Lévy processes and Fourier multipliers

We study Fourier multipliers which result from modulating jumps of Lévy processes. Using the theory of martingale transforms we prove that these operators are bounded in Lp(Rd) for 1<p<∞ and we obtain the same explicit bound for their norm as the one known for the second order Riesz transforms.     

The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.     

切削刀具倒棱刃口挤压力的理论计算

根据试验观察．揭出了刀具刃口带负倒棱时的切削模型。在此模型中,刀具刃口 存在一个“金属死区”。以新模型为基础．采用能量法,对高温、高应变率下刀具刃 口的挤压力进行了理论计算。所做工作的特点是：１）在材料变形分析中计入了挤压 层金属绕过刀具刃口时的过剩变形;２）进行有关材料变形与物理特性的计算时,考 虑了温度与应变率的影响。利用新研制的压电式切削测力仪进行验证试验,其结果表 明,理论计算值与实测数据较好一致。     

Donor-acceptor properties, catalytic activity, and negative charge exoemission from the alumina surface modified with lithium cations

Donor-acceptor properties of alumina modified with lithium cations were studied by ESR of paramagnetic complexes of adsorbed anthraquinone. The results were compared with the data on negative ion emission (exoemission) accompanying the decomposition of isopropyl alcohol in the adsorption layer. The data on the activity measured by the pulse microcatalytic technique in isopropyl alcohol decomposition are discussed. Small additives of lithium were found to promote catalytic activity of the samples. The role of acid and basic sites in isopropyl alcohol decomposition was discussed. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 616–621, April, 2006.     

Influence of the conditions of manufacture of nanomeric zirconium dioxide,stabilized with yttrium oxide,on its catalytic properties in the oxidation of CO

The morphological and catalytic properties of samples of nanomeric zirconium dioxide, stabilized with yttrium oxide, manufactured via the effect of a UHF field during the process of drying precipitated zirconium hydroxide and calcination at temperatures from 300 to 1000 °C, were studied. It was shown that the highest activity in the oxidation of CO occurred with 40 nm particles of zirconium dioxide prepared at 1000 °C. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 43, No. 2, pp. 96–101, March–April, 2007.     

ESR study of products of transformation of 3,6-tert-butylpyrocatechol on alumina, zinca, silica, and titania

The formation of semiquinone and phenoxazyl radicals and metallocomplexes with semiquinone ligands was observed by ESR during the interaction of di-tert-butylpyrocatechol with Al₂O₃, ZnO, SiO₂, and TiO₂. In the case of different modifications of SiO₂, admixtures of TiO₂ exhibit a higher reactivity in complex formation with the organic substrate. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1975–1978, October, 1998.     

Enzymatic kinetic of cellulose hydrolysis

The ethanol effect on the Trichoderma reesei cellulases was studied to quantify and clarify this inhibition type. To determine inhibition parameters of crude cellulase and purified exoglucanase Cel7A, integrated Michaelis-Menten equations were used assuming the presence of two inhibitors: cellobiose as the reaction product and ethanol as a possible bioproduct of cellulose fermentation. It was found that hydrolysis of cellulose by crude enzyme follows a model that considers noncompetitive inhibition by ethanol, whereas Cel7A is very slightly competitively inhibited. Crude cellulase is much more inhibited (K _iul=K _icl=151.9 mM) than exoglucanase Cel7A (K _icl=1.6 × 10¹⁵ mM). Also, calculated inhibition constants showed that cellobiose inhibition is more potent than ethanol inhibition both for the crude enzyme as well as exoglucanase Cel7A.     

On-line determination of organophosphorus pesticides in water by solid-phase microextraction and gas chromatography with thermionic-selective detection

This paper describes the extraction of 49 organophosphorus pesti-cides (OPPs) from water samples using solid-phase microextraction (SPME). Three fibers, including a 15-μm XAD-coated fiber, a 85-μm polyacrylate-coated fiber, and a 30-μm polydimethylsilox-ane-coated fiber (PDMS), were evaluated here. The effects of stirring and the addition of NaCl to the sample were examined for the polyacrylate-coated fiber. The precision of the technique was examined for all three fibers and the extraction kinetics were investigated using the XAD- and polyacrylate-coated fibers. With some exceptions, the XAD- and polyacrylate-coated fibers performed better than the PDMS-coated fiber. The superiority of the XAD-nd polyacrylate-coated fiber. The superiority of the XAD- and polyacrylate-coated fibers over the PDMS-coated fibers can be attribuibuted to the aromatic functionalities of the XAD and the polar functionalities in the polyacrylate. The relatively high percent RSDs indicate that the SPME technique needs to be further refined before it can be used for anything other than screening. A more effective form of agitation than mechanical stirring may be neccessary to reduce variability and achieve a faster equilibrium between the sample and the SPME fiber.     

一种新型联萘基旋光共轭聚合物的圆二色谱和圆偏振荧光光谱

众所周知 ,聚合物的光电性质依赖于聚合物链的构象和 (或 )组成 ,通过在聚合物上引入手性单元 ,采用圆二色谱 ( CD)和圆偏振荧光光谱 ( CPL)等方法可表征聚合物结构 [1] .近年来 ,由于圆偏振光可用作光数据存储和液晶显示器背景光 [2 ] ,人们开始注重共轭聚合物圆偏振光材料的研究 .共轭聚合物的光致和电致圆偏振光的现象由一种带手性侧链的聚噻吩[3 ] 和一种带手性侧链的聚 (对苯撑乙烯 ) [4 ]产生 ,但它们的圆偏振荧光度 (用不对称因子 glum=2 ( IL-IR) / ( IL+IR)表示 ,IL 和 IR 分别指左圆偏振光强度和右圆偏振光强度 )相对较低 …