THE SOLUTION OF _b－EQUATION OF （P，Q）－FORMS AND IT＇S L~P＆HOLDER ESTIMATES ON A STEIN MANIFOLD

ＴＨＥＳＯＬＵＴＩＯＮＯＦ_ｂ－ＥＱＵＡＴＩＯＮＯＦ（Ｐ，Ｑ）－ＦＯＲＭＳＡＮＤＩＴ＇ＳＬ￣Ｐ＆ＨＯＬＤＥＲＥＳＴＩＭＡＴＥＳＯＮＡＳＴＥＩＮＭＡＮＩＦＯＬＤ￥ＷｕＸｉａｏｑｉｎ（ＤｅｐｔｏｆＭａｔｈ，ＪｉｍｅｉＴｅａｃｈｅｒｓＣｏｌｌｅｇｅＸｉａ?..     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

Trace anion determination in concentrated hydrofluoric acid solutions by two-dimensional ion chromatography II. Method performance study with a hydroxide eluent and a low noise suppressor

The two-dimensional ion exclusion chromatography/ion chromatography (ICE-IC) approach is considered to be the method of choice for the determination of trace anions in concentrated hydrofluoric acid (48-50%, w/w). In order to achieve lower detection limits, this method was for the first time used with electrolytically generated and purified hydroxide eluents in combination with a low noise electrochemical suppressor. Compared to carbonate based eluents, the achieved gain in peak height sensitivity for chloride, sulfate, nitrate and phosphate is a factor of 6, 7, 16 and 13, respectively. The instrumental detection limits, based on the background noise, are 2, 0.2, 0.4 and 1.4 microg/kg HF 50% (w/w) for the same anions. Their method detection limits, calculated according to SEMI, are all within the 6-10microg/kg HF 50% (w/w) range and thus at least 10 times lower than the current Tier C grade requirements. The chromatographic run time could be shortened with some 10 min by the use of a relatively fast high-capacity hydroxide selective anion exchange column.     

Chemical separation and inductively coupled plasma–atomic emission spectrometric determination of seventeen trace metals in thorium oxide matrix using a novel extractant – Cyanex-923

Comprehensive studies have been carried out on the extraction behaviour of thorium matrix vis-a-vis 17 trace metallic elements using a novel extractant viz. Cyanex-923. The near total extraction of thorium and quantitative separation of these metals has been established using inductively coupled argon plasma–atomic emission spectrometry (ICP–AES). The recovery of few representative elements has been confirmed by radio-active tracer studies. The studies carried out here have enabled determination of μg/l amounts of all analyte elements with a precision of better than 1% RSD with prior chemical separation from as low as 1 g thorium sample in just five chemical extractions.     

New Temperature Integral Approximate Formula for Non-isothermal Kinetic Analysis

A new approximate formula for temperature integral is proposed. The linear dependence of the new fomula on x has been established. Combining this linear dependence and integration-by-parts, new equation for the evaluation of kinetic parameters has been obtained from the above dependence. The validity of this equation has been tested with data from numerical calculating. And its deviation from the values calculated by Simpson's numerical integrating was discussed. Compared with several published approximate formulae, this new one is much superior to all other approximations and is the most suitable solution for the evaluation of kinetic parameters from TG experiments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Analysis and Speciation of Traces of Arsenic in Environmental,Food and Industrial Samples by Voltammetry: a Review

Voltammetric approaches for the determination of arsenic and speciation at trace levels are critically appraised in a review covering the literature from 1970 to 2002. Special attention is devoted to stripping modes and to issues related to the choice of working material and supporting electrolyte. A section is dedicated to the management of real samples and aspects of sample preparation. An extensive compilation, organized by real sample type, gathers essential experimental conditions. Potentiometric stripping analysis is introduced for sake of comparison. The coupling of voltammetric detection or preaccumulation with FIA, chromatography, capillary electrophoresis and ICP techniques is also addressed.     

关于Taylor公式中Lagrange余项的再研究

在Azpeitja对Taylor公式中Lagrange余项的"中间点"渐近性的研究基础上,又建立几个易于验证和推广的结果.     

On the leading term and the degree of the polynomial trace mapping associated with a substitution

Using the trace mapping and the reduced trace mapping associated with a substitution, one obtaines the spectral properties of one-dimensional Schrödinger operators of the formH=–+V onl ², where is the discrete Laplacian andV is a diagonal operator with elements derived from a substitution rule. In particular, the reduced trace mapping is closely related to the leading term of the original trace mapping. In this paper, the explicit expression of the leading term is given and its properties are discussed.     

Universality in the length spectrum of integrable systems

The length spectrum of periodic orbits in integrable hamiltonian systems can be expressed in terms of the set of winding numbers {M ₁,…,M _f} on thef-tori. Using the Poisson summation formula, one can thus express the density, Σδ(T−T _M), as a sum of a smooth average part and fluctuations about it. Working with homogeneous separable potentials, we explicitly show that the fluctuations are due to quantal energies. Further, their statistical properties are universal and typical of a Poisson process as in the corresponding quantal energy eigenvalues. It is interesting to note however that even though long periodic orbits in chaotic billiards have similar statistical properties, the form of the fluctuations are indeed very different.     

Algebraic and Differential Nonlinear Superposition Formulas

Knowledge of the Lax pair and the Darboux transformation for a completely integrable system provides an iterative approach for generating exact solutions. This approach involves solving for the eigenfunction of the Lax pair at each step. But this process can be considerably simplified using the Bäcklund transformation and Bianchi's permutability theorem. This allows constructing the so-called nonlinear superposition formula, which provides a new solution of the system in terms of three previous solutions. The advantage of this approach is that the differential order of the nonlinear superposition formulas is lower than that of the Lax pairs, and in some cases, these formulas reduce to algebraic equations. We consider the construction of new nonlinear superposition formulas in the form of both differential equations and algebraic equations.