一类非线性常微分方程振荡解的渐近表示

在本文中,我们讨论了非线性常微分方程y"=a0|x|αy3 a1|x|βy2 α2|x|γy α3|x|δ振荡解的渐近表示．在这个方程中将α0,α,α1,β,α2,γ,α3,δ分别换成0,0,6,0,0,0,sgn(x),1就是著名的第一类Painleve方程,而将α0,α,α1,β,α2,γ,α3,δ分别换成2,0,0,0,sgn(x),1,α0,就是著名的第二类Painleve方程．当α0,α,α1,β,α2,γ,α3,δ分别换成-β/3γ,0,0,0,1/γ,1,α,0时,可用于组合KdV方程孤立子解的化简．     

MgxZn1-xO结构性质

采用第一性原理计算模拟了不同组分的Mg_xZn_1-xO半导体混晶的晶格常数、总能、结构,以及禁带宽度的变化。计算结果显示,随着Mg组分的增加,晶格常数逐渐减小,晶体逐渐偏离纤锌矿结构。对各种不同的Mg原子排列情况进行比较认为,Mg_xZn_1-xO的结构随组分x的增大,发生从纤锌矿到岩盐矿的结构相变的可能性高于发生相分离。另一方面,禁带宽度随组分增大主要由价带顶的移动所致。进一步分析Mg原子各种电子态对价带的影响表明,Mg对价带顶附近能带的贡献依次来自p、d、s态电子。随着组分x的增加,p态电子在价带顶附近的密度明显提高,说明sp轨道杂化不但对晶体的几何结构产生影响,而且对其电子结构也起重要作用。     

Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law

For independent identically distributed random vectors belonging to the generalized Domain of Attraction of the multivariate normal law, we define two partial sum processes analogous to that of Donsker's Theorem. We prove that each converges in distribution to a Brownian Motion in the space of continuous functions. One process uses nonrandom operator normalization, and the other is a studentization of the first, using normalization by the empirical covariance operator.     

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

Speckle fields are the random light wave distributions produced when the light fields are scattered from random surfaces or a random medium. They appear in many optical phenomena that are related to light propagations[1,2] and have found wide appli-cations in a variety of scientific and technical fields. The examples of the recent impor-tant applications of speckles include the analysis of the movement of the granules[3], the three-dimensional imaging for the microstructures of metal nanocryst…     

Identification of nonstationary axisymmetric load distributed along a cylindrical shell

The paper outlines a procedure to identify the space-and time-dependent external nonstationary load acting on a closed circular cylindrical shell of medium thickness. Time-dependent deflections at several points of the shell are used as input data to solve the inverse problem. Examples of numerical identification of various nonstationary loads, including moving ones are presented. The relationship between the external load and the stress-strain state of the shell is described by the Volterra equation of the first kind. The identification problem is solved using Tikhonov's regularization method and Apartsin's h-regularization method __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 91–100, July 2008.     

关于曲线积分中值定理“中间点”的一个一般性结果

讨论了第一类曲线积分中值定理“中间点”的渐近性质,得到了更具一般性的新结果.     

The Equivalence of Several Basic Theorems for Subdifferentials

Several different basic tools are used for studying subdifferentials. They are a nonlocal fuzzy sum rule in (Borwein et al., 1996; Zhu, 1996), a multidirectional mean value theorem in (Clarke and Ledyaev, 1994; Clarke et al., 1998), local fuzzy sum rules in (Ioffe, 1984, 1990) and an extremal principle in (Kruger and Mordukhovich, 1980; Mordukhovich, 1976, 1980, 1994). We show that all these basic results are equivalent and discuss some interesting consequences of this equivalence.     

Fast computation of a rational point of a variety over a finite field

We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety.

     

Structural and magnetic characterization of Mn3IrGe and Mn3Ir(Si1−xGex): experiments and theory

The structural and magnetic properties of a new ternary Ir-Mn-Ge phase, Mn₃IrGe, as well as the solid solution Mn₃Ir(Si_1−xGe_x), 0?x?1, have been investigated by means of X-ray and neutron powder diffraction, magnetization measurements and first principles calculations. The crystal structure is cubic, of the AlAu₄-type (an ordered form of the β-Mn structure), Z=4, space group P2₁3, and the unit-cell dimension varies linearly with the silicon content. For all compositions, antiferromagnetic ordering is found below a critical temperature of about 225 K. The magnetic structure is noncollinear, as a result of frustrated magnetic interactions on a triangular network of Mn atoms, on which the moments rotate 120° around the triangle axes. The magnitude of the magnetic moment at 10 K is 3.39(4) μ_B for Mn₃IrGe. The theoretical calculations reproduce with very good accuracy the magnitudes as well as the directions of the experimentally observed magnetic moments.     

STRUCTURING ＆ RHEOLOGY OF MOLTEN POLYMER／CLAY NANOCOMPOSITES

The evolution and the origin of “solid-like state” in molten polymer/clay nanocomposites are studied. Using polypropylene/clay hybrid (PPCH) with sufficient maleic anhydride modified PP (PP-MA) as compatibilizer, well exfoliation yet solid-like state was achieved after annealing in molten state. Comprehensive linear viscoelasticity and non-linear rheological behaviors together with WAXD and TEM are studied on PPCH at various dispersion stages focusing on time,temperature and deformation dependencies of the “solid-like” state in molten nanocomposites. Based on these, it is revealed that the solid-structure is developed gradually along with annealing through the stages of inter-layer expansion by PP-MA,the diffusion and association of exfoliated silicate platelets, the formation of band/chain structure and, finally, a percolated clay associated network, which is responsible for the melt rigidity or solid-like state. The network will be broken down by melt frozen/crystallization and weakened at large shear or strong flow and, even more surprisingly, may be disrupted by using trace amount of silane coupling agent which may block the edge interaction of platelets. The solid-like structure causes characteristic non-linear rheological behaviors, e.g. residual stress after step shear, abnormal huge stress overshoots in step flows and, most remarkably, the negative first normal stress functions in steady shear or step flows. The rheological and structural arguments challenge the existing models of strengthened entangled polymer network by tethered polymer chains connecting clay particles or by chains in confined melts or frictional interaction among tactoids. A scheme of percolated networking of associated clay platelets, which may in band form of edge connecting exfoliated platelets, is suggested to explain previous experimental results.