Isotopic families of contact manifolds for elliptic PDE

A test for a function to be a solution of an elliptic PDE is given in terms of extensions, as solutions, from the boundaries inside the domains belonging to an isotopic family. It generalizes a result of Ehrenpreis for spheres moved along a straight line.

     

Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity

The interferometric intensity patterns from a 2D shearing interferometer are shown and discussed. The intensity patterns can be obtained in two different approaches incorporating differential and extended wavefront controlled displacements. The reliable directional sensitivity of this interferometer allows the optimization of the measurement parameters to estimate the wavefront of the intensity patterns by regularization techniques.     

Banach空间二阶非线性微分方程的弱Carathéodory解

本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果     

Odd-Excited Binomial States of the Radiation Field and Some of Their Statistical Properties

In this paper a new state called odd-excited binomial state (OEBS) is introduced. It interpolates between the odd number state and the odd-excited coherent state. We discuss some statistical properties, such as the Glauber second-order correlation function and squeezing phenomenon (normal and amplitude-squared squeezing) for this state. The quasiprobability distribution functions (Husimi Q-function and Wigner W-function) are also examined.     

Study on crystalline properties of Er-Si-O compounds in relation to Er-related 1.54 μm photoluminescence and electrical properties

Er-Si-O crystalline compounds, which exhibit superlattice structures and sharp and strong Er-related 1.54 μm photoluminescence (PL) spectra at room temperature have been formed by self-assembling growth mechanism. Oxidation of the starting materials which have Si and Er at an atomic ratio of 2:1 are prepared and then oxidation and succeeding high-temperature annealing in Ar above 1250 °C cause a self-assembled superlattice-structured Er-Si-O crystalline compounds. The control of the ratio of Si and Er, as well as the following oxidation and annealing processes, is found to be sensitive to the crystalline properties, PL spectra and electrical properties. In this study, Er-Si-O crystalline thin films are formed on Si substrates by sol-gel and MOMBE methods, and their crystalline properties such as crystalline orientation and concentration ratio of Er, Si and O are investigated. Crystalline Er-Si-O films of high orientation are successfully grown on Si(1 0 0) and its inclined surface. The PL and excitation spectra, fluorescence decay and the electrical properties are found to be strongly related to the crystalline properties. Excess O causes a broader 1.54 μm PL spectra, slower fluorescence decay, lower carrier-mediated excitation and higher resistivity. A precise control of O is found to be necessary to grow superlattice-structured Er-Si-O compounds, which are semiconducting and are excitable via carrier-mediated excitation mechanism.     

Necessary Conditions for Differentiability of Distance Functions

Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained.     

Nonsensitiveness Regions for Threshold Ellipsoids

The problem is to determine nonsensitiveness regions for threshold ellipsoids within a regular mixed linear model.     

On the duration of the total eclipse of a satellite of a body

This paper solves the problem of the duration of the total eclipseof a satellite of a body, provided that (a) the body is sphericalin shape and the mass distribution inside the body is sphericallysymmetrical; (b) the satellite is a very small object; (c) thesatellite's orbit around a body is circular and the satellitecan pass through the centre of its shadow; (d) a source of lightis the source of the conical body's shadow (umbra) and it doesnot change its apparent position in the sky; (e) there are noperturbations on the satellite's orbit. The solution presentedrepresents the general discussion of the problem based on utilizationof some parts of the theory of contraction mappings.     

激光等离子体2660紫外探针及干涉系统

成功地在六路高功率Nd玻璃激光装置上建立了2660紫外激光探针和适合紫外波段的Normaski干涉仪,首次将可见波长的连续激光应用于紫外干涉仪中靶成像调整和光路准直。利用该紫外光干涉仪,在铜柱状靶(φ500μm)上测量了厚等离子体中高达0.6n。的电子密度。     

General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas

We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find the most general effective Lagrangian consistent with both general coordinate and conformal invariance to leading and next-to-leading orders in the momentum expansion. At the leading order the Lagrangian contains one phenomenological constant and reproduces the results of the Thomas-Fermi theory and superfluid hydrodynamics. At the next-to-leading order there are two additional constants. We express various physical quantities through these constants.