An inequality connecting entropy distance,Fisher Information and large deviations

In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large deviation rate functional. In addition to possessing various favourable properties, we show that this generalised Fisher Information converges to the classical Fisher Information in an appropriate limit. We then use this generalised Fisher Information and the aforementioned inequality to qualitatively study coarse-graining problems for jump processes on discrete spaces.     

System Identification Models of the Equivalent Permittivity for Rain Medium

The dielectric constant for rain medium is investigated by utilizing the system identification method. The rain rate model and frequency model of permittivity in millimeter waves band for rain medium are presented. The results obtained with models are in very good agreement with references in calculating the attenuation of electromagnetic waves induced by rain, which Shows that the obtained models are valid and practicable. The cross-polar discrimination gotten with rain rate model is in agreement with references.     

Generalized 3G theorem and application to relativistic stable process on non-smooth open sets

Let G(x,y) and GD(x,y) be the Green functions of rotationally invariant symmetric α-stable process in Rd and in an open set D, respectively, where 0<α<2. The inequality GD(x,y)GD(y,z)/GD(x,z)?c(G(x,y)+G(y,z)) is a very useful tool in studying (local) Schrödinger operators. When the above inequality is true with c=c(D)∈(0,∞), then we say that the 3G theorem holds in D. In this paper, we establish a generalized version of 3G theorem when D is a bounded κ-fat open set, which includes a bounded John domain. The 3G we consider is of the form GD(x,y)GD(z,w)/GD(x,w), where y may be different from z. When y=z, we recover the usual 3G. The 3G form GD(x,y)GD(z,w)/GD(x,w) appears in non-local Schrödinger operator theory. Using our generalized 3G theorem, we give a concrete class of functions belonging to the non-local Kato class, introduced by Chen and Song, on κ-fat open sets. As an application, we discuss relativistic α-stable processes (relativistic Hamiltonian when α=1) in κ-fat open sets. We identify the Martin boundary and the minimal Martin boundary with the Euclidean boundary for relativistic α-stable processes in κ-fat open sets. Furthermore, we show that relative Fatou type theorem is true for relativistic stable processes in κ-fat open sets. The main results of this paper hold for a large class of symmetric Markov processes, as are illustrated in the last section of this paper. We also discuss the generalized 3G theorem for a large class of symmetric stable Lévy processes.     

Optical bistability of planar metal/dielectric nonlinear nanostructures

We study theoretically a nonlinear response of the planar metal/dielectric nanostructures constituted from periodical array of ultra thin silver layers and the layers of Kerr-like nonlinear dielectric. We predict hysteresis-type dependences of the components of the tensor of effective dielectric permittivity on the field intensity allowing the change in material transmission properties from transparent to opaque and back at extremely low intensities of the light. It makes possible to control the light by light in all-optical nanoscale devices and circuits.     

Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

On fencing problems

Fencing problems regard the bisection of a convex body in a way that some geometric measures are optimized. We introduce the notion of relative diameter and study bisections of centrally symmetric planar convex bodies, bisections by straight line cuts in general planar convex bodies and also bisections by hyperplane cuts for convex bodies in higher dimensions. In the planar case we obtain the best possible lower bound for the ratio between the relative diameter and the area.     

苯乙烯和丙烯酸-β-羟乙酯不同温度的竞聚率测定

苯乙烯和丙烯酸 β 羟乙酯不同温度的竞聚率测定吴平平吴玉芳陆琛杨全兴韩哲文（华东理工大学材料科学研究所上海２００２３７）陈顺喜朱清仁（中科院中国科技大学结构分析开放实验室合肥２３００２６）关键词苯乙烯，丙烯酸 β 羟乙酯，共聚合，竞聚率丙烯酸 β?..     

Dielectric relaxation studies of 1-hexanol and 1,2-hexanediol in heptane

Solutions of 1-hexanol and 1,2-hexanediol in heptane have been investigated tigated by means of dielectric time domain spectroscopy (TDS). The permittivity spectrum of 1-hexanol in heptane is characterized by a model function containing a sum of three elementary Debye dispersions, while 1,2-hexanediol in heptane is best described by a Cole-Davidson model function. It is shown that dilute solutions of 1-hexanol in heptane have a completely different behavior to that of 1,2-hexanediol. For the diol, the relaxation time levels off at a high value indicating an existence of higher hydrogen bonded complexes. It is possible to quantify the relative amount of monomeric 1-alcohol molecules from the dielectric spectrum. The monomerization rate for 1-hexanol upon dilution with heptane is initially low, but increases rapidly for mole fractions of heptane exceeding 0.4.     

The dielectric properties of water in its different states of interaction

A tutorial on dielectric (relaxation) spectrometry of liquids is given in this article. Some methods of measuring complex (electric) permittivity spectra are briefly described. Results for water are presented and related to characteristic properties of the liquid structure and to models of the molecular dynamics, particularly as resulting from computer simulation studies. Dielectric spectra for aqueous solutions of low weight electrolytes, polyelectrolytes, small molecules, and polymers are discussed to illustrate effects of kinetic depolarization, structure saturation, as well as positive, negative, and hydrophobic hydration. Reference is also made to fluctuations in the hydrogen bond network of mixtures of water with liquids that are completely miscible with this unique solvent.