Approach to block entropy modeling and optimization

This paper introduces an approach to the block entropy modeling of stationary signals. The block entropies, constructed according to the Tsallis generalized formalism, are optimized with respect to the block length and the partition of the signal value domain, to appropriately measure the complexity of the signal. The optimal partition is known to be addressed by the Euclidean mean, expressing the signal optimized level based on the least squares fitting method. However, this is valid only for random signal values following a symmetric distribution. Alternatively, and within the framework of fitting methods based on non-Euclidean metrics, we implement the qth order means to consistently describe the optimal signal level, and to clearly present the difference between the optimal signal level and the optimal partition. The signal optimization is utilized for detecting the distribution modes, developing a technique, being resistant to the noise corruption, that can be useful for detecting the optimal partition. Moreover, the mechanisms that affect the optimal partition are identified and thoroughly investigated. We first consider random signals following an arbitrary distribution, where the block entropy modeling reveals that the optimal partition is located at the median. Thereafter, we consider persistent signals, specifying a degree of determinism, where the optimal partition is found to be driven far from the median and close to the persistent mode. The existence of persistent modes of small hitting time is the key point of this dissertation, highlighting their implications on the block entropy modeling. Finally, efforts towards block entropy modeling of non-stationary signals are discussed.     

Maximal subclasses of local fitting classes

A Fitting class $ \mathfrak{F} A Fitting class is said to be π-maximal if is an inclusion maximal subclass of the Fitting class of all finite soluble π-groups. We prove that is a π-maximal Fitting class exactly when there is a prime p ∊ π such that the index of the -radical in G is equal to 1 or p for every π-subgroup of G. Hence, there exist maximal subclasses in a local Fitting class. This gives a negative answer to Skiba’s conjecture that there are no maximal Fitting subclasses in a local Fitting class (see [1, Question 13.50]). Original Russian Text Copyright ? 2008 Savelyeva N. V. and Vorob’ev N. T. __________ Vitebsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 6, pp. 1411–1419, November–December, 2008.     

两个Fitting类的例子

给出了两个特殊的群类,即R={H|C_H(F(H))≤F(H)}和S={G|1≠K⊿G~((∞)),G~((∞))=KC_(G(∞))(K)},证明了他们都是Fitting类,这两个Fitting类都和单群理论有密切联系.各自都包含了一些很值得注意的群,对每个Fitting类给出了群G属于该Fitting类的一个充要条件.     

极大子群的性质对有限群结构的影响

设H为有限群G的一个子群。称H在G中是s-半正规的,若对任意的素数p||G|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G);称H在G中是c-可补的,若存在G的子群N,使得G=HN且H∩N≤HG=CoreG(H)。证明了下面定理设F是一个包含超可解群类U的饱和群系,H△G,且G/H∈F。则G∈F,若下列条件之一成     

褐煤颗粒表面官能团的分布特征

采用原位傅里叶红外光谱漫反射测试了北皂褐煤在粒度为40—60目、60—80目、80—100目、100—160目和160目—0.1mm的官能团分布特征,对比分析了不同粒度范围内的红外测试谱图。结果表明,粒度在40—60目以后,官能团区域可识别的特征吸收峰基本一致,可识别的官能团主要是醇羟基、多元醇及缔合羟基,甲基亚甲基,不饱和醛、脂肪烃链式饱和羧酸盐、烯烃,以及苯环取代;在160目—0.1mm的粒度范围内,指纹区验证更加准确,谱图峰型峰位以及峰面积更加准确,能够满足定量分析的要求。研究成果对研究煤不同粒度的宏观特性以及红外特征的定性分析具有重要的指导作用。     

Fitting maps of the plane to experimental data

This paper is motivated by the problem of fitting a differential equation to experimental data; a first step is to fit the time 1 map of the corresponding flow, as described in Section 1, and these time 1 maps are the diffeomorphisms in the title of the present paper. The negative part of statement (ii) of Theorem 3.1 implies that there is no algorithm which fits diffeomorphisms of the plane to observed data in a way that depends continuously on the observed data and only on the observed data.     

Solvent-free,catalyst-free aza-Michael addition of cyclohexylamine to diethyl maleate: Reaction mechanism and kinetics

The aza-Michael reaction is the addition of an amine to an electron deficient C=C double bond. This reaction is also used in the synthesis of precursors of polymeric networks. In this study, we paid attention to the kinetics and mechanism of the aza-Michael addition of cyclohexylamine (CHXA) to diethyl maleate (DEM) performed as a solvent-free, catalyst-free reaction and to concurrent reactions. In situ Raman spectroscopy, NMR spectroscopy and gas chromatography/mass spectrometry have shown the occurrence of three simultaneous reactions: (i) the aza-Michael addition of CHXA to DEM leading to diethyl 2-(cyclohexylamino)succinate, (ii) isomerization of DEM to diethyl fumarate (DEF), and (iii) the aza-Michael addition of CHXA to DEF formed by the reaction (ii). All of these reactions proceed with third order kinetics, first order in DEM or DEF and second order in CHXA. We propose a kinetic model that allows kinetic constants to be estimated. Furthermore, a numerical solution of the set of differential equations confirms the expected kinetic equations of reactions (i) and (ii) and gives values of rate constants comparable to the estimated ones. A DFT mechanistic study illustrates the structure of the reaction intermediates and transition states of all reactions and explains the contribution of the second amine molecule in the reaction mechanism.     

Auxiliary basis sets for main row atoms and transition metals and their use to approximate Coulomb potentials

We present auxilliary basis sets for the atoms H to At – excluding the Lanthanides – optimized for an efficient treatment of molecular electronic Coulomb interactions. For atoms beyond Kr our approach is based on effective core potentials to describe core electrons. The approximate representation of the electron density in terms of the auxilliary basis has virtually no effect on computed structures and affects the energy by less than 10⁻⁴ a.u. per atom. Efficiency is demonstrated in applications for molecules with up to 300 atoms and 2500 basis functions. Received: 17 December 1996 / Accepted: 8 May 1997     

强度比定标法分析激光诱导击穿碳谱线

 利用激光诱导击穿光谱技术,使样品在大气常压环境下被击穿形成等离子体,探测等离子体发射信号。选择混合样品所含的基体元素硅作为内标元素,分别根据碳谱线峰值强度、分析线和内标线峰值强度比建立不同的定标曲线。对两种定标曲线的拟合度、测量重复性以及定量分析结果准确度进行了研究。研究结果表明:强度比定标法在一定程度上可以提高定标曲线的拟合度和测量重复性,减小强度比定标法定量分析结果的误差,提高测量准确度。     

关于SQ-补子群

假定Fitting子群F(G)或广义Fitting子群F^*(G)的某些子群在G中SQ-补来研究包含超可解群的饱和群系s,这里G∈s.一些已知结果被推广.