Young measure solutions of some nonlinear mixed‐type equations

This contribution deals with measure‐valued solutions to two types of nonlinear partial differential equations for which, in general, the results on the existence of classical or weak solutions fail. These are the potential equation for transonic flow and the associated unsteady problem (forward–backward diffusion equation). The solutions are constructed by an iteration scheme (Katchanov method) and additional time discretization (Rothe method) in the second case. The existence is proved in the sense of spatial gradient Young measures. Copyright © 2010 John Wiley & Sons, Ltd.     

ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.     

二阶椭圆问题新的混合元格式

本文基于二阶椭圆问题一种新的混合变分形式,给出同时满足强椭圆性和B-B条件的任意次的求解格式.理论分析表明这些单元论证简单而且用了较少的自由度达到最优误差估计.同时我们还给出了它们在各向异性网格下的误差估计.     

多元协方差阵扰动模型岭估计的影响分析

本文研究了多元线性同归模型岭估计的影响分析问题.利用最小二乘估计方法,获得了多元协方差阵扰动模型与原模型参数阵之间的岭估计的一些关系式,给出了度量影响大小的基于岭估计的广义Cook距离.     

具V-不变凸性的一类多目标控制问题的混合对偶性

本文研究了一类多目标控制问题的混合对偶性.利用函数的广义V-不变凸性条件,得出了关于有效解的弱对偶定理、强对偶定理和严格逆对偶定理,推广了多目标控制问题的对偶性结论.     

一般对偶混合体积不等式(英文)

本文研究了星体的对偶仿射均质积分问题.利用H(o)lder不等式和Blaschke-Santaló不等式.获得了一般对偶均质积分的Minkowski不等式,Brunn-Minkowski不等式以及定理3.从而不等式推广了文献[7]的结果.     

Hansen Solubility Parameters in the Analysis of Solvent–Solvent Interactions by Inverse Gas Chromatography

The Flory–Huggins interaction parameters, for a solute with pure nonvolatile solvents and with binary mixtures of nonvolatile solvents were evaluated using Inverse Gas Chromatography (IGC) data at 403.15 K. The five solvents used have similar structure and nearly the same molar volume and their mixtures form regular solutions. The values were used to evaluate the Hansen solubility parameters (HSP) for the pure solvents and mixed solvent systems. The HSP are plotted as a function of composition of the polar solvent. The dispersion component, , and the polar component, , exhibited negative deviation whereas the hydrogen bonding component, , showed positive deviation in the four mixtures. However, the total solubility parameter was found to be almost linear with composition in the four binary systems. Further the total solubility parameter, , was used to calculate the molar excess heat of vaporization for the solvents (C78 + POH, C78 + PCN, C78 + TTF, and C78 + TMO) that was found to be negative for C78 (19,24-dioctadecyldotetracontane) + POH(18,23-dioctadecylhentetracontan-1-ol) and C78 + PCN(1-cyano-18,23-dioctadecylhentetracontane) systems and positive for C78 + TTF [19,24-bis(18,18,18-trifluorooctadecyl)-1,1,1,42,42,42-hexafluorodotetracontane), and C78 + TMO(17,22-bis-(16-methoxyhexadecyl)-1,38-dimethoxyoctatriacontane] and the other systems.     

Effect of Non‐Ideal Mixed Solvents on Dimensions of Poly(N‐Vinylpyrrolidone) and Poly(Methyl Methacrylate) Coils

An addition of a small amount of non‐solvent tetrahydrofuran (THF) to good solvent water gave rise to a strong solvent power for poly(N‐vinylpyrrolidone) (PVP). It was found that PVP coils in mixtures of water and THF first swelled as the fraction of THF was increased, and then the coils contracted after a critical composition of the solvent mixture based on the measurement of dilute solution viscosities. It was reached that the power of the mixed solvents was not the simple average of the power of individual components. The influence of the non‐ideal mixing of water and THF on the power of these mixtures for PVP and the dimensions of PVP coils was taken into account. Especially the formation of pseudo‐clathrate hydrate structure with the composition φ _THF ≈ 0.44 was found to be an important factor to change the solvation and dimensions of PVP coils. Some other solvent mixtures for PVP and poly(methyl methacrylate) (PMMA) were also found to be non‐ideal mixtures. The viscosities of these solvent mixtures could show positive or negative deviation from the values obtained from the addition rule. It was shown again that the influence of the non‐ideality of these solvent mixtures on the dimensions of polymer coils was great. The action of mixed solvents changed the dimension of polymer coils, not only because of excluded volume effects but also because of the different molecular interactions present in these mixed solvents.     

Effect of Temperature on Cononsolvency of Polyvinylpyrrolidone in Water/Methanol Mixture

The behavior of polyvinylpyrrolidone in mixed water/methanol solvents was studied by rheoviscosimetry over a temperature range of 20°C–40°C. For the lower temperatures of this range, the intrinsic viscosity variation of the polymer vs. methanol molar fraction shows structural transitions (coil–globule–coil). This transition, which is usually attributed to the cononsolvency phenomenon, agrees with our previously published results obtained by dynamic light scattering. For higher temperatures, near 40°C, the intrinsic viscosity increase shows an expansion of the polymer over the alcohol molar fraction range 0.2 < X _A < 0.5. This last result can be attributed to the water/alcohol complex destruction under temperature increase. The “excess viscosity” of the polymer-mixed solvents vanishes with increasing temperature and becomes positive at 40°C. So, the polymer chain tends to transit from a globular to an ideal chain in the middle composition range of the mixed solvents.     

Investigation of radiation-induced mixed interstitial configurations in a dilute nickel 1 at.% silicon alloy

Abstract

X-ray energy spectra induced by 1 MeV protons and the energy spectra of the backscattered protons have been examined in the <100> and <110> directions of Ni crystals containing 1 at.% Si. The channeling method was used to investigate interactions between the radiation-induced defects and the silicon atoms. From the measured minimum yields and from the shape of the angular scans the fraction of silicon atoms is determined, which are displaced into the <100> and <110> channels due to proton or helium irradiations and subsequent annealing treatments. In undamaged crystals about 98 % of the silicon atoms are on normal lattice sites. After irradiation a dose dependent fraction of the silicon atoms is displaced 0.05 nm away from the substitutional position indicating the formation of a mixed dumbbell consisting of one selfinterstitial atom and one silicon atom. However, the experimental data can also be interpreted by the assumption of a NiSi₂ complex, in which the silicon atoms are displaced 0.08 nm from the lattice site. Subsequent annealing from 50 K to 160 K does not change the configuration and the concentration of the silicon complexes. At room temperature the silicon atoms in the complex are positioned 0.04 nm from the lattice position. The silicon complexes were totally am ihilated at 400 K.