A result on hypothesis testing for a multivariate normal distribution when some observations are missing

Let U_i = (X_i, Y_i), i = 1, 2,…, n, be a random sample from a bivariate normal distribution with mean μ = (μ_x, μ_y) and covariance matrix

. Let X_i, i = n + 1,…, N represent additional independent observations on the X population. Consider the hypothesis testing problem H₀ : μ = 0 vs. H₁ : μ ≠ 0. We prove that Hotelling's T² test, which uses (X_i, Y_i), i = 1, 2,…, n (and discards X_i, i = n + 1,…, N) is an admissible test. In addition, and from a practical point of view, the proof will enable us to identify the region of the parameter space where the T²-test cannot be beaten. A similar result is also proved for the problem of testing μ_x ? μ_y = 0. A Bayes test and other competitors which are similar tests are discussed.     

On the automatic restricted-step rational-function-optimization method

The rational function optimization algorithm is one of the widely used methods to search stationary points on surfaces. However, one of the drawbacks of this method is the step reduction procedure to deal with the overstepping problem. We present and comment on a method such that the step obtained from the solution of the rational function equations possesses the desired correct length. The analysis and discussion of the method is mainly centered on the location and optimization of transition states. Received: 18 June 1998 / Accepted: 17 September 1998 / Published online: 23 November 1998     

Vibrational spectra of 2-biphenylmethanol. Spectrum simulation and molecular structure

The vibrational spectra of a solid crystalline sample of 2-biphenylmethanol have been measured at room temperature. The IR absorption spectra were recorded in the range 400 cm^–1–3600 cm^–1; Raman spectra were measured in the range 10 cm^–1–1640 cm^–1. The direct mechanical and optoelectronic problems were solved using the fragment method realized as Lev-100 software; the intensity distribution in the IR spectrum of 2-biphenylmethanol was obtained by the same method. The experimental Raman and IR absorption spectra were interpreted by analyzing the calculated data on the frequencies and forms of normal vibrations and their intensities in the IR spectra. IR absorption spectra were simulated for several models of 2-biphenylmethanol conformers that differ in the mutual orientation of fragments. Based on the results of simulation and comparison of the calculated and experimental spectra of conformers we suggested a model for the conformer realized in the solid phase under normal conditions.Original Russian Text Copyright © 2004 by L. M. Babkov, J. Baran, N. A. Davydova, J. I. Kukielskii, and S. V. TrukhachevTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 624–631, July–August, 2004.This revised version was published online in April 2005 with a corrected cover date.     

A class of multiple shrinkage estimators

Based on a sample of size n, we investigate a class of estimators of the mean of a p-variate normal distribution with independent components having unknown covariance. This class includes the James-Stein estimator and Lindley's estimator as special cases and was proposed by Stein. The mean squares error improves on that of the sample mean for p3. Simple approximations imations for this improvement are given for large n or p. Lindley's estimator improves on that of James and Stein if either n is large, and the coefficient of variation of is less than a certain increasing function of p, or if p is large. An adaptive estimator is given which for large samples always performs at least as well as these two estimators.     

Application of HPLC to measure vanadium in environmental,biological and clinical matrices

Vanadate and vanadium compounds exist in many environmental, biological and clinical matrices, and despite the need only limited progress has been made on the analysis of vanadium compounds. The vanadium coordination chemistry of different oxidation states is known, and the result of the characterization and speciation analysis depends on the subsequent chemistry and the methods of analysis. Many studies have used a range of methods for the characterization and determination of metal ions in a variety of materials. One successful technique is high performance liquid chromatography (HPLC) that has been used mainly for measuring total vanadium level and metal speciation. Some cases have been reported where complexes of different oxidation states of vanadium have been separated by HPLC. Specifically reversed phase (RP) HPLC has frequently been used for the measurement of vanadium. Other HPLC methods such as normal phase, anion-exchange, cation-exchange, size exclusion and other RP-HPLC modes such as, ion-pair and micellar have been used to separate selected vanadium compounds. We will present a review that summarizes and critically analyzes the reported methods for analysis of vanadium salts and vanadium compounds in different sample matrices. We will compare various HPLC methods and modes including sample preparation, chelating reagents, mobile phase and detection methods. The comparison will allow us to identify the best analytical HPLC method and mode for measuring vanadium levels and what information such methods provide with regard to speciation and quantitation of the vanadium compounds.     

Functionality map analysis of the active site cleft of human thrombin

Summary The Multiple Copy Simultaneous Search methodology has been used to construct functionality maps for an extended region of human thrombin, including the active site. This method allows the determination of energetically favorable positions and orientations for functional groups defined by the user on the three-dimensional surface of a protein. The positions of 10 functional group sites are compared with those of corresponding groups of four thrombin-inhibitor complexes. Many, but not all features, of known thrombin inhibitors are reproduced by the method. The results indicate that certain aspects of the binding modes of these inhibitors are not optimal. In addition, suggestions are made for improving binding by interaction with functional group sites on the thrombin surface that are not used by the thrombin inhibitors. Abbreviations: MCSS, multiple copy simultaneous search; PPACK, d-phenylalanyl-l-propyl-l-arginine chloromethane; NAPAP, N -(2-naphthylsulfonylglycyl)-d-para-amidinophenylalanylpiperidine; argatroban, (2R,4R)-4-methyl-1-[N -(3-methyl-1,2,3,4-tetrahydro-8-quinolinylsulfonyl)-l-arginyl]-2-piperidine carboxylic acid; rms, root mean square. The thrombin residues are numbered according to the chymotrypsin-based numbering by Bode et al. [8]. P1, P2, P3, etc., denote the peptide inhibitor residues on the amino-terminal side of the scissile peptide bond, and S1, S2, S3, etc., the corresponding subsites of thrombin     

An investigation of glasses for capillary chromatography

An investigation was conducted of various glasses, other than soda lime or borosilicate, for use in glass capillary gas chromatography. The work has uncovered some unique chromatographic qualities in the use of potash soda lead and fused silica glasses as materials for making glass capillary columns. The fused silica proved to be an ideal material for capillary column construction, being inherently more inert than glass containing metal oxides. It has been shown that through the use of thin wall capillary tubing of high flexibility many of the mechanical problems associated with glass capillary columns, such as fragility and column straightening, can be avoided.     

TH型区间值模糊正规子群

本文在区间值模糊集空间上，引入了幂等区间范数ＴＨ，在此基础上，定义了ＴＨ型区间值模糊正规子群，并研究了它的一些性质和结构特征，从而拓广了区间值模糊集的理论。     

LOCALIZED PATTERNS OF THE CUBIC-QUINTIC SWIFT-HOHENBERG EQUATIONS WITH TWO SYMMETRY-BREAKING TERMS

Homoclinic snake always refers to the branches of homoclinic orbits \mbox{near} a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodic orbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking terms (non-reversible term and non-k-symmetry term) are investigated by using multiple scale method, and their bifurcation diagrams are initially studied by numerical simulations. Typically, we predict numerically the existence of so-called round-snakes and round-isolas upon particular two symmetric-breaking perturbations.     

FOURIER-TRANSFORM RAMAN AND INFRARED SPECTRA AND VIBRATIONAL ASSIGNMENT FOR SOLID GLUTARIMIDE

Abstract

The FT-Raman and FT-IR spectra of crystalline glutarimide and its N-deuterated derivative have been recorded in the range 4000-100 cm^?1. A complete vibrational assignment is given for all internal modes and is supported by normal coordinate analysis based on a general valence force field. The calculated frequencies are in very good agreement with experiment. A close similarity is found for frequencies of the corresponding vibrations of glutarimide and uracils in the solid state. It is concluded that the strength of hydrogen bonding in glutarimide is very similar to that in crystalline pyrimidine nucleic bases.