Optimal error estimates of a locally one-dimensional method for the multidimensional heat equation

For the multidimensional heat equation in a parallelepiped, optimal error estimates inL ₂(Q) are derived. The error is of the order of +¦h¦² for any right-hand sidef L ₂(Q) and any initial function ; for appropriate classes of less regularf andu ₀, the error is of the order of ((+¦h¦² ), 1/2<1.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 185–197, August, 1996.     

Convergence of distorted Brownian motions and singular Hamiltonians

We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind .We obtain convergence in total variation norm of the corresponding probability measures on the path space C(₊;^d) under hypotheses which, for example, are satisfied in the case of H _loc ¹ ( ^d )-convergence of the 's, but we can allow more singular situations as regards the approximating sequences. We use then these results to give a criterion of convergence for generalized Schrödinger operators in which the potential function should not necessarily exists as a measurable function. We obtain convergence not only in strong resolvent sense, but we also obtain convergence in the uniform operator topology up to sets of arbitrarily small Lebesgue measure. Applications to the problem of the approximation of ordinary Schrödinger operators by generalized ones corresponding to zero-range interactions are given.     

Impossibility of a Certain Cyclotomic Equation with Applicationsto Difference Sets

Under certain conditions, we show the nonexistence ofan element in the p-th cyclotomicfield over , that satisfies . As applications, we establish the nonexistence ofsome difference sets and affine difference sets.     

CLIMATIC CHANGE SINCE LITTLE ICE AGE RECORDED BY DUNDE ICE CAP

The climatic change since the Little Ice Age recorded in the Dunde Ice Cap is presentedin this paper. There have been three cold periods and three warm periods since 1400AD.Among them, the coldest one was in the 17th century. Many evidences verified the three coldand warm variations recorded in the Dundc Ice Cap. But it was found from the comparison between the Dunde Icc Cap climatic record and thewinter temperature record in Shanghai that there was a temporal dfference in climatic changebetween East China and West China. The general trend is that the cooling and warmingprocesses in West China were earlier than that in East China. In the Dunde Ice Cap, it isnow in an anomalous warm period, while it is not as warm as in Dunde Ice Cap recordaccording to the winter temperature in Shanghai. In addition to the possible cause of temporaldifference in climatic change between West China and East China, another possible cause isthat the greenhouse effect of CO_2 may already be recognizable in the Dunde Ice Cap a     

Synthesis of inorganic-organic hybrids by incorporation of inorganic components into organic polymer using metal alkoxides

Inorganic-organic hybrids have been synthesized by incorporation of the inorganic component of Ti(OC₂H₅)₄ into the organic polymer of ethyl cellulose. The inorganic-organic hybrids did not dissolve in toluene used as a solvent for the starting materials. The ethanol was formed as a by-product of the alcoholysis condensation reaction between Ti(OC₂H₅)₄ and ethyl cellulose. These results suggest that ethoxy groups of Ti(OC₂H₅)₄ react with hydroxy groups of ethyl cellulose to form cross-linking bonds of –O–Ti–O–. The reaction of Ti(OC₂H₅)₄ with ethyl cellulose was further investigated by Fourier transform infrared (FT-IR) spectroscopy. The FT-IR spectroscopic experiments revealed that the Ti–O bond state of Ti(OC₂H₅)₄ was changed by refluxing a toluene solution of Ti(OC₂H₅)₄ with ethyl cellulose. The inorganic-organic hybrids have an interesting dielectric property; their dielectric constant is higher than that of ethyl cellulose and that of a simple mixture of TiO₂ and ethyl cellulose.     

用ICP研究鹿科动物骨质疏松症的微量元素特征

鹿科动物的骨质疏松症是近几年出现的一种疾病，它影响鹿的生长发育和繁殖，病重者死亡。我们采集梅花鹿和白唇鹿的毛，血样，用低温灰化方法和温法消解处理样品，用ＩＣＰ分析了毛，血清中微量元素的含量。病梅花鹿毛样中Ｍｇ，Ａｌ，Ｃａ，Ｔｉ，Ｆｅ，Ｃｕ，Ｚｎ的含量比正常组高，Ｔｉ，Ｃｕ，Ｚｎ的偏差率大于１５％，而Ｓｉ，Ｍｎ，Ｐ，Ｐ，Ａｇ，Ｂａ，Ｌａ，Ｃｅ，Ｐｂ比正常组低，Ｖ，Ａｇ，Ｂａ，Ｌａ，Ｃｅ，Ｐｂ存在...     

~(13)C化学位移在达玛烷型皂甙结构研究中的应用

本文将迄今为止国内外文献报道的200余种达玛烷型皂甙类化合物的~(13)C化学位移按其结构特征分类整理,以原人参二(三)醇等为模型化合物,讨论了皂甙元结构变化引起的位移变化(Δδ_C)规律。     

On the modelling of solid state reactions.Synthesis of YAG

There is a model of yttrium aluminium garnet (YAG) synthesis presented in this article. The developed model is based on nonlinear reaction–diffusion partial differential equations. The solution was carried out numerically using finite difference techniques. We got dependability curves for diffusion and reaction rates and offered possible method to localize values of diffusion and reaction rate constants precisely enough.AMS subject classification: 35K57, 65M06     

The hole-pressure problem

There is a need to unify present hypotheses of the nature and role of the hole-pressure,p _e , and thus provide consolidation on which to base future research and understanding. This paper is intended to meet this need. Attention is directed towards the calculation ofp _e from the velocity and stress fields for viscoelastic fluids flowingacross rectangular holes. The constitutive models used are the Newtonian, Second-order and Maxwell models, for values of Reynolds number up to 10 and Weissenberg number up to 0.1.The numerical complications involved are studied through an investigation of the constituent parts ofp _e . Verification of present theory is then sought, from which justification may be derived for the estimation of elasticity fromp _e measurements. Attention is directed towards the predictions of Higashitani and Pritchard and the extension to the Tanner and Pipkin theory for Second-order fluids. The effects of variation of geometric dimensions and flow type uponp _e are also discussed.     

Relative kinetics of the radical addition of benzyl bromide to unsaturated compounds

The relative rate constants of the addition of the C₆H₅CH₂ radical to unsaturated compounds CH₂=CHX (X = C₄H₉, SiMe₃, CF₃, CO₂Me, CN) were determined under the conditions of initiation by the Fe(CO)₅ + DMF system or by benzoyl peroxide. Depending on the values of the relative addition rate constants, the monomers can be arranged into the following series (X): CF₃C₄H₉32Me5 + DMF system, the addition stage proceeds by a free radical mechanism.A. N. Nesmeyanov Institute of Heteroorganic Compounds, Russian Academy of Sciences, 117813 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 9, pp. 2017–2022, September, 1992.