Particles and “bumps” in quantum field configurations

We study an approach to making a precise identification of particles with bumps in quantum field configurations. The problem requires some effort because typical field configurations are distributions and not elements of the classical configuration space at all. We show that the part of a configuration consisting of vacuum fluctuations may be identified and filtered out in a very natural way, leaving a function which is in the classical configuration space. The filtered field configuration depends on the state of the field, and for ann-particle state withn particles well localized and well separated in the Newton-Wigner sense, the filtered field configuration hasn bumps located where the particles are. We close with a discussion of observation in the Schrödinger representation for the free field in terms of our results.This paper is dedicated to the memory of Paola Calderoni.     

Opacity calculations on plasmas with open M and N shell configurations

The relative importance of different ion configurations to the opacity of partially ionised Niobium is investigated using computed results and experimental data. Data for a Nb plasma with an almost full M shell and an N shell with around 3 bound electrons [D. Hoarty et al. High Energy Density Physics 3 (2007) 325] are used to test the output of an opacity code as increasingly large numbers of ion configurations are considered. We find that in the conditions afforded by the experimental data, only a small subset of ion configurations need to be included; evidence is also seen that if the ion configurations included allow the average plasma ionisation to be reproduced (by correcting for the neglected populations of high n states), convergence occurs rapidly.     

类钠离子的电子碰撞电离截面

利用相对论修正扭曲波玻恩交换近似,计算了8个类钠离子的电子碰撞直接电离和激发自电离截面.基于这些结果,给出了计算类钠等电子系离子(18≤Z≤39)直接电离和激发自电离截面的高精度拟合公式.计算结果与现有的实验值和其他理论值比较,相当一致 关键词： 电离截面 组态相互作用 扭曲波玻恩交换近似 拟合公式     

On the Comparison of Two Strategies to Formulate Orthotropic Hyperelasticity

The main goal of this work is to clarify the relation between two strategies to formulate constitutive equations for orthotropic materials at large strains. On the one hand, the classical approach is based on the incorporation of structural tensors into the free energy function via an enriched set of invariants. On the other hand, a fictitious isotropic configuration is introduced which renders an anisotropic, undeformed reference configuration via an appropriate linear tangent map. This formulation results in a reduced (with respect to the more general setting based on structural tensors) but nevertheless physically motivated set of invariants which are related to the invariants defined by structural tensors. As a main conceptual advantage standard isotropic constitutive equations can be applied and moreover, due to the reduced set of physically motivated invariants, the numerical treatment within a finite element setting becomes manageable.     

Equation of State of Dense Plasma Mixtures: Application to the Sun Center

We present a self‐consistent approach to the modeling of dense plasma mixtures in local thermodynamic equi‐librium. In each electron configuration the nucleus is totally screened by electrons in a Wigner‐Seitz sphere (ion‐sphere model). Bound and free electrons are treated quantum‐mechanically. The assumption that all species should have the same electronic environment leads to the equality of the electronic pressure for all ions of all elements having therefore different cell volumes. The variation of the average atomic radii of the different elements with respect to temperature is investigated, and the procedure is applied to the determination of pressure in the Sun center (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

一类由正四面体和正八面体组成的共轭套中心构型

A new case configuration in R3,the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed.If the configuration is a central configuration,then all masses of outside layer are equivalent,the masses of inside layer are also equivalent.At the same time the following relation between p(r=√3/3ρ is the radius ratio of the sizes)and mass ratio r=～m/m must be satisfied r=-m/m=ρ(ρ+3)(3+2ρ+ρ2)-3/2+ρ(-ρ+3)(3-2ρ+ρ2)-3/2-4.2-3/2ρ-2-4-1ρ-2/2(1+ρ)(3+2ρ+ρ2)-3/2+2(ρ-1)(3-2ρ+ρ2)-3/2-4(2√2)-3ρ,and for any mass ratio T,when mass ratio T is in the open interval(0,0.03871633950…),there exist three central configuration solutions(the initial configuration conditions who imply hamagraphic solutions)corresponding radius ratios are r1,r2,and r3,two of them in the interval(2.639300779…,+∞)and one is in the interval(0.7379549890…,1.490942703…).when mass ratio T is in the open interval(130.8164950…,+∞),in the same way there have three corresponding radius ratios,two of them in the interval(0,0.4211584789…)and one is in the interval(0.7379549890…,1.490942703…).When mass ratio T is in the open interval(0.03871633950…,130.8164950…),there has only one solution T in the interval (0.7379549890…,1.490942703…).     

The symbolic defect of an ideal

Let I be a homogeneous ideal of $\mathbb{k}[x_0,\dots ,x_n]$. To compare $I^{(m)}$, the m-th symbolic power of I, with $I^m$, the regular m-th power, we introduce the m-th symbolic defect of I, denoted $\mathrm{sdefect}(I,m)$. Precisely, $\mathrm{sdefect}(I,m)$ is the minimal number of generators of the R-module $I^{(m)}/I^m$, or equivalently, the minimal number of generators one must add to $I^m$ to make $I^{(m)}$. In this paper, we take the first step towards understanding the symbolic defect by considering the case that I is either the defining ideal of a star configuration or the ideal associated to a finite set of points in ${\mathbb{P}}^2$. We are specifically interested in identifying ideals I with $\mathrm{sdefect}(I,2)=1$.     

Affine Configurations and Pure Braids

We show that the fundamental group of ordered affine-equivalent configurations with at least five points in the real plane is isomorphic to the pure braid group in as many strands, modulo its centre. In the case of four points, this fundamental group is free with 11 generators. This work was carried out at the Instituto de Matemáticas, UNAM and partially funded by the Sistema Nacional de Investigadores and a doctoral fellowship from CONACyT México.     

Absolute Configuration OP Secondary Alcohols: Refinement and Extension of a Gas-Chromatographic Modification of Horeau's Method

Abstract

In our adaptation of Horeau's method of partial kinetic resolution, excess α-phenylbutyric anhydride is converted to diastereomeric amides for determination of its optical composition by gas-liquid chromatography. A modified procedure allows the use of as little as 1 μmole of substrate. The validity of configurational assignments based on these methods has been explored for a wide range of chiral alcohols, including a number of alkaloids. Important areas of potential application of the new procedures are delineated.