington method.Comment: 9 page
Observation of inhomogeneous domain nucleation in epitaxial Pb(Zr,Ti)O3 capacitors
We investigated domain nucleation process in epitaxial Pb(Zr,Ti)O3 capacitors
under a modified piezoresponse force microscope. We obtained domain evolution
images during polarization switching process and observed that domain
nucleation occurs at particular sites. This inhomogeneous nucleation process
should play an important role in an early stage of switching and under a high
electric field. We found that the number of nuclei is linearly proportional to
log(switching time), suggesting a broad distribution of activation energies for
nucleation. The nucleation sites for a positive bias differ from those for a
negative bias, indicating that most nucleation sites are located at
ferroelectric/electrode interfaces
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