On hermitian polynomial optimization

We compare three levels of algebraic certificates for evaluating the maximum modulus of a complex analytic polynomial, on a compact semi-algebraic set. They are obtained as translations of some recently discovered inequalities in operator theory. Although they can be stated in purely algebraic terms, the only known proofs for these decompositions have a transcendental character. Received: 27 June 2005     

The condition on the stability of stationary lines in a curvature flow in the whole plane

The long time behavior of a curve in the whole plane moving by a curvature flow is studied. Studying the Cauchy problem, we deal with moving curves represented by entire graphs on the x-axis. Here the initial curves are given by bounded functions on the x-axis. It is proved that the solution converges uniformly to the solution of the Cauchy problem of the heat equation with the same initial value. The difference is of order O(t−1/2) as time goes to infinity. The proof is based on the decay estimates for the derivatives of the solution. By virtue of the stability results for the heat equation, our result gives the sufficient and necessary condition on the stability of constant solutions that represent stationary lines of the curvature flow in the whole plane.     

关于Fuzzy聚类分析及其在脊髓灰质炎中的应用

本文用Fuzzy数学的观点探讨了Fuzzy聚类分析，并通过对脊髓灰质炎病毒抗体水平的Fuzzy聚类分析，获得了良好的聚类效果，为该项问题的研究提供了科学依据。     

Heat “polynomials” for a singular differential operator on (0, ∞)

We generalize the theory of the heat polynomials introduced by P. V. Rosenbloom and D. V. Widder for a more general class of singular differential operator on (0, ). The heat polynomials associated with the Bessel operator and studied by D. T. Haimo appear as a particular case in this paper. In the special cases of second derivative and Bessel operators the heat polynomials are in fact polynomials inx andt, however, this property does not hold in general.Communicated by Tom. H. Koornwinder.     

Algorithms for non-linear huber estimation

The Huber criterion for data fitting is a combination of thel ₁ and thel ₂ criteria which is robust in the sense that the influence of wild data points can be reduced. We present a trust region and a Marquardt algorithm for Huber estimation in the case where the functions used in the fit are non-linear. It is demonstrated that the algorithms converge under the usual conditions.     

The absorption of pulsed CO2-laser radiation by ethylene at total pressures from 25 to 3000 Torr

The absorption of pulsed CO₂-laser radiation by ethylene has been measured at total pressures from 25 to 3000 Torr, using the P(12) and P(14) lines in the 10.6 m band, with incident fluences from 0.1 to 0.7 J/cm². Marked deviations from the Beer-Lambert absorption law were observed, with the effective absorption coefficient varying with pressure, fluence, absorption path-length and the addition of non-absorbing gas. Pressure broadening of the rotational lines of the ethylene absorption spectrum was shown to be the major cause of these deviations, together with lesser effects which can be attributed to the rise in temperature of the absorbing gas during the laser pulse.     

Accurate determination of wavenumbers for iodine molecular lines in the red spectral region

The hyperfine structure of various absorption lines of molecular iodine with wavenumbers between 12980 and 13890 cm^–1 has been resolved using Doppler-free polarization spectroscopy. The wavenumbers of theo-component of 17 rovibrational lines of I₂ due to the transitionB ³ _ou ⁺ –X¹ _g ⁺ with even rotational quantum numbers have been determined with an accuracy of 0.001 cm^–1. A comparison of the centers of gravity of these 17 lines with the values of the iodine atlas of Gerstenkorn et al. yields a difference of thus corroborating the data of the iodine atlas in the red region within limits of error.     

Identifying potential binding modes and explaining partitioning behavior using flexible alignments and multidimensional scaling

A method is described for the rapid and automatic analysis of flexible molecular alignments using multidimensional scaling and a normalized scoring scheme. A projection scheme was devised to separate orientational and conformational effects. It is shown that the approach can be utilized for the identification of common binding orientations or to the study of differences in partioning behavior. It is suggested that the method can be employed as a novel approach exploring molecular similarity as a dynamic property, so that it includes aspects of motion (by way of mutual orientations), conformations and molecular properties.     

Optimization of sucrose ethanol fermentation for K,Na, Ca,and cu metal contents

The effect of the trace metals Cu, K, Na, and Ca, separately or in mixture, on fermentation time, ethanol production rate, and cell growth in the fermentation of synthetic media containing sucrose is discussed. The results are related to the range of contents found in raw materials, molasses and raisins, in order to determine their optimum concentrations for alcohol production.     

目视催化褪色计时法测定超痕量钒的研究

本文基于在酸性介质中钒(V)催化溴酸钾氧化酸性铬蓝K褪色的新指示反应,建立了一个催化褪色计时法测定超痕量钒的新方法。在体系中引入活化剂抗坏血酸,灵敏度达2×10~(-12)ng/ml,测定范围在0.0l～3.0ng/ml,同时探讨了反应机理。确立了反应速率方程,方法简便经济,已用于天然水中痕量钒的测定。