Compact Matrix Expressions for Generalized Wald Tests of Equality of Moment Vectors

Asymptotic chi-squared test statistics for testing the equality of moment vectors are developed. The test statistics proposed are generalized Wald test statistics that specialize for different settings by inserting an appropriate asymptotic variance matrix of sample moments. Scaled test statistics are also considered for dealing with nonstandard conditions. The specialization will be carried out for testing the equality of multinomial populations, and the equality of variance and correlation matrices for both normal and nonnormal data. When testing the equality of correlation matrices, a scaled version of the normal theory chi-squared statistic is proven to be an asymptotically exact chi-squared statistic in the case of elliptical data.     

最大无关组的判定定理及其它

本文给出了一个判定最大无关组的充要性定理及其证明．同时对用矩阵的行变换求最大无关组这一问题进行了点滴分析并介绍了一个解齐次线性方程组的简便方法。     

Gamow Vectors in Exactly Solvable Models

Through two examples: the Friedrichs model and a particular case of central potential scattering, we illustrate the way of constructing Gamow vectors.     

Backward extensions of subnormal operators

The concept of backward extension for subnormal weighted shifts is generalized to arbitrary subnormal operators. Several differences and similarities in these contexts are explored, with emphasis on the structure of the underlying measures.

     

一类最高权向量环的Krull维数

本文给出Om×GLn作用于Cm,n上的复多项式环上的最高权向量环的Krull维数公式,从而改正了Aslaksen,Tan及Zhu的一个错误.     

Adaptive application of operators in standard representation

Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could be shown under the assumption that the entries in properly compressed standard representations are known or computable in average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption is justified in the context of elliptic boundary value problems. Dedicated to Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55. This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1.     

Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors

We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta–gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.     

Quantitative study on selective stacking of zwitterions in large-volume sample matrix by moving reaction boundary in capillary electrophoresis

The paper advanced the theoretical procedures for quantitative design on selective stacking of zwitterions in full capillary sample matrix by a cathodic-direction moving reaction boundary (MRB) in capillary electrophoresis (CE) under control of electroosmotic flow (EOF). With the procedures, we conducted the theoretical computations on the selective stacking of two test analytes of L-histidine (His) and L-tryptophan (Trp) by the MRB created with 30 mM pH 3.0 formic acid-NaOH buffer and 2-80 mM sodium formate. The results revealed the following three predictions. At first, the MRB cannot stack His and Trp plugs if less than 12.5 mM sodium formate is used to form the MRB and prepare the sample matrix. Second, the MRB can stack His and/or Trp sample plugs completely if higher than 50 mM sodium formate is chosen to form the MRB. Third, the MRB can only focus His plug completely, but stack Trp plug partially if 20-50 mM sodium formate is used; this implied the complete MRB-induced selective stacking to His rather than Trp. All the three predictions were quantitatively proved by the experiments. With great dilution of sample matrix and control of EOF, controllable, simultaneous and MRB-induced selective stacking and separation of zwitterions were achieved. The theoretical results hold evident significances to the quantitative design of selective stacking conditions and the increase of detection sensitivity of zwitterions in CE. In addition, the control of EOF by cetyltrimethylammonium bromide (CTAB) can evidently improve the stacking efficiency to both His and Trp.     

Analysis of the disaccharides derived from hyaluronic acid and chondroitin sulfate by capillary electrophoresis with sample stacking

CE conditions for monitoring the unsaturated disaccharides of hyaluronic acid (di-HA) and chondroitin sulfate (di-CS) using an alkaline tetraborate buffer, electrokinetic sample injection, and UV absorption detection at 232 nm are reported. Separations were performed in an uncoated fused-silica capillary having reversed polarity and reversed electroosmosis generated with the addition of CTAB to the buffer. The influence of various separation parameters, including the concentration of CTAB, buffer pH, concentration of tetraborate, and applied voltage, on the resolution of the two disaccharides was investigated. Baseline separation was obtained with 25 mM tetraborate at pH 10.0 and having 0.05 mM CTAB. Chloride and phosphate in the sample are beneficial for the stacking of the disaccharides, with di-HA forming a much sharper peak than di-CS. Using samples prepared in 25 mM Tris-HCl (pH 7.5) and electrokinetic injection at the cathode at -10 kV for 40 s, linear relationships between the corrected peak area and the concentration of the disaccharides have been found in the ranges of 1.0-400.0 and 0.1-1.0 microg/mL (0.2-1.0 microg/mL for di-CS), with correlation coefficients being >0.9933 in all cases. The RSDs of detection times and corrected peak areas were between 1.13-1.24 and 1.57-2.13%, respectively. Applied to human serum samples that were prepared by ethanol precipitation and depolymerization of the two polysaccharides with chondroitinase ABC reveals comigration of endogenous compounds with di-HA and a sample-dependent detection time. The di-HA content in the serum sample can be estimated via subtraction of the blank peak that is obtained without enzymatic hydrolysis.     

A combined diffraction and dielectric properties investigation of Ba3MnNb2O9 complex perovskites

A combined synthesis, diffraction and dielectric properties investigation of the dependence (and effect) of Mn²⁺/Nb⁵⁺ ordering in Ba₃MnNb₂O₉ (BMN) upon annealing atmosphere and processing conditions has been carried out. Annealing in different atmospheres was not found to significantly alter either nominal stoichiometry or structure type. The obtained structure type (disordered metrically cubic or ordered trigonal) as well as the measured electrical properties (in particular, the dielectric loss) were, however, found to be sensitive to the synthesis route. Samples obtained via solid-state reaction were found to be predominantly of 1:2 Mn²⁺/Nb⁵⁺ ordered, trigonal structure type whereas samples obtained via an aqueous solution route were found to be of a Mn²⁺/Nb⁵⁺ ‘disordered’, metrically cubic structure type. All solid-state synthesized samples showed reasonable dielectric properties. The microwave dielectric constant and dielectric quality factor, Q, at 8 GHz of an as-synthesized BMN sample were 38 and 100, respectively. By contrast, the dielectric loss of the metrically cubic, Mn²⁺/Nb⁵⁺ ‘disordered’ samples obtained via an aqueous solution synthesis process were significantly worse.