Effect of Zn Substitution on Magnetic Properties of CuFe_2O_4: a High-Temperature Series Expansions Study

The magnetic properties of spinel ferrites Cu_(1-x)Zn_xFe_2O_4 are studied using high-temperature series expansions combined with the Padé approximates. The exchange interactions, inter and intra-sublattices J_(AA), J_(BB) and J_(AB) are obtained using a probability distribution law. The critical exponent associated with the magnetic susceptibility is obtained.     

An On-Line Library of Extended High-Temperature Expansions of Basic Observables for the Spin-S Ising Models on Two- and Three-Dimensional Lattices

We present an on-line library of unprecedented extension for high-temperature expansions of basic observables in the Ising models of general spin S, with nearest-neighbor interactions. We have tabulated through order ²⁵ the series for the nearest-neighbor correlation function, the susceptibility and the second correlation moment in two dimensions on the square lattice, and, in three dimensions, on the simple-cubic and the body-centered cubic lattices. The expansion of the second field derivative of the susceptibility is also tabulated through ²³ for the same lattices. We have thus added several terms (from four up to thirteen) to the series already published for spin S = 1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 5, .     

Heat Kernel Expansions on the Integers

In the case of the heat equation u _t =u _xx +Vu on the real line, there are some remarkable potentials V for which the asymptotic expansion of the fundamental solution becomes a finite sum and gives an exact formula.We show that a similar phenomenon holds when one replaces the real line by the integers. In this case the second derivative is replaced by the second difference operator L ₀. We show if L denotes the result of applying a finite number of Darboux transformations to L ₀ then the fundamental solution of u _t =Lu is given by a finite sum of terms involving the Bessel function I of imaginary argument.     

Zn Doping Effect on Magnetic Properties of Znx Cdl-xCr2S4 Systems by High-Temperature Series Expansions

The effect of Zn doping on the magnetic properties of CdCr2S4 systems is studied by mean field theory and high-temperature series expansion （HTSE）. The nearest neighbouring and the next-neighbouring super-exchange interactions Jl（x） and J2（x） are evaluated for the spinel system Zn, Cd1-xCr2S4 in the range 0 〈 x 〈 1. The intra-planar and the inter-planar interactions are deduced. The HTSE combined with the Padd approximant method （PA） is applied to the spinel system ZnxCdl-,Cr2S4. The magnetic phase diagram, i.e. Tc versus dilution x, is obtained. The critical exponents associated with the magnetic susceptibility 7 and the correlation length u are deduced. The obtained theoretical results are in agreement with the experimental data obtained by magnetic measurements.     

A Perspective on Regularization and Curvature

A global connection on the Connes Marcolli renormalization bundle relates β-functions of a class of regularization schemes by gauge transformations, as well as local solutions to β-functions over curved space–time.     

托贝莫来石晶体的高温相变规律研究

通过差热分析(TGA/DSC)、X射线衍射分析(XRD)、傅里叶变换红外光谱分析(FTIR)等测试技术,对实验室制备的纯净托贝莫来石的高温相变规律进行系统的研究。DSC结果表明,托贝莫来石结构中有四个层间分子水,加热到300 ℃时四个层间分子水逐渐失去。当温度升高到724 ℃时,部分Si—O—H键断裂,失去羟基。XRD结果表明托贝莫来石晶体结构在724 ℃时已经破坏,衍射峰基本消失,煅烧后的样品为无定形的非晶态。当温度持续升高到861 ℃时,发生晶型重构,硅灰石晶体出现,结构转变为有序的、稳定的晶体结构。当温度到达1 000 ℃的时候,完全转变为2M型硅灰石晶体结构。托贝莫来石的高温相变经历了“托贝莫来石→脱水托贝莫来石→脱羟基托贝莫来石→硅灰石”一系列转变过程。     

High-Temperature Infrared Emission Measurements on HNC

The emission spectrum of HNC has been measured from 400 to 4100 cm(-1). The HNC was observed as an equilibrium mixture of HCN and HNC in a fused quartz cell heated to 1370 K. The three fundamental bands and many hot bands of HNC were measured with resolutions ranging from 0.006 cm(-1) for the lowest fundamental to 0.033 cm(-1) for the other two. High rotational levels up to J=62 were observed as well as vibrational levels up to v(2)=5. Now all the quadratic contributions to the vibrational and rotational term values have been determined, as well as some higher order terms. Copyright 2001 Academic Press.     

Regularization of chiral gauge theories

The regularization of chiral gauge theories is reviewed from the “overlap” point of riew. This is a brief and biased review containing no references. Contribution dedicated to Lawrence Horwitz on the occasion of his 65th birthday     

Regularization of synchronized chaotic bursts

The onset of regular bursts in a group of irregularly bursting neurons with different individual properties is one of the most interesting dynamical properties found in neurobiological systems. In this paper we show how synchronization among chaotically bursting cells can lead to the onset of regular bursting. In order to clearly present the mechanism behind such regularization we model the individual dynamics of each cell with a simple two-dimensional map that produces chaotic bursting behavior similar to biological neurons.     

On the Equivalence of Regularization Schemes

We illustrate via the sunset diagram that dimensional regularization ‘deforms‘ the nonlocal contentsof multi-loop diagrams with its equivalence to cutoff regularization scheme recovered only after sub-divergence wassubtracted. Then we employed a differential equation approach for calculating loop diagrams to verify that dimensionalare argued especially in nonperturbativc perspective.     

Implicit Regularization and Renormalization of QCD

We apply the Implicit Regularization (IR) technique in a non-abelian gauge theory. We show that IR preserves gauge symmetry as encoded in relations between the renormalization constants required by the Slavnov–Taylor identities at the one-loop level of QCD. Moreover, we show that the technique handles divergencies in massive and massless QFT on equal footing.     

The Generalized Eigenvector Expansions of the Liouville Operator

In this paper, we study the generalized eigenvector expansions of the Liouville operator, and construct the corresponding rigged Liouville space. As an example, we obtain the rigged Liouville space for the harmonic oscillator of one-dimensional.     

Viscous Regularization of Breaking Faraday Waves

The effect of the viscosity of a liquid on the parameters of standing surface gravity waves in a vertically oscillating rectangular vessel has been experimentally studied. It has been shown for the first time that a 60-fold increase in the viscosity of a working medium as compared to water fundamentally changes the parameters of the second nonlinear wave mode: waves are regularized in the total absence of their breaking. The effect of viscosity on the resonance dependences and process of damping of waves has been studied. The numerical analysis of the dispersion relation for gravity waves has shown that the effects observed in the experiment are due to the presence of short-range perturbations in the cutoff region, where viscous dissipation becomes a dominant factor and short waves are suppressed.     

Expansions of Algebras and Superalgebras and Some Applications

After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the ?nönü–Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32).     

Shorter Expansions of Molecular Integrals in Hylleraas-CI Calculations

Over Cartesian Gaussian orbitals, Clementi and his co-workers have recently derived the formulas of molecular integrals appearing in the Hylleraas-CI method. There are many terms which exactly cancel one another in their formulas. By using the approach of generating functions, these terms are removed, giving rise to shorter expansions and simpler expressions for the molecular integrals.     

基于非凸正则化项的合成孔径雷达图像分割新算法

合成孔径雷达图像中乘性噪音的存在使合成孔径雷达图像分割变得非常困难.针对这一难题,本文以提高分割准确度,保护图像的几何结构边缘和提高算法的鲁棒性为目的,提出了一种适用于处理合成孔径雷达图像分割的新模型.新模型结合合成孔径雷达图像的区域和边缘信息,首先通过引入非凸的正则化项,定义了能量泛函;然后极小化能量泛函,建立了水平集函数演化的偏微分方程;最后对水平集演化方程的数值求解,实现了对合成孔径雷达图像感兴趣区域的分割.分别采用仿真图像和实测合成孔径雷达图像对新模型进行验证,结果表明,新模型对合成孔径雷达图像具有很强的边缘定位能力,能使目标区域分割更完整.     

On the Calculation of Two-Center Overlap Integrals with STO's Using Zeta-Function Method and Multipole Moments

One electron two-center overlap integrals are re-derived using Barnett's -function method and Guseinov electric-multipole-moments translation technique. To evaluate these integrals a computer program has been constructed. The obtained results are in good agreement with literature.     

基于非凸正则化项的合成孔径雷达图像分割新算法

合成孔径雷达图像中乘性噪音的存在使合成孔径雷达图像分割变得非常困难.针对这一难题,本文以提高分割准确度,保护图像的几何结构边缘和提高算法的鲁棒性为目的,提出了一种适用于处理合成孔径雷达图像分割的新模型.新模型结合合成孔径雷达图像的区域和边缘信息,首先通过引入非凸的正则化项,定义了能量泛函;然后极小化能量泛函,建立了水平集函数演化的偏微分方程;最后对水平集演化方程的数值求解,实现了对合成孔径雷达图像感兴趣区域的分割.分别采用仿真图像和实测合成孔径雷达图像对新模型进行验证,结果表明,新模型对合成孔径雷达图像具有很强的边缘定位能力,能使目标区域分割更完整.