解初值问题y″=g(x，y)的含参数块方法

1引言对于二阶常微分方程的初值问题y″=g(x,y),y(x_0)=y_0,y′(x_0)=y_0′,x_0(?)x(?)T(1)的数值解法的研究引起人们的广泛兴趣．对于直接积分(1),自从1976年J．D．Lambert和I．A．Waston提出二阶P-稳定方法和1978年G．Dahlquist证明P-稳定常系数线性多步方法的最高相容阶不超过2的重要结论以来,截止目前,已积累了许多高于2阶的P-稳定方法．例如,修正的Numerov方法,混合法(特殊形式RK的方法),多导法,Obrechkoff方法,显式RKN方法,单隐方法和对角隐式RKN方法等(顺便指出,文献[5,16]中所说的高阶方法的相容阶均不超过4)．所有这些方法,有些相     

从结构电算谈设计概念

使用计算机进行结构设计虽然能大大减轻计算工作量，但不能取代人的设计概念，只有在设计人员具备较全面的设计概念；有一定设计经验；同时深入了解程度的情况下，才能确保工程设计的质量。     

Dimension Theory and Nonstable K 1

This article provides an introduction to A. Bak's theory of group-valued functors on categories with structure and dimension and applies this theory to the algebraic K-theory functors nonstable K ₁ and K ₂.     

Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments

We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks.     

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.     

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.