On multiplication groups of relatively free quasigroups isotopic to Abelian groups

If Q is a quasigroup that is free in the class of all quasigroups which are isotopic to an Abelian group, then its multiplication group Mlt Q is a Frobenius group. Conversely, if Mlt Q is a Frobenius group, Q a quasigroup, then Q has to be isotopic to an Abelian group. If Q is, in addition, finite, then it must be a central quasigroup (a T-quasigroup).This work was supported by institutional grant MSM 113200007, and by Grant Agency of Czech Republic, grant number 201/99/0263.     

On Distribution of Error of Linear Wavelet Estimator of Probability Density

We establish the asymptotic normality of the squared L ²-norm of the approximation error of a linear wavelet estimator of the density of a distribution. The calculations are based on the smallness of correlations between the coefficients of the high-frequency part of the multiresolution expansion of the estimator.Supported by the FCT Foundation (Portugal) in the framework of the project Probability and Statistics (2000–2002), Centro de Matematica, Universidade da Beira Interior.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 2, pp. 184–207, April–June, 2005.     

Theory of quantum fluctuations and the Onsager relations

A microscopic model is constructed within the theory of normal fluctuations for quantum systems, yielding an irreversible dynamics satisfying the Onsager relations. The property of return to equilibrium and the principle of minimal entropy production are proved.     

Synthesis,Characterization and Migration of Ionic Polyferrocenyl Compounds of 5‐Ferrocenyl‐1H‐tetrazole and Their Effects During Combustion

Eighteen ionic polyferrocenyl compounds with 5‐ferrocenyl‐1H‐tetrazolate as anion and mono‐ and dinuclear ferrocenyl‐alkylammonium as cations were synthesized and characterized by ¹H NMR, ¹³C NMR, FT‐IR, and UV/Vis spectroscopy, and elemental analysis. Molecular structures of three compounds were further confirmed by single‐crystal X‐ray diffraction. Their thermal stability was evaluated by TG and DSC and found that they are of high thermal stability. The cyclic voltammetry analysis suggested that each of the compounds exhibits only an irreversible redox wave of the ferrocene units in the molecule. Both migration and volatility test results showed that, on comparison with those of Catocene, all tested compounds exhibit much more excellent anti‐migration ability and most of the tested compounds have lower volatility. Their effects on the thermal disintegration of ammonium perchlorate (AP), 1,3,5‐trinitro‐1,3,5‐triazacyclohexane (RDX), and 1,2,5,7‐tetranitro‐1,3,5,7‐tetraazacyclooctane (HMX) were measured by DSC. The results revealed that most of the compounds exhibit significant catalytic effects on the thermal degradation of AP and RDX. Particularly, most of the compounds containing one ferrocene unit in their cations show higher activity than that of Catocene. These compounds can be used as alternatives to Catocene in the composite solid propellants.     

具有导子的李三系的中心扩张与形变

考虑具有导子的李三系.由李三系和一个导子称为LietsDer对.定义系数在表示中的LietsDer对的上同调理论.研究LietsDer对的中心扩张.接下来,将形变理论推广到由李三系和导子构成LietsDer对上,它由带有系数的LietsDer对的上同调所支配.     

Supersymmetric invariance and universal central extensions of lie supertriple systems

In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland's theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations.     

On large deviations for some sequences of weighted means of Gaussian processes

In this paper we study some sequences of weighted means of continuous real valued Gaussian processes. More precisely we consider suitable generalizations of both arithmetic and logarithmic means of a Gaussian process with covariance function which satisfies either an exponential decay condition or a power decay condition. Our aim is to provide limits of variances of functionals of such weighted means which allow the application of some large deviation results in the literature.     

关于一些概率统计理论的一点认识

近来,林群从哲学的角度用公式相对真理/绝对真理=0.9阐述了微积分的内涵,并探究了计算数学、概率统计等学科领域乃至日常生活现象也同样蕴藏着该哲学公式.基于林群等在《概率论初步设想》中对大数定律和中心极限定理等概率统计学理论的哲学内涵分析,用一些数值算例展示概率统计学中这些常用理论所蕴含的这一哲学公式.     

The optimal upper bound of the number of generalized Euler configurations

Consider a generalized 3-body problem. The attraction force between any two bodies is proportional to the two masses and the b-th power of the mutual distance. Albouy and Fu have obtained the optimal upper bound of the number of generalized Euler configurations for the cases b 1 and b = 2, 3. This paper obtains the optimal upper bound for the remaining real values of b in a systematic way.     

光漏斗聚光定向传光中央接收太阳能集热系统

提出了一种新型中央接收式太阳能高温集热系统,介绍了系统的运行原理,分析了系统的热效率影响因素。这个新型的太阳能高温集热系统具有如下特点:可将多个光漏斗和偏光器组成一个太阳能聚光器阵列,每个聚光器都能将低能流密度的太阳光束会聚成高能流密度的平行光束,并由偏光器传送到中央接收器,于是中央接收器可获得很高的太阳光照射能流,转化为热能后将产生很高的温度,从而实现太阳光高温聚能。本系统的中央接收器无需建在高塔上,节省了建设费用,而且所有光漏斗跟踪太阳的方式相同,控制策略简单,定向偏光器的出光方向设定后可以固定不变,因而使整个系统结构简单,技术上易于实现。