Formal Elimination for Multidimensional Systems and Applications to Control Theory

Following Douglas's ideas on the inverse problem of the calculus of variations, the purpose of this article is to show that one can use formal integrability theory to develop a theory of elimination for systems of partial differential equations and apply it to control theory. In particular, we consider linear systems of partial differential equations with variable coefficients and we show that we can organize the integrability conditions on the coefficients to build an “intrinsic tree”. Trees of integrability conditions naturally appear when we test the structural properties of linear multidimensional control systems with some variable or unknown coefficients (controllability, observability, invertibility, …) or for generic linearization of nonlinear systems. Date received: June 29, 1998. Date revised: January 29, 2000.     

Effective atomic numbers of some composite mixtures including borax

Effective atomic numbers for (PbO and Na₂B₄O₇10H₂O) and (UO₂(NO₃)₂, and Na₂B₄O₇10H₂O) mixtures against changing contents of PbO, Na₂B₄O₇10H₂O, and UO₂(NO₃)₂ were measured in the X-ray energy range from 25.0 to 58.0 keV. The gamma rays emitted by a ²⁴¹Am annular source have been sent on the absorbers which emits their characteristic X-rays to be used in transmission arrangement. The X-rays were counted by a Si(Li) detector with a resolution of 146 eV at 5.90 keV. The changing compositions of the compounds were assigned to be 0, 0.167, 0.333, 0.500, 0.666, 0.833 and total masses of the mixtures were adjusted to be identical. Also, the total effective atomic numbers of each mixture were estimated by using the mixture rule. The measured values were compared with estimated values for the mixtures.     

Involvement of a Hydrophobic Pocket and Helix 11 in Determining the Modes of Action of Prenylated Flavonoids and Isoflavonoids in the Human Estrogen Receptor

Six prenylated (iso)flavonoids were purified from a licorice root extract and subjected to competition experiments with six commercially available (iso)flavonoids. The agonistic and antagonistic activities of these compounds towards both hERα (human estrogen receptor alpha) and hERβ were determined. Differences in the modes of action (agonist or antagonist) were observed for the various compounds tested. In general, each compound had the same mode of action towards both ERs. In silico modeling was performed in order to study the differences in estrogenicity observed between the compounds. It is suggested that prenyl chains fit into a hydrophobic pocket present in the hER, resulting in an increased agonistic activity. In addition, it was shown that an increase in length (≈1.7 Å) of pyran prenylated isoflavonoids resulted in an antagonistic mode of action. This might be caused by collision of the pyran ring with helix 11 in the ligand binding cavity of the hER.     

Simulation of the Decontamination Efficiency of PET Recycling Processes based on Solid‐state Polycondensation

The recollection rates for postconsumer poly(ethylene terephthalate) (PET) bottles and the recycling capacities are increasing year by year. The postconsumer PET bottles were recycled either to fibres or to new packaging applications. For packaging applications, the so‐called super‐clean recycling technologies are applied to decontaminate the postconsumer PET pellets. Most of these processes are based on solid‐state polycondensation processes. Because experimental determination of the cleaning efficiency is a time‐consuming and expensive procedure, it would be useful to predict the cleaning efficiencies, e.g. for process development and optimization. Within this study, the decontamination kinetics of a PET super‐clean recycling process based on solid‐state polycondensation was determined. From the decontamination kinetics, the diffusion coefficients were calculated. By use of the diffusion coefficients, the decontamination kinetics was simulated using migration modelling approaches for spherical pellets. The result of this study shows that the decontamination of PET pellets in solid‐state polycondensation processes follows Fickian laws. The diffusion coefficients of the investigated migrants are not influenced by vacuum or inert gas process conditions. The diffusion equations used in commercially available software packages for migration calculation can be used for the simulation of the decontamination efficiencies of PET recycling processes. Copyright © 2012 John Wiley & Sons, Ltd.     

Preparation of fibrous TiO2 photocatalyst and its optimization towards the decomposition of indoor ammonia under illumination

Aqueous dispersion containing TiO₂ particles was firstly prepared and then mixed with silicone or acrylic additives to establish a treating bath. And the fibrous TiO₂ photocatalysts were produced by padding three woven fabrics including cotton, polyester and flax fabrics as support materials with this treating bath and some factors affecting the preparation process were discussed. Moreover, the fibrous TiO₂ photocatalysts were characterized by X-ray diffractometer, infrared Fourier transform spectrometer and scanning electron microscope, and evaluated with respect to the removal efficiency of ammonia under UV irradiation in air stream by a specifically designed photocatalytic reactor and environmental condition simulated chamber. The results showed that ammonia gas could well be decomposed by the fibrous TiO₂ photocatalysts based on cotton and flax fabrics. Increasing the dosage of TiO₂ aqueous dispersion led to the improved ammonia decomposition level of the fibrous TiO₂ photocatalysts. The additives caused the reduced ammonia decomposition level of the fibrous TiO₂ photocatalysts, but provided it with the enhanced resistance to water washing. The ammonia photocatalysis of the fibrous TiO₂ photocatalysts was not much affected by curing temperature and dyed cotton fabrics when preparing.     

New Determinations of Diffusion Coefficients for Various Dopants in Liquid Silicon

The objective of this article is to propose new determinations of the diffusion coefficients of various dopants in liquid silicon. The approach of this work is based on an analysis of the effective segregation coefficients obtained by Kodera in Czochralski growth of silicon-based alloys. However, it will be shown that the solidification model used by Kodera presents some serious deficiencies as it does not account for (i) the dependence of the solute boundary layer thickness on the interface velocity and (ii) the effect of density change upon freezing. In addition, the values of the thermophysical parameters used by Kodera can be questioned in view of recently published data. The approach proposed in the present work can be used to provide a much sounder physical basis for the analysis of the data, but it should be stated that the uncertainty on the partition coefficients is such that a measurement technique based on solidification experiments cannot be expected to be very accurate. In this respect, the scatter of the data, hardly avoidable in Czochralski growth experiments, is also discussed. To put things on a quantitative basis, an error analysis is carried out to quantify the error bar attainable by such a measurement technique.     

Resistance of spherical fills in the case of flow of single- and two-phase media

The results of experimental investigations of the hydrodynamic resistance in spherical fills as applied to the cores of nuclear reactors with spherical fuel elements are presented. The experimental setup and the procedures of preparation of models, measurement, and processing of experimental data are described. The criterial dependences satisfactorily describing data on resistance in motion of single- and two-phase media in spherical fills are obtained. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 2, pp. 283–288, March–April, 2009.     

Wave scattering by a circular cylinder half-immersed in water with an ice-cover

The problem of scattering of water waves obliquely incident on a fixed long circular cylinder half-immersed in deep water with an ice-cover is investigated here. The ice-cover is modelled as an elastic plate of very small thickness. The problem is formulated using the method of multipoles. This leads to an infinite system of linear equations which are solved numerically by truncation. The reflection and transmission coefficients are obtained and depicted graphically against the wave number for various values of the angle of incidence and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. The effect of ice-cover is seen to increase the reflection coefficient and to decrease the transmission coefficient.     

子波最小相位对最小平方反褶积效果影响

常规地面地震勘探中,地震波高频损失的影响因素有许多。为此,人们研究了各类反褶积方法提高分辨率。但是这些方法很多都是带有一定假设的,比如,假设子波是最小相位而且稳定的。本文研究了子波的最小相位性在提高地震资料分辨率中的重要性。准确的提取出地层的反射系数,是地震资料处理过程中重要而关键的一步。本文研究了不同相位子波(最小相位和混合相位)和对反褶积效果的影响,并且用最小平方反褶积来验证。实验结果表明,子波的最小相位性对最小平方反褶积效果有显著影响。     

一种推进剂分解机理的量子化学方法分析

运用量子化学方法,优化计算得到了硝酸异丙酯的稳定几何构型,结合该构型对其静态性质进行了分析.使用两种不同的算法,分别计算了气相状态下硝酸异丙酯热分解和碱性环境下水解反应的路径及其活化能,并与实验值进行了对比.结果显示,量化方法能够比较准确地预测和计算分解路径,但对活化能的准确计算有待进一步研究.