240,758 research outputs found
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
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
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
Interpolation function of the genocchi type polynomials
The main purpose of this paper is to construct not only generating functions
of the new approach Genocchi type numbers and polynomials but also
interpolation function of these numbers and polynomials which are related to a,
b, c arbitrary positive real parameters. We prove multiplication theorem of
these polynomials. Furthermore, we give some identities and applications
associated with these numbers, polynomials and their interpolation functions.Comment: 14 page
Measuring |V_{td} / V_{ub}| through B -> M \nu \bar\nu (M=\pi,K,\rho,K^*) decays
We propose a new method for precise determination of |V_{td} / V_{ub}| from
the ratios of branching ratios BR(B -> \rho \nu \bar \nu ) / BR(B ->\rho l \nu
) and BR(B -> \pi \nu \bar \nu ) / BR(B -> \pi l \nu ). These ratios depend
only on the ratio of the Cabibbo-Kobayashi-Maskawa (CKM) elements |V_{td} /
V_{ub}|$ with little theoretical uncertainty, when very small isospin breaking
effects are neglected. As is well known, |V_{td} / V_{ub}| equals to (\sin
\gamma) / (\sin \beta) for the CKM version of CP-violation within the Standard
Model. We also give in detail analytical and numerical results on the
differential decay width d\Gamma(B -> K^* \nu \bar \nu ) / dq^2 and the ratio
of the differential rates dBR(B -> \rho \nu \bar \nu )/dq^2 / dBR(B -> K^* \nu
\bar \nu )/dq^2 as well as BR(B -> \rho \nu \bar \nu ) / BR(B -> K^* \nu \bar
\nu) and BR(B -> \pi \nu \bar \nu ) / BR(B -> K \nu \bar \nu).Comment: LaTeX with 2 figures, 12 page
A note on q-Euler numbers and polynomials
The purpose of this paper is to construct q-Euler numbers and polynomials by
using p-adic q-integral equations on Zp. Finally, we will give some interesting
formulae related to these q-Euler numbers and polynomials.Comment: 6 page
A note on q-Bernoulli numbers and polynomials
By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials
of higher order.Comment: 8 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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