Existence and uniqueness of mild solutions of nonlinear difference-integrodifferential equation with nonlocal condition

In this paper we investigate the existence, uniqueness and continuous dependence of solutions of the difference-integrodifferential equations. The results are obtained by using the well known Banach fixed point theorem, the theory of semigroups and the inequality established by B. G. Pachpatte

EXISTENCE AND UNIQUENESS OF SOLUTION OF DIFFERENTIAL EQUATION OF FRACTIONAL ORDER VIA S-ITERATION

In this paper, we study the existence, uniqueness and other properties of solutions of differential equation of fractional order involving the Caputo fractional derivative. The tool employed in the analysis is based on application of S− iteration method. The study of qualitative properties in general required differential and integral inequalities, and here S−iteration method itself has equally important contribution to study various properties such as dependence on initial data, closeness of solutions and dependence on parameters and functions involved therein. Finally, we present an example in support of all proved results

Instabilities in the Nuclear Energy Density Functional

In the field of Energy Density Functionals (EDF) used in nuclear structure and dynamics, one of the unsolved issues is the stability of the functional. Numerical issues aside, some EDFs are unstable with respect to particular perturbations of the nuclear ground-state density. The aim of this contribution is to raise questions about the origin and nature of these instabilities, the techniques used to diagnose and prevent them, and the domain of density functions in which one should expect a nuclear EDF to be stable.Comment: Special issue "Open Problems in Nuclear Structure Theory" of Jour.Phys.G - accepted. 7 pages, 2 figure

On the Thermodynamic Geometry of BTZ Black Holes

We investigate the Ruppeiner geometry of the thermodynamic state space of a general class of BTZ black holes. It is shown that the thermodynamic geometry is flat for both the rotating BTZ and the BTZ Chern Simons black holes in the canonical ensemble. We further investigate the inclusion of thermal fluctuations to the canonical entropy of the BTZ Chern Simons black holes and show that the leading logartithmic correction due to Carlip is reproduced. We establish that the inclusion of thermal fluctuations induces a non zero scalar curvature to the thermodynamic geometry.Comment: 1+17 pages, LaTeX, 4 eps figure

Correlation functions of eigenvalues of multi-matrix models, and the limit of a time dependent matrix

We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of different matrices of the chain. Eventually, we consider the limit of the infinite chain of matrices, which can be interpreted as a time dependent one-matrix model, and give the correlation functions of eigenvalues at different times.Comment: Tex-Harvmac, 27 pages, submitted to Journ. Phys.

Pressure formulas for liquid metals and plasmas based on the density-functional theory

At first, pressure formulas for the electrons under the external potential produced by fixed nuclei are derived both in the surface integral and volume integral forms concerning an arbitrary volume chosen in the system; the surface integral form is described by a pressure tensor consisting of a sum of the kinetic and exchange-correlation parts in the density-functional theory, and the volume integral form represents the virial theorem with subtraction of the nuclear virial. Secondly on the basis of these formulas, the thermodynamical pressure of liquid metals and plasmas is represented in the forms of the surface integral and the volume integral including the nuclear contribution. From these results, we obtain a virial pressure formula for liquid metals, which is more accurate and simpler than the standard representation. From the view point of our formulation, some comments are made on pressure formulas derived previously and on a definition of pressure widely used.Comment: 18 pages, no figur

Probing a massive radio galaxy with gravitational lensing

The gravitational lens system CLASS B2108+213 has two lensed images separated by 4.56 arcsec. Such a wide image separation suggests that the lens is either a massive galaxy, or is composed of a group of galaxies. To investigate the structure of the lensing potential we have carried out new high resolution imaging of the two lensed images at 1.7 GHz with the VLBA and at 5 GHz with global VLBI. Compact and extended emission is detected from the two lensed images, which provides additional constraints to the lensing mass model. We find that the data are consistent with either a single lensing galaxy, or a two galaxy lens model that takes account of a nearby companion to the main lensing galaxy within the Einstein radius of the system. However, for an ensemble of global power-law mass models, those with density profiles steeper than isothermal are a better fit. The best-fitting profile for a single spherical mass model has a slope of $\gamma=$~2.45$_{-0.18}^{+0.19}$. The system also has a third radio component which is coincident with the main lensing galaxy. This component is detected at milli-arcsecond scales for the first time by the 1.7 GHz VLBA and 5 GHz global VLBI imaging. However, the third radio component is found not to be consistent with a core lensed image because the radio spectrum differs from the two lensed images, and its flux-density is too high when compared to what is expected from simple mass models with a variable power-law density profile and/or a reasonable core radius. Furthermore, 1.4 GHz imaging of the system with the MERLIN finds extended lobe emission on either side of the main lensing galaxy. Therefore, the radio emission from the third radio component is almost certainly from an AGN within the main lensing galaxy, which is classified as an FR I type radio source.Comment: 11 pages, 7 figures, 4 tables, MNRAS accepte

Logarithmic corrections to black hole and black ring entropy in tunneling approach

The tunneling approach beyond semiclassical approximation has been used to calculate the corrected Hawking temperature and entropy for various black holes and FRW universe model. We examine their derivations, and prove that the quantity $H$ in the corrected temperature is the explicit function of the only free parameter $\mathcal{A}$ (which is an auxiliary parameter defined by $\mathcal{A}=\hbar S_{BH}$). Our analysis improves previous calculations, and indicates that the leading order logarithmic correction to entropy is a natural result of the corrected temperature and the first law of thermodynamics. Additionally, we apply the tunneling approach beyond semiclassical approximation to neutral black rings. Based on the analysis, we show that the entropy of neutral black rings also has a logarithmic leading order correction.Comment: 13 pages, rewritte

High Temperature Proton Exchange Membranes With Enhanced Proton Conductivities At Low Humidity and High Temperature Based On Polymer Blends and Block Copolymers of Poly(1,3-Cyclohexadiene) and Poly(ethylene Glycol)

Hot (at 120 °C) and dry (20% relative humidity) operating conditions benefit fuel cell designs based on proton exchange membranes (PEMs) and hydrogen due to simplified system design and increasing tolerance to fuel impurities. Presented are preparation, partial characterization, and multi-scale modeling of such PEMs based on cross-linked, sulfonated poly(1,3-cyclohexadiene) (xsPCHD) blends and block copolymers with poly(ethylene glycol) (PEG). These low cost materials have proton conductivities 18 times that of current industry standard Nafion at hot, dry operating conditions. Among the membranes studied, the blend xsPCHD-PEG PEM displayed the highest proton conductivity, which exhibits a morphology with higher connectivity of the hydrophilic domain throughout the membrane. Simulation and modeling provide a molecular level understanding of distribution of PEG within this hydrophilic domain and its relation to proton conductivities. This study demonstrates enhancement of proton conductivity at high temperature and low relative humidity by incorporation of PEG and optimized sulfonation conditions

Nucleus-Electron Model for States Changing from a Liquid Metal to a Plasma and the Saha Equation

We extend the quantal hypernetted-chain (QHNC) method, which has been proved to yield accurate results for liquid metals, to treat a partially ionized plasma. In a plasma, the electrons change from a quantum to a classical fluid gradually with increasing temperature; the QHNC method applied to the electron gas is in fact able to provide the electron-electron correlation at arbitrary temperature. As an illustrating example of this approach, we investigate how liquid rubidium becomes a plasma by increasing the temperature from 0 to 30 eV at a fixed normal ion-density $1.03 \times 10^{22}/cm^3$. The electron-ion radial distribution function (RDF) in liquid Rb has distinct inner-core and outer-core parts. Even at a temperature of 1 eV, this clear distinction remains as a characteristic of a liquid metal. At a temperature of 3 eV, this distinction disappears, and rubidium becomes a plasma with the ionization 1.21. The temperature variations of bound levels in each ion and the average ionization are calculated in Rb plasmas at the same time. Using the density-functional theory, we also derive the Saha equation applicable even to a high-density plasma at low temperatures. The QHNC method provides a procedure to solve this Saha equation with ease by using a recursive formula; the charge population of differently ionized species are obtained in Rb plasmas at several temperatures. In this way, it is shown that, with the atomic number as the only input, the QHNC method produces the average ionization, the electron-ion and ion-ion RDF's, and the charge population which are consistent with the atomic structure of each ion for a partially ionized plasma.Comment: 28 pages(TeX) and 11 figures (PS