2D LOCUS CONFIGURATIONS AND THE TRIGONOMETRIC CALOGERO–MOSER SYSTEM

A central hyperplane arrangement in ?² with multiplicity is called a "locus configuration" if it satisfies a series of "locus equations" on each hyperplane. Following [4], we demonstrate that the first locus equation for each hyperplane corresponds to a force-balancing equation on a related interacting particle system on ?*: the charged trigonometric Calogero-Moser system. When the particles lie on S¹ ? ?*, there is a unique equilibrium for this system. For certain classes of particle weight, this is enough to show that all the locus equations are satisfied, producing explicit examples of real locus configurations. This in turn produces new examples of Schrödinger operators with Baker–Akhiezer functions.     

Pseudodifferential Operators of Several Variables and Baker Functions

The KP hierarchy consists of an infinite system of nonlinear partial differential equations and is determined by Lax equations, which can be constructed using pseudodifferential operators. The KP hierarchy and the associated Lax equations can be generalized by using pseudodifferential operators of several variables. We construct Baker functions associated to those generalized Lax equations of several variables and prove some of the properties satisfied by such functions.     

On multiply-connected Fatou components in iteration of meromorphic functions

Let be a transcendental meromorphic function with at most finitely many poles. We mainly investigated the existence of the Baker wandering domains of f(z) and proved, among others, that if f(z) has a Baker wandering domain U, then for all sufficiently large n, fn(U) contains a round annulus whose module tends to infinity as n→∞ and so for some 0<d<1,

     

紫外可见分光光度法测定不同产地龙牙百合中皂苷含量

为建立龙牙百合总皂苷的测定方法,并确定不同产地龙牙百合中皂苷的含量,以便控制龙牙百合药材的质量,采用香草醛-高氯酸显色,在535 nm处,利用紫外可见分光光度法测定了10个批次的龙牙百合中总皂苷的含量.结果表明,10个不同产地龙牙百合中皂苷的含量,分别是:8.39%、8.11%、8.24%、7.62%、7.38%、9....     

Innovation in the cluster validating techniques

To detect database records containing approximate and exact duplicates because of data entry error or differences in the detailed schemas of records from multiple databases or for some other reasons is an important line of research. Yet no comprehensive comparative study has been performed to evaluate the effectiveness of Silhouette width, Calinski & Harbasz index (pseudo F-statistics) and Baker & Hubert index (γ index) algorithms for exact and approximate duplicates. In this paper, a comparative study and effectiveness of these three cluster validation techniques which involve measuring the stability of a partition in a data set in the presence of noise, in particular, approximate and exact duplicates are presented. Silhouette width, Calinski & Harbasz index and Baker & Hubert index are calculated before and after inserting the exact and approximate duplicates (deliberately) in the data set. Comprehensive experiments on glass, wine, iris and ruspini database confirms that the Baker & Hubert index is not stable in the presence of approximate duplicates. Moreover, Silhouette width, Calinski and Harbasz index and Baker & Hubert indice do not exceed the original data indice in the presence of approximate duplicates.     

A new bioactive prenylated dihydroflavanoid from Dolichos tenuicaulis （Baker） Craib

A new prenylated dihydroflavonoid was obtained from the root of Dolichos tenuicaulis （Baker） Craib. The structure was elucidated as （2S）-5,2＇,6＇-trihydroxy-3＇″, 8-di （γ,γ-dimethyl-allyl）-2＇″, 2＇″-dimethylpyrano-[5＇″,6＇″： 6,7]-2＇″″,4＇″″-cyclohexadiene-1 ＇″″-one-[2＇″″,3＇″″： 3＇,4＇]-flavanone, named dolichnin A, by spectroscopic methods including UV, IR, HR-EI-MS, 1D NMR and 2D NMR techniques, and subsequently, the anticancer activity of this compound to inhibit human cancer cells＇ growth including A549, BEL-7402, Hep-3B, SMMC7721, HT-29, MCF-7, SGC-7902, K562, A498 and PC3 cell lines by MTT method was evaluated in vitro.     

关于丢番图方程的一个注记

本文得到了Ｓｈｏｒｅｙ和Ｔｉｊｄｅｍａｎ关于不定方程的一个猜想的一个结果，并且基本上解决了Ｅｄｇａｒ的关于上述不定方程的一个猜想．     

A rigorous formalism of information transfer between dynamical system components. I. Discrete mapping

We put the concept of information transfer on a rigorous footing and establish for it a formalism within the framework of discrete maps. The resulting transfer measure possesses a property of directionality or transfer asymmetry as emphasized by Schreiber [T. Schreiber, Measuring information transfer, Phys. Rev. Lett. 85 (2) (2000) 461]; it also verifies the transfer measure for two-dimensional systems, which was obtained by Liang and Kleeman [X.S. Liang, R. Kleeman, Information transfer between dynamical system components, Phys. Rev. Lett. 95 (24) (2005) 244101] through a different avenue. Connections to classical formalisms are explored and applications presented. We find that, in the context of the baker transformation, there is always information flowing from the stretching direction to the folding direction, while no transfer occurs in the opposite direction; we also find that, within the Hénon map system, the transfer from the quadratic component to the linear component is of a simple form as expected on physical grounds. This latter result is unique to our formalism.     

Unitary quasi-affine transforms of contractions

The unitary quasi-affine transforms of contractions are the cornerstone of the exact theory of irreversibility introduced by Misra, Prigogine and Courbage. This work shows that the class of contractions with unitary quasi-affine transforms is just C⋅1 and that every unitary quasi-affine transform of a contraction is unitarily equivalent to the residual part of its Sz.-Nagy-Foia? dilation. Some connections with the Grossmann theory of nested Hilbert spaces and generalized eigenvalues are established. These results are applied to the study of the baker map.