A modified steepest descent method with applications to maximizing likelihood functions

In maximizing a non-linear function G(), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1–1 transformation on the variables , so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihood functions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well.     

Grouped coordinate minimization using Newton's method for inexact minimization in one vector coordinate

Letf(x,y) be a function of the vector variablesx R ⁿ andy R ^m. The grouped (variable) coordinate minimization (GCM) method for minimizingf consists of alternating exact minimizations in either of the two vector variables, while holding the other fixed at the most recent value. This scheme is known to be locally,q-linearly convergent, and is most useful in certain types of statistical and pattern recognition problems where the necessary coordinate minimizers are available explicitly. In some important cases, the exact minimizer in one of the vector variables is not explicitly available, so that an iterative technique such as Newton's method must be employed. The main result proved here shows that a single iteration of Newton's method solves the coordinate minimization problem sufficiently well to preserve the overall rate of convergence of the GCM sequence.The authors are indebted to Professor R. A. Tapia for his help in improving this paper.     

The effect of a coriolis force on Taylor-Couette flow

Taylor-Couette flow subject to a Coriolis force is studied experimentally and numerically. In the experiment, the Couette apparatus is mounted on a turntable with the axis of the cylinders orthogonal to the rotation vector of the turntable. The Coriolis force stabilizes the fluid against the onset of Taylor vortices and alters the velocity fields, both above and below the transition from the initial flow. At small dimensionless turntable frequencies, the transition yields time-independent Taylor vortices which are tilted with respect to the cylinder axis. At larger there is a direct transition to turbulence. We determine the first-order correction to the classical Couette initial flow, to account for the effects of the Coriolis force, by expanding in powers of. We present numerical results for the axial velocity (the only nonvanishing correction term to order) in the infinite-cylinder approximation.     

新型Ni—Pd/碳化树脂催化剂的制备及在微量测定有机氧元素中的应用

本文报道一种新型Ni—Pd／碳化树脂催化剂的制备方法，用该法制备的催化剂具有高金属分散度和高机械强度，用于库仑法微量测定有机氧元素取得满意结果。文中对Ni和Pd颗粒在催化剂上表面形貌和分布、催化活性等作了初步探讨。     

Fluorous reverse-phase silica gel-supported Lewis acids as recyclable catalysts in water

Fluorous reverse-phase silica gel (FRPSG)-supported Lewis acids which have fluorous ligands acted as effective catalysts of Baeyer-Villiger and Diels-Alder reactions in water. Direct esterification of carboxylic acid with alcohol in organic media was also catalyzed. The FRPSG-supported Lewis acids could be recycled by simple filtration after the reaction.     

Thermal decomposition of sodium nitrite and sodium nitrate pre-adsorbed on TiO2 surfaces

The thermal decomposition of sodium nitrite or nitrate pre-adsorbed upon TiO₂ surfaces has been investigated by employing several techniques as infrared spectroscopy (IR) and temperature programmed desorption in conjunction with mass spectrometry analysis (TPD-MS) to study the features observed during these thermal decompositions. Differential thermal analysis (DTA) in combination with X-ray diffraction analysis (XRD) were used to investigate the possibility of a solid state chemical reaction between the solid products originated from the thermal decomposition of the pre-adsorbed species and the TiO₂. On the basis of our results, various characteristic features of these thermal decomposition reactions will be discussed.This work was supported by JUNTA DE ANDALUCIA (financial support for research groups/1990).     

New Methods for the Synthesis of Glycosides and Oligosaccharides—Are There Alternatives to the Koenigs-Knorr Method? [New Synthetic Methods (56)]

Glycoproteins, glycolipids, and glycophospholipids (glycoconjugates) are components of membranes. The oligosaccharide residue is responsible for intercellular recognition and interaction; it acts as a receptor for proteins, hormones, and viruses and governs immune reactions. These significant activities have stimulated interest in oligosaccharides and glycoconjugates. With their help it should be possible to clarify the molecular basis of these phenomena and to derive new principles of physiological activity. Major advances in the synthesis of oligosaccharides have been made by the use of the Koenigs-Knorr method, in which glycosyl halides in the presence of heavy-metal salts are employed to transfer the glycosyl group to nucleophiles. The disadvantages of this procedure have led to an intensive search for new methods. Such methods will be discussed in this article. Emphasis is placed on glycoside and saccharide formation by 1-O-alkylation, on the trichloroacetimidate method, and on activation through the formation of glycosylsulfonium salts and glycosyl fluorides.     

CuAl2O4 powder synthesis by sol-gel method and its photodegradation property under visible light irradiation

Nanocrystalline spinel CuAl₂O₄ powders were prepared by sol-gel method from nitrate Cu(NO₃)₂·3H₂O, Al(NO₃)₃·9H₂O and complex C₆H₈O₇·H₂O. Sintering was carried out at 400, 500, 600, 700, 800°C respectively for 2 h in air. The XRD patterns started to appear CuAl₂O₄ peaks after sintering of 500°C and consist of only CuAl₂O₄ peaks as spinel crystal after sintering of 700°C. The powders were analyzed by TEM and UV-vis diffuse reflectance spectrum to be round, about 10–30 nm in size and Eg=1.77 eV. Photodegradation property of nanocrystalline CuAl₂O₄ powders was investigated by using methyl orange as model pollutant and mercury lamp (λ>400 nm) as energy source. The results indicated that CuAl₂O₄ powders sintered at 700°C had the excellent visible photocatalytic property. Under the irradiation of visible light, methyl orange could be degraded 97% in 120 min.     

Kinetic model of CO oxidation on heterophase surface analyzed regarding COads spillover, I. Homotopic method. Effect of temperature and CO pressure

The homotopic method has been used to analyze the kinetic models of CO oxidation on two surface patches conjugated by CO_ads spillover. On each patch reaction proceeds via a three-stage mechanism but with different constants. The stability of steady-states solution has been studied. CO_ads spillover from one patch to another changes substantially the bifurcation picture of steady states and produces islands.     

The acidity functionsH 0 s of HCl solutions in EtOH with low water content

The acidity functionsH ₀ ^s of HCl solutions in EtOH-H₂O solvents containing 1.09, 3.0, and 5.0% water have been measured at 25 and 40 °C by the indicator method. The concentration of HCl changes from 10^–2 to 36m. Nitroanilines, for which a protonation mechanism is realized in the studied systems, were used as indicators.For each solvent,H ₀ ^s is temperature independent atm _HCl < 4, and acidity atm _HCl > 4 mol L^–1 increases more rapidly at 25 °C than at 40 °C. The acidity functions of aqueous and water-ethanol solutions of HCl were compared, and the concentrations of proton solvates of different compositions and their relative protonating ability were evaluated.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1722–1725, October, 1994.This work was financially supported by the Russian Foundation for Basic Research (Project No. 93-03-18356).