Pták sum of a Boolean algebra with an effect algebra and its completeness

The aim of the present paper is to show that a bounded Boolean power of an effect algebra has all the analogous properties required for Pták's sum of a Boolean algebra and an orthomodular lattice and to prove a theorem about its completeness. We also give for elements of that Pták sum an important form for their expression.     

Parton distribution and decay functions

We define parton distribution and decay functions in QCD and prove some of their basic properties. These include renormalization, light-cone expansions and sum rules.     

Kramers-Kronig relations and sum rules of negative refractive index media

Negative refractive index media have become a hot topic in physics due to their proposed revolutionary properties, which would have drastic consequences in design of novel optical devices. We show that Kramers-Kronig relations connecting the real and imaginary parts of the complex refractive index of absorbing media are valid even though the real refractive index may take negative value at some spectral range. In addition universal sum rules for linear optical constants of negative index media are also valid. This means that negative refractive index media are not fundamentally different from regular media. Hence, any spectrum measured from negative refractive index media can be analyzed using dispersion relations and sum rules, which have so far provided information on the optical properties of materials.Received: 13 May 2004, Published online: 30 September 2004PACS: 77. Dielectrics, piezoelectrics, and ferroelectrics and their properties - 78.20.Ci Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity)     

对规范粒子极化矢量的一些讨论

对规范粒子的极化矢量做了较为系统的论述. 讨论内容包括极化矢量的具体形式和性质、求和规则和规范传播子之间的关系以及由其张成的投影算子的性质. 通过若干精选的例子, 进一步演示了计算牵涉规范粒子的过程时采用的基本方法和应当注意事项.     

Sum rules for nuclear collective excitations

Characterizations of the response function and of integral properties of the strength function via a moment expansion are discussed. Sum rule expressions for the moments in the RPA are derived. The validity of these sum rules for both density independent and density dependent interactions is proved. For forces of the Skyrme type, analytic expressions for the plus three energy weighted sum rules are given for isoscalar monopole and quadrupole operators. From these, a close relationship between the monopole and quadrupole energies is shown and their dependence on incompressibility and effective mass is studied. The inverse energy weighted sum rule is computed numerically for the monopole operator, and an upper bound for the width of the monopole resonance is given. Finally the reliability of moments given by the RPA with effective interactions is discussed using simple soluble models for the hamiltonian, and also by comparison with experimental data.     

机械振动理论方法与直链烷烃性质研究

将直链烷烃分子看成是一个多自由度振动系统 ,用机械振动理论中的传递矩阵法计算了C2 ～C3 2 直链烷烃的固有频率 ,分析了固有频率随化合物结构单元的变化规律 .发现各阶固有频率中的基频与直链烷烃的结构型性质呈现出优良的相关性 ,用各阶固有频率之和表示的总频与直链烷烃的加和型性质也呈现出优良的相关性 ,将两者组合后还能够反映直链烷烃的凝聚型性质的变化规律 .在此基础上建立了直链烷烃的物化性能与基频和总频之间的定量相关模型 .用该模型对直链烷烃的电离能、沸点、临界温度、临界压力、密度、粘度、标准生成焓、离子标准生成焓、常压热容、折光指数等 10种不同类型性质的实验数据进行回归分析 ,相关系数均大于 0 .999.     

Photon Excitations Excitated the Sqeezing Properties of the Excited Entangled Coherent States

In our previous paper, we have introduced a new kind of continuous-variable-type entangled states, called double-mode excited entangled coherent states. In this paper, we study sum squeezing properties of such excited entangled coherent states. We focus on discussing the influence of photon excitations on sum squeezing properties. It is found that the photon excitations seriously affected sqeezing properties of the excited entangled coherent states. With increasing the number of the photon excitations m, the higher-order terms move away from its initial state |ψ ₀〉 and the degrees of sum squeezing are increasing. In this sense, it implies that the photon excitations excitated the sum sqeezing properties of the double-mode excited entangled coherent states.     

Molecular mean field theory for liquid water

Attractive bonding interactions between molecules typically have inherent conservation laws which influence the statistical properties of such systems in terms of corresponding sum rules. We have considered lattice water as an example, and we have enunciated the consequences of the sum rule through a general computational procedure called molecular mean field theory. Fluctuations about the mean field are computed and many of the liquid properties have been deduced and compared with Monte Carlo simulation, molecular dynamics, and experimental results. Large correlation lengths are seen to be a consequence of the sum rule in the liquid phase. Long-range Coulomb interactions are shown to have minor effects on our results.     

The simplest decomposition of a turbulent field

In this paper we will present some recent results concerning the simplest decomposition of a turbulent field. The large scale filtering operator is simply given by the two-point sum in space and the associated fluctuation is given by the two-point difference. In the paper we will present the general properties of this simple decomposition and their particular relations with the subgrid stresses and the generalized central moments associated to a generic filtering operator.     

Disentangling the nature of resonances in coupled-channel models

We present several possible hadronic states found in coupled-channel models within the on-shell approximation. The interaction potential is constructed as a sum of the tree-level Feynman diagrams calculated with the effective Lagrangians. Based on the recent empirical data, we illustrate the possible existence of several baryonic and mesonic states with definite quantum numbers in the model. We give their properties for the purpose of further study and discuss the potential of finding them in future experiments.     

On the validity of sum rules and Fermi-liquid properties in calculations for strongly correlated electrons

A thorough account is given on the accuracy of assumptions and the validity of mathematical manipulations underlying the derivation of the Friedel sum rule and the so called density of states sum rule for electrons with strong local correlations. While possible exceptions are pointed out and discussed, the sum rules should hold rather well for realistically chosen parameters in models describing e.g. heavy fermion systems. They are used to assert the correctness of NCA calculations for large degeneracyN and to estimate their shortcomings forN=2. A discussion of the corresponding violation of Fermiliquid properties is extended to the case of an applied magnetic field and put into context with the calculation of (magneto-) transport properties of Kondo impurities and Kondo lattices.This work was performed within the research program of SFB 252 Elektronisch hochkorrelierte metallische Materialien     

Meson fields, exchange currents and progenitor sum rules

The theory of the integrated photoabsorption cross section and the dipole sum rule is reviewed. A new progenitor sum rule, in which meson fields appear explicitly, is derived from a field theory of interacting pions and nucleons. The relation of this sum rule to previous results obtained in a potential theory is elucidated, and the role of neutron-proton correlations in nuclear ground states is discussed in terms of their effect on the dipole sum rule. The inclusion of ρ-mesons (again in an oversimplified theory) and their contribution to progenitor sum rules is also mentioned.     

Light neutrinos in cosmology

Neutrinos can play an important role in the evolution of the Universe, modifying some of the cosmological observables. We describe how the precision of present cosmological data can be used to learn about neutrino properties, in particular their mass. We show how the analysis of current cosmological observations provides an upper bound on the sum of neutrino masses, with improved sensitivity from future cosmological measurements.     

Bound-state perturbation method via SVZ sum rules in quantum mechanics

The perturbation method for bound states within the framework of the Shifman-Vainshtein-Zakharov sum rule method is studied on simple systems (linear harmonic oscillator, hydrogen atom) in external electric fields. It is pointed out that for stronger fields reasonable results for the ground-state energy can only be achieved when sum rules are written for the correction to the Euclidean Green function caused by the external field. Moreover, if the system is bound by a singular (Coulomb) potential, one needs to sum higher perturbative corrections to the Green function and to find a realistic approximation of the continuum contribution to the sum rules. The results are of relevance e.g. for calculations of nucleon magnetic moments and toponium properties via SVZ sum rules in QCD.     

Determination of the Disperse Composition of a PbO Suspension Containing Aggregates of Particles of Lamellar Shape by the Laser-Polarimetry Method

The results of measurements of the scattering matrix at a wavelength of 0.63 μm in the range of scattering angles of 10°–155° are presented for an aqueous suspension of lead oxide containing particles of plate form and their aggregates of monomers with dimensions of ~5 nm. The results of the measurements are compared with the results of calculations for axially symmetric scatterers (ellipsoids of rotation, cylinders). It is shown that the presence of aggregates affects the scattering properties of such a medium. The results of reconstructing the distribution of particles of a disperse medium in sizes from the measurements data of the scattering matrix are presented. The reconstruction of the distributions was carried out by solving the problem of optimizing the sum of the squared deviations of the experimental and calculated values of matrix elements in the framework of the model of axially symmetric scatterers. It is shown that the distribution of particles by sizes is more accurately reconstructed by minimizing the sum of the squares of the deviations for the sum of the diagonal elements. The obtained distribution is compared with the distribution measured by the method of dynamic light scattering.     

and as Vertex Operator Extensions¶of Dual Affine Algebras

We discover a realisation of the affine Lie superalgebra and of the exceptional affine superalgebra as vertex operator extensions of two algebras with “dual” levels (and an auxiliary level-1 algebra). The duality relation between the levels is . We construct the representation of on a sum of tensor products of , , and modules and decompose it into a direct sum over the spectral flow orbit. This decomposition gives rise to character identities, which we also derive. The extension of the construction to is traced to the properties of embeddings into and their relation with the dual pairs. Conversely, we show how the representations are constructed from representations. Received: 29 July 1999 / Accepted: 6 February 2000     

Separation of spin and orbital angular coherence momenta in the second-order coherence theory of vector electromagnetic fields

In analogy with the separation of the total optical angular momentum into a spin and an orbital part in electrodynamics, we introduce a new concept of spin and orbital angular coherence momenta into the general coherence theory of vector electromagnetic fields. The properties of the newly introduced spin and orbital angular coherence momenta are investigated through the decomposition of the total coherence angular momentum into the sum of these two components, and their separate conservations have been derived for what is believed to be the first time.     

Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial–vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson–Schwinger equations.     

Skyrme Forces and Their Applications in Low Energy Nuclear Physics

This paper reviews the present status of Skyrme forces and their applications in the field of low energy nuclear physics as an effective nucleon-nucleon interaction. Their applications in the following five domains are presented:1). Hartree-Fock (HF), selfconsistent semiclassical (SCSC) calculations and nuclear ground state properties;2). random phase approximation (RPA), sum rule approach and properties of nuclear giant resonances;3). calculations of microscopic nucleon-nucleus optical potentials and related quantities;4). calculations of nucleus-nucleus optical potentials and fusion barriers;5). multifragmentation, liquid-gas phase transition and instability of hot/compressed nuclei.     

Collaborate,compete and share

We introduce and study a model of an interacting population of agents who collaborate in groups which compete for limited resources. Groups are formed by random matching agents and their worth is determined by the sum of the efforts deployed by agents in group formation. Agents, on their side, have to share their effort between contributing to their group’s chances to outcompete other groups and resource sharing among partners, when the group is successful. A simple implementation of this strategic interaction gives rise to static and evolutionary properties with a very rich phenomenology. A robust emerging feature is the separation of the population between agents who invest mainly in the success of their group and agents who concentrate in getting the largest share of their group’s profits.