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

The effects of rotational flow, viscosity, thickness, and shape on transonic flutter dip phenomena

The transonic flutter dip phenomena on thin airfoils, which are employed for propfan blades, is investigated using an integrated Euler/Navier-Stokes code and a two degrees of freedom typical section structural model. As a part of the code validation, the flutter characteristics of the NACA 64A010 airfoil are also investigated. In addition, the effects of artificial dissipation models, rotational flow, initial conditions, mean angle of attack, viscosity, airfoil thickness and shape on flutter are investigated. The results obtained with a Euler code for the NACA 64A010 airfoil are in reasonable agreement with published results obtained by using transonic small disturbance and Euler codes. The two artificial dissipation models, one based on the local pressure gradient scaled by a common factor and the other based on the local pressure gradient scaled by a spectral radius, predicted the same flutter speeds except in the recovery region for the case studied. The effects of rotational flow, initial conditions, mean angle of attack, and viscosity for the Reynold's number studied seem to be negligible or small on the minima of the flutter dip

Enhancement of gluonic dissociation of J/ψJ/\psi in viscous QGP

We have investigated the effect of viscosity on the gluonic dissociation of $J/\psi$ in an equilibrating plasma. Suppression of $J/\psi$ due to gluonic dissociation depend on the temperature and also on the chemical equilibration rate. In an equilibrating plasma, viscosity affects the temperature evolution and also the chemical equilibration rate, requiring both of them to evolve slowly compared to their ideal counter part. For Au+Au collisions at RHIC and LHC energies, gluonic dissociation of $J/\psi$ increases for a viscous plasma. Low $P_T$ $J/\psi$'s are found to be more suppressed due to viscosity than the high $P_T$ ones. Also the effect is more at LHC energy than at RHIC energy.Comment: 3 pages, 1 figur

Numerical Study of the Lowest Energy Configurations for Global String-Antistring Pairs

We investigate the lowest energy configurations for string - antistring pairs at fixed separations by numerically minimizing the energy. We show that for separations smaller than a critical value, a region of false vacuum develops in the middle due to large gradient energy density. Consequently, well defined string - antistring pairs do not exist for such separations. We present an example of vortex - antivortex production by vacuum bubbles where this effect seems to play a dynamical role in the annihilation of the pair. We also study the dependence of the energy of an string-antistring pair on their separation and find deviations from a simple logarithmic dependence for small separations.Comment: 14 pages, in LATEX, 7 figures (not included

Hierarchical ResNeXt Models for Breast Cancer Histology Image Classification

Microscopic histology image analysis is a cornerstone in early detection of breast cancer. However these images are very large and manual analysis is error prone and very time consuming. Thus automating this process is in high demand. We proposed a hierarchical system of convolutional neural networks (CNN) that classifies automatically patches of these images into four pathologies: normal, benign, in situ carcinoma and invasive carcinoma. We evaluated our system on the BACH challenge dataset of image-wise classification and a small dataset that we used to extend it. Using a train/test split of 75%/25%, we achieved an accuracy rate of 0.99 on the test split for the BACH dataset and 0.96 on that of the extension. On the test of the BACH challenge, we've reached an accuracy of 0.81 which rank us to the 8th out of 51 teams

A Review on Microstrip Patch Antenna and its Miniaturization Techniques

Volume 7 Issue 7 (July 201

Quantum dissipation induced noncommutative geometry

The quantum statistical dynamics of a position coordinate x coupled to a reservoir requires theoretically two copies of the position coordinate within the reduced density matrix description. One coordinate moves forward in time while the other coordinate moves backward in time. It is shown that quantum dissipation induces, in the plane of the forward and backward motions, a noncommutative geometry. The noncommutative geometric plane is a consequence of a quantum dissipation induced phase interference which is closely analogous to the Aharanov-Bohm effect.Comment: 12 pages, 2 figure