Weak convergence of the U-statistic and weak invariance of the one-sample rank order statistic for Markov processes and ARMA models

Harel and Puri (1989, J. Multivariate Anal. 29) studied the asymptotic behavior of the U-statistic and the one-sample rank order statistic for nonstationary absolutely regular processes. In this note, we present some applications of these results for Markov processes as well as ARMA processes.     

On Representing Concepts in Finite Models

We present a method of transferring Tarski's technique of classifying finite order concepts by means of truth‐definitions into finite mode theory. The other considered question is the problem of representability relations on words or natural numbers in finite models. We prove that relations representable in finite models are exactly those which are of degree ≤ o′. Finally, we consider theories of sufficiently large finite models. For a given theory T we define sl(T) as the set of all sentences true in almost all finite models for T. For theories of sufficiently large models our version of Tarski's technique becomes practically the same as the classica one. We investigate also degrees of undecidability for theories of sufficiently large finite models. We prove for some special theory ST that its degree is stronger than 0′ but still not more than Σ⁰₂.     

Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences

Recently, Fishbum and Lavalle (1995) and Lefèvre and Utev (1996) have considered some stochastic order relations specific for arithmetic random variables. The present work is concerned with these orderings, together with two other classes of stochastic order relations closely related. First, attention is paid to characterizations and various properties of all these orderings. Then, sufficient conditions of crossing-type for the two new classes of orderings are derived and extrema among discrete random variables are deduced. This is applied in actuarial sciences to obtain new bounds for the classical single life premiums as well as for the probability of ruin in the compound binomial risk model.     

On the quintuple product identity

In this note we present a new proof of the quintuple product identity which is based on our study of order theta functions with characteristics and the identities they satisfy. In this context the quintuple product identity is another example of an identity which when phrased in terms of theta functions, rather than infinite products and sums, has a simpler form and is much less mysterious.

     

Dispersion of quasi-particles in high Tc cuprates

The interplay between superconductivity (SC) and antiferromagnetism (AFM) is studied in strongly correlated systems of high T _c Cuprate superconductors. It is assumed that superconductivity arises due to BCS pairing mechanism in presence of AFM in Cu lattices of Cu-O planes. The total Hamiltonian of the system is mean field one and has been solved exactly by writing the equations of motion for the single particle Green’s functions. Equations for the appropriate single particle co-relation functions are derived and the order parameters corresponding to SC and AFM are determined. It is assumed that the Fermi energy ∈ _F = 0 and the renormalized localized f energy level coincide with the Fermi level. All the quantities in the final equation for h and Δ are made dimensionless by dividing by 2t, where t is the hopping integral. The temperature dependent values of staggered magnetic field (h) and SC gap (Δ) were determined by solving self-consistent equations for h and Δ. The quasiparticle energy bands are function of AFM gap (h), SC gap (Δ) and hybridization (V). Then the dispersion of quasi-particles are studied at different temperatures by considering temperature dependent values of h and Δ and varying other different model parameters.      

基于法布里-珀罗干涉仪的液体浓度实时检测系统的研究

设计了一种对透明液体浓度进行高精度测量的动态跟踪系统。该系统根据液体的浓度与折射率关系以及折射率与光纤法布里珀罗(F-P)干涉仪干涉光波波长、级次之间关系,通过测量法布里珀罗干涉仪干涉级次的变化量,获得液体浓度的变化量。系统中光源选用He-Ne激光器,波长为632.8 nm,输出功率为2 mW,法布里珀罗干涉腔反射面的反射系数为0.9~0.95,平行度为(1/10~1/20)光波波长,平面度为(1/20~1/100)光波波长,接收干涉条纹的器件采用电荷耦合器件(CCD),对电荷耦合器件输出的信号进行二值化处理时采用阈值浮动措施,消除光强波动带来的测量误差。通过对一组不同浓度酒精进行测量,该系统可识别出0.01?的浓度变化。     

How should one define a (weak) crystal?

We compare two proposals for the study of positional long-range order: one in terms of the spectrum of the translation operator, the other in terms of the Fourier spectrum. We point out that only the first one allows for the consideration of molecular, as opposed to atomic, (weakly) periodic structures. We illustrate this point on the Thue-Morse system.     

几何光学传递函数及其计算方法

本文借助Bessel函数、数值积分和样条函数插值给出几何光学传递函数的数值计算方法,这种方法有益于保证精度和节省计算量。     

Michael reaction. IV. NaNH2 catalyzed one stage reaction between phenylacetic acid dialkylamides and cinnamic acid methyl ester or dialkylamides. Influence of reaction conditions on the stereochemistry

The NaNH₂ catalyzed one stage reaction between phenylacetic acid dialkylamides and cinnamic acid methyl ester or dialkylamides was studied under various conditions. Conditions were found for easy preparation of each of the both possible diastereomeric derivatives of 2,3-diphenylglutaric acid. It was proved that catalytic amounts of NaNH₂ take part in the reaction. It is assumed that the observederythro/threo equilibrium ratios are determined by an isomerization via two different carbanions (at C₂ and C₄) of the reaction products.Part III:J. Stefanovsky andL. Viteva, Comun. Dept. Chem. Bulg. Acad. Sci.4, 159 (1971).     

A unique reversal of elution order during direct enantiomeric resolution of amide derivatives of 1-phenyl-2-aminopropane by high performance liquid chromatography on chiral stationary phases

Enantiomeric amide derivatives of (S)- and (R)-1-phenyl-2-aminopropane (dextro- and levoamphetamine, respectively) were resolved by high performance liquid chromatography on commercially available ionically and covalently bonded chiral stationary phases ((R)-N-(3,5-dinitrobenzoyl)phenylglycine). Ten enantiomeric amide pairs were synthesized and chromatographed on the columns by using a mobile phase of hexane-isopropanol (97 : 3), a flow rate of 2 ml/min, and a column temperature of 20°C. The (R)-isomer of all 10 amides eluted first on the covalent column as did the (R)-isomer of nine derivatives on the ionic column. however, the 3,5-dinitrobenzoyl amide of (S)- amphetamine eluted before the (R)-isomer on the ionic column. This reversal in enantiomeric elution order reveals the complexity of the interactions occurring on these columns and emphasizes the hazards of relying on observed elution order as an a priori indication of absolute configuration.