An Inexact Newton Method Derived from Efficiency Analysis

We consider solving an unconstrained optimization problem by Newton-PCG like methods in which the preconditioned conjugate gradient method is applied to solve the Newton equations. The main question to be investigated is how efficient Newton-PCG like methods can be from theoretical point of view. An algorithmic model with several parameters is established. Furthermore, a lower bound of the efficiency measure of the algorithmic model is derived as a function of the parameters. By maximizing this lower bound function, the parameters are specified and therefore an implementable algorithm is obtained. The efficiency of the implementable algorithm is compared with Newtons method by theoretical analysis and numerical experiments. The results show that this algorithm is competitive.Mathematics Subject Classification: 90C30, 65K05.This work was supported by the National Science Foundation of China Grant No. 10371131, and Hong Kong Competitive Earmarked Research Grant CityU 1066/00P from Hong Kong University Grant Council     

One-step estimation for varying coefficient models

A one-step method is proposed to estimate the unknown functions in the varying coefficient models, in which the unknown functions admit different degrees of smoothness. In this method polynomials of different orders are used to approximate unknown functions with different degrees of smoothness. As only one minimization operation is employed, the required computation burden is much less than that required by the existing two-step estimation method. It is shown that the one-step estimators also achieve the optimal convergence rate. Moreover this property is obtained under conditions milder than that imposed in the two-step estimation method. More importantly, as only one minimization operation is employed, the full asymptotic properties, not only the asymptotic bias and variance, but also the asymptotic distributions of the estimators can be derived. The asymptotic distribution results will play a key role for making statistical inference.     

Stability of the Gumowski-Mira equation with period-two coefficient

We investigate the stability of solutions of the Gumowski-Mira equation with a period-two coefficient:

     

Thermodynamics of electrolytes. IX. Rare earth chlorides,nitrates, and perchlorates

The extensive data for the osmotic coefficients, heats of dilution, and densities of aqueous solutions of rare earth chlorides, nitrates, and perchlorates are fitted to a single type of equation found satisfactory for many other solutes Good agreement is obtained. The various parameters do not show simple trends with cation radius. While there are some plausible explanations of these complexities, the total picture is far from clear.     

Application of Pitzer's equations on the system HCl+MnCl2+H2O at various temperatures. V.

Activity coefficients of hydrochloric acid in mixed solutions of manganous chloride at twelve ionic strengths, from 0.1 to 5.0 mole-kg^–1, were obtained from emf measurements of cells without liquid junction at five temperatures from 5 to 45°C. The data were interpreted in terms of the simple and convenient Pitzer treatment. Activity coefficients for manganous chloride in the mixtures were also derived using Pitzer's equations. Hydrochloric acid follows Harned's rule fromI=0.1 to 3.0 mole-kg^–1, as concluded by Downes, whereas quadratic terms are warranted fromI=3.5 to 5.0 mole-kg^–1. Contrary to Downes' conclusion, Harned's rule clearly does not hold true for manganous chloride at most ionic strengths.     

Nuclear matter test for a separable non-localN-N interaction

A nuclear matter test has been conducted on a separable non-localN-N interaction proposed by Sirohi and Srivastava. The potential had been constructed by fitting the phase-shifts. The results obtained compare with those obtained by Tabakin in each partial wave. The binding energy per particle and the symmetry energy coefficient obtained are 19.4 MeV and 66.5 MeV respectively atk _F=1.65 fm⁻¹, while the best estimated values for these quantities are 16 MeV and 30–35 MeV atk _F=1.5 fm⁻¹. Single particle potential generated out of this NLSI has in general the same shape as the one obtained through Tabakin potential. Finally as a test of non-locality the integrated photoabsorption cross-section parameterh has been calculated and the value of 1.03 agrees with other reported values.     

On the dependence of the condensation coefficient on surface curvature

It is concluded that there is as yet no adequate theoretical solution for the size dependence of the condensation coefficient, the Okuyama-Zung approach to this problem being discounted.     

Quadrupole interaction of tantalum impurities in bismuth metal

The time differential perturbed angular correlation technique has been used in the measurement of the electric quadrupole interaction of Ta impuritiy in bismuth metal. The interaction frequencies at 293, 400 and 500 K have been observed to be 288±1.5, 266.9±3 and 244.5±4.3 MHz respectively. The electric field gradient at 293 K is 4.75±0.3 × 10¹⁷ V/cm² with the temperature coefficientB=2.2±0.2 × 10⁻⁵ (K)^−3/2.     

Theoretical prediction of maxima in association constants for complex formation between flavin mononucleotide and indoleacetate in the presence of polyelectrolytes

The effects of ionene polymers (6,3-ionene, 6,6-ionene, 6,8-ionene, and 6,12-ionene) with various charge densities upon association constants K for the complexation between flavin mononucleotide and indoleacetate have been studied. Except for 6,12-ionene, K increases with increasing polymer concentration then passes through a maximum, and declines at high polymer concentrations. The value of the maximum K increases in the order 6,8-ionene > 6,3-ionene > 6,6-ionene. In contrast, 6,12-ionene gives only a monotone increasing curve with increasing polymer concentration. These curves are analyzed using the theory of the partition coefficient proposed in the previous paper. The types of the curves that the theory predicts are classified in greater detail than in the previous paper, and examples are given. © 1993 John Wiley & Sons, Inc.     

Recent advancements of moiré and microscopic moiré interferometry for thermal deformation analyses of microelectronics devices

Moiré and microscopic moiré interferometry are reviewed as they are applied to thermal deformation analyses of microelectronics devices. Applications to diverse problems are illustrated to demonstrate wide applicability of the methods. The whole-field displacement information, with various sensitivity and resolution scales, is ideally suited for the deformation study of a broad range of problems in deformation analyses of microelectronics devices.