Non-simply connected copes

Let (W⁴,?W⁴) be a 4-manifold. Let f₁,f₂,…,f_k:(D²,?D²)→ (W⁴,?W⁴) be transverse immersions that have spherical duals $\text{α}{}_1\text{,α}{}_2\text{,…,α}{}_{\mathrm{k}}\text{:S}{}^2\text{→}\text{W}\text{?}$. Then there are open disjoint subsets V₁, V₂,…,V_k of W, such that for each 1?i?k, (a) ?V_i=V₁∩?W and ?V_i is an open regular neighborhood of f_i(?D²) in ?W, and (b) (V_i,?V_i,f_i(?D²)) is proper homotopy equivalent to (M, ?M, d)—a standard object in which d bounds an embedded flat disk. If we could get a homeomorphism instead of a proper homotopy equivalence, then we would be able to prove a 5-dimensional s-cobordism theorem.     

Dual Focus Optical Head for 0.6 mm and 1.2 mm Disks

We propose a dual focus optical head with a holographic optical element (HOE) which corrects spherical aberrations in order to read both 0.6 mm disks and 1.2 mm disks. The thin disks are read using transmitted light and the thick disks are read using +1st order diffracted light of the blazed HOE. The good quality of the focused spots and the focusing error signals was experimentally confirmed. No influence of unnecessary diffracted light was observed.     

Area-interaction point processes

We introduce a new Markov point process that exhibits a range of clustered, random, and ordered patterns according to the value of a scalar parameter. In contrast to pairwise interaction processes, this model has interaction terms of all orders. The likelihood is closely related to the empty space functionF, paralleling the relation between the Strauss process and Ripley'sK-function. We show that, in complete analogy with pairwise interaction processes, the pseudolikelihood equations for this model are a special case of the Takacs-Fiksel method, and our model is the limit of a sequence of auto-logistic lattice processes.     

球面反应扩散方程传播算子值域的刻画

在本文中我们给出了球面反应扩散方程传播算子值域的完全刻画。     

The Central Limit Theorem in Texture Component Fit Methods

This note is concerned with implications of spherical analogues of the central limit theorem of probability in Euclidean space. In particular, it is concerned with the presumption that the analogy holds in terms of interpreting a special spherical limiting distribution, the hyperspherical Brownian distribution, as the distribution of the resultant rotation composed by a sequence of successive random rotations under similarly mild assumptions as applied in the central limit theorem for Euclidean space. This interpretation has been stressed at several instances to indicate the superiority of the spherical Brownian distribution for applications in texture component fit methods. Here it is shown, however, that this presumption is false. Thus, an explicit correspondence of the Brownian form of texture components and processes causing preferred crystallographic orientations cannot be inferred from a central limit type argument.     

Fast direct solvers for Poisson equation on 2D polar and spherical geometries

A simple and efficient class of FFT‐based fast direct solvers for Poisson equation on 2D polar and spherical geometries is presented. These solvers rely on the truncated Fourier series expansion, where the differential equations of the Fourier coefficients are solved by the second‐ and fourth‐order finite difference discretizations. Using a grid by shifting half mesh away from the origin/poles, and incorporating with the symmetry constraint of Fourier coefficients, the coordinate singularities can be easily handled without pole condition. By manipulating the radial mesh width, three different boundary conditions for polar geometry including Dirichlet, Neumann, and Robin conditions can be treated equally well. The new method only needs O(MN log₂ N) arithmetic operations for M × N grid points. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 56–68, 2002     

Nonlinear dielectric effect of dipolar fluid mixtures

The linear and nonlinear dielectric effect for two- and three-component dipolar fluid mixtures are studied within the framework of the mean spherical approximation (MSA) of dipolar hard sphere mixtures. In our approach, equally sized dipolar hard spheres with different dipole moments are considered. Based on earlier results for the electric field dependence of the polarization our analytical equations show the so-called normal saturation effects, which are in good agreement with corresponding canonical ensemble Monte Carlo simulation data. Comparisons between the MSA based theoretical results and the corresponding Langevin and Debye-Weiss theories are also made.     

X射线连续谱法诊断铝丝阵Z箍缩等离子体温度

用球面石英弯晶衍射、CCD记录测量铝丝阵Z箍缩中的时间积分X射线连续能谱,并由连续谱斜率拟合出电子温度.该法获得的拟合数据点多,能有效筛除含线辐射的数据,减弱线辐射的影响,求得更可靠的等离子体核心高温区的温度.以发次09076为例,核心温度约为250 eV,在95%的置信度范围里,其变化范围约241—258 eV. 关键词： 球面弯晶 连续谱 电子温度 Z箍缩     

Uniform spherical grids via equal area projection from the cube to the sphere

We construct an area preserving map from a cube to the unit sphere S², both centered at the origin. More precisely, each face F_i of the cube is first projected to a curved square S_i of the same area, and then each S_i is projected onto the sphere by inverse Lambert azimuthal equal area projection, with respect to the points situated at the intersection of the coordinate axes with S². This map is then used to construct uniform and refinable grids on a sphere, starting from any grid on a square.     

外腔式He-Ne激光器的调整方法

本文提出了一套外腔式He-Ne激光器的调整方法,研究了腔长变化对纵模的影响,进而发展出一种可以有效提高谱线单色性的技术.