具有位数3和4的双随机循环矩阵中的素元

本文研究了双随机循环矩阵中素元的分类问题．由于任一n阶双随机循环矩阵都可以唯一地表示为移位的n-1次一元多项式,从而可把双随机循环矩阵中素元的分类问题简化为解双随机循环矩阵上的一个方程．应用此原理,本文完全解决了判别具有位数3的n阶双随机循环矩阵是否为素元的问题,并给出了n阶双随机循环矩阵中一类具有位数4的素元．     

Optimal infrastructure design and expansion of broadband wireless access networks

This paper investigates the important infrastructure design and expansion problem for broadband wireless access networks subject to user demand constraints and system capacity constraints. For the problem, an integer program is derived and a heuristic solution procedure is proposed based on Lagrangean relaxation. In the computational experiments, our Lagrangean relaxation based algorithm can solve this complex design and expansion problem quickly and near optimally. Based on the test results, it is suggested that the proposed algorithm may be practically used for the infrastructure design and expansion problem for broadband wireless access networks.     

Numerical simulation of pollution and oil spill spreading by the stochastic discrete particle method

The features of the stochastic discrete particle method are discussed as applied to the simulation of pollutant advection and diffusion in a turbulent flow and to the spread of a thin film of a viscous substance (oil) on the surface of water. The diffusion tensor in the former problem depends on the scale of the pollution cloud, and the diffusivity in the latter problem depends nonlinearly on the desired function. For pollution dispersion by a turbulent flow, a stochastic discrete particle algorithm is constructed in the case when the diffusion tensor corresponds to the Richardson 4/3 law. The numerical and analytical results are shown to agree well. The problem of oil film spreading is described by a quasilinear advection-diffusion equation. For this problem, a random walking algorithm is constructed in which the variance of the walking particle step depends on the desired function. For both instantaneous and time-continuous sources of pollutants, the solution produced by the stochastic discrete particle method agrees well with the analytical and/or numerical solutions to the test problems under consideration.     

模型不确定非线性随机系统的鲁棒性能准则设计

对于一类模型不确定非线性随机系统,用耗散性的观点发展了鲁棒性能准则理论.特别地,将确定性非线性系统理论中的耗散性概念引入到模型不确定随机非线性系统中,并以此作为基础来发展H∞理论.在精确模型随机非线性系统H∞基础上,建立了模型不确定系统L2增益和HJI不等式的可解性的关系.由于HJI偏微分方程难于求解,考虑模型参数满足某种适当匹配条件的系统的鲁棒性能准则问题,我们不需要通过求解HJI方程就可以得到此类系统的H∞控制律.     

Thermoelasticity and stress relaxation behavior of polychloroprene/organoclay nanocomposites

Polychloroprene/organoclay nanocomposites (ENC) were characterized by X-ray scattering, DSC and stretching calorimetry techniques.The infinite cluster of highly anisometric organoclay particles was likely to set on at filler volume fraction as low as ? ? 0.04. Quantitative analysis of thermoelastic behavior over the entire range of relative elongations provided additional support for the concept of strain-dependent strain amplification factor as the major parameter controlling the thermomechanical properties of the ENC. Low values of the fitting parameter C in the modified equation for the total heats of stretching were regarded as evidence for the reduced exothermal effects of external friction between organoclay nanoparticles coated with the boundary interphase. Stress relaxation behavior of the ENC was qualitatively consistent with the original assumption that after initial stretching to the highest elongation (λ_lim) the pre-existing infinite clusters of filler particles were broken into isolated clusters which remained structurally similar, whatever the subsequent stretching to λ_f < λ_lim.     

High‐resolution solid‐state NMR study of the domain structure and molecular motion in drawn films of a vinylidene fluoride and trifluoroethylene copolymer with 73 mol % vinylidene fluoride

The heterogeneous higher order structure and molecular motion in a single crystalline film of a vinylidene fluoride (VDF) and trifluoroethylene (TrFE) copolymer with 73 mol % VDF was investigated with the ¹H–¹³C cross‐polarization/magic‐angle spinning NMR technique. A transient oscillation was observed in plots of the ¹³C peak intensity versus the contact time for the CH₂, CHF, and CF₂ groups. On the basis of the extended cross‐relaxation theory of spin diffusion, we determined that the oscillation behavior was caused by the TrFE‐rich segments in the chain and that the crystal consisted of VDF‐rich and TrFE‐rich domains. The former had TrFE‐rich segments in VDF and TrFE fractions of 0.24 and 0.27, respectively, and the latter had VDF‐rich segments in a VDF fraction of 0.49. The spin–lattice relaxation time T_1ρH in the rotating frame for each group was minimal in the three temperature regions of β, α_b, and α_c (↑) on heating and in the two temperature regions of α_1D and α_c (↓) on cooling. The α_c (↑) and α_c (↓) processes depended on the first‐order ferroelectric phase‐transition regions on heating and cooling, respectively. The motional modes for the other processes were confirmed by the T_1ρH minimum behavior of the VDF and TrFE groups in the TrFE‐rich domain and the VDF‐rich segments in the VDF‐rich domain. The β and α_b processes were attributed to the flip–flop motion of the TrFE‐rich segments and the competitive motion of the TrFE‐ and VDF‐rich segments in the ferroelectric phase, respectively. The α_1D process was due to the one‐dimensional diffusion motion of the conformational defects along the chain in the paraelectric phase, accompanied by the trans and gauche transformation of the VDF conformers of ttg⁺tg^? and g⁺tg^?tt. The effect of the competitive motion of the TrFE‐rich segment on the thermal stability of the VDF‐rich segment in the chain near the Curie temperature was examined. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1026–1037, 2002     

具分布参数的广义随机神经网络的镇定

研究具分布参数的Cohen—Grossberg广义随机神经网络的镇定性。将所考虑的系统的解随机场关于空间变量的积分视为相应的由随机常微分方程描述的神经网络的解过程来讨论其镇定性。具体实施方法是运用Ito↑^微分公式沿系统对构造的关于空间变量平均的Lyapunov函数进行微分，从而克服了研究具分布参数随机系统无相应Ito↑^公式的困难。     

Superparamagnetic relaxation Mössbauer spectra by phonon–magnon interaction using the multilevel method

The formation of local moments and the effect of charge carrriers in dilute magnetic semiconductors can be well understood using local probe techniques like Mossbauer Spectroscopy. We report here on Mossbauer studies in the systems Fe_0.008Ge_{1 ? x} D _x (D = As, Bi), Fe_0.008Ge_{1 ? x} In _x , and Fe_0.008Ge_{1 ? x} Sn _x . At room temperature magnetic interactions were observed for donor (D) impurities at the Fe site in the Fe_0.008Ge system. No such magnetic ordering was observed for acceptor (In) or neutral (Sn) impurities.     

Configurational Effects in Statistical Theory of Branched Non-Random Polycondensation

The statistical theory of gelation in the simplest process of the non-random polycondensation (S. I. Kuchanov, T. V. Zharnikov, J. Stat. Phys., 111(5/6), 1273 (2003)) has been refined as to be able to take into account the effect of a monomer configuration on topological characteristics of the polymer network of the gel. Proceeding from the kinetic analysis of such a polycondensation, we rigorously prove that it can be described in terms of some stochastic branching process. The parameters of the process depend on the overall number of functional groups in the monomer as well as on the pattern of their mutual arrangement. Examples of some model systems illustrate the effect of kinetic and configurational factors on the topology of a polymer network formed in the course of non-random polycondensation.     

金融数学的发展及其在证券投资组合中的应用

论述了金融科学中一种新兴的数学工具和数学技术——倒向随机微分方程，通过运用倒向随机微分方程，研究当投资者以将来某一时刻获取一定数额的适应性收益为投资目标时，如何确定当前证券投资组合中各证券的投资比例．