微观世界探索(续)

论文系统地阐述了从原子、原子核到基本粒子内部结构研究的历史及现状，讨论了微观物理理论和实验研究的前景和展望．论文还阐述了微观物理与宏观物理(宇宙论和天体物理等)的结合与交叉，以无可争辨的实验事实阐明了微观世界和宏观世界的无限性．     

平面物体在曲面状态下扫描仪图像的校正理论

平面物体在曲面状态下经扫描仪扫描后,其图像将发生复杂的畸变。提出将其分类为灰度畸变、投影畸变和成像畸变。通过理论分析,提出了在二元曲面模型下对投影畸变和成像畸变进行数字校正的方法,给出了对灰度畸变进行数字校正的实用方法。     

半参数回归模型中小波估计的随机加权逼近速度

把小波光滑方法和随机加权方法结合在一起，获得了半参数回归模型中参数分量的小波估计的随机加权逼近速度为σ(n^-1/2)。因此，从大样本意义上说，小波光滑方法和随机加权方法对半参数回归模型是可用的。     

网络图在产品配送中的应用

面对多样化的市场需求，企业的销售渠道也变得异常复杂，利用网络图可以简化实际问题，并能形象地描述它。本根据网络知识建立了产品分销模型，探求企业在市场需求固定和随机时的最优收益。最后，章还进行实例验算，并做出相应的结果分析。     

Crossover Critical Behavior in the Three-Dimensional Ising Model

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussed.     

Time-domain simulations of sound propagation through screen-induced turbulence

A flow model in combination with a statistical-dynamical turbulence generator and a linearised Euler time-domain model for sound waves were used to simulate the effect of screen-induced turbulence on the noise level in the acoustical shadow of a screen in wind. Instead of simulating a great number of different frozen turbulence realisations, the concept of transient turbulence was successfully tested and applied. This concept is adequate to the time-domain model and reduces the computational demands. Several two-dimensional simulations allowed to isolate the individual effects of wind and screen on the propagation of 500 Hz sound waves over a 4-m high noise barrier. At a distance of 250 m from the source (240 m behind the screen) the sheltering effect of the screen and the refraction effect of the wind are in the order of 6 and 4 dB, respectively. The screen-induced turbulence leads to fluctuations in the noise level with a standard deviation of 1.2 dB and a maximum amplitude of 3 dB. However, the time averaged effect turned out to be in the order of merely 0.2 dB. The effect of the screen-induced turbulence on the average noise level behind the screen is therefore negligible.     

Symmetry specified enumeration of substituted derivatives: an easy solution to the complex problem

Several sophisticated methods to solution of symmetry specified enumeration problems are available in the modern literature. In this paper we propose a simple technique that allows one to manually compute the exact numbers of fixed-symmetry derivatives for a given structure either with inclusion or ignoring the substitution patterns. The basic idea of the method suggested consists in the derivation of Pólya-like cycle indices for the automorphism groups of specially constructed orbit partition graphs; the expansion of these indices and subsequent simple calculations result in the desired numbers of substituted derivatives with achiral substituents. Limitations of the new technique (and a method suggested earlier) depend on the relevance of the orbit partitions for particular subgroups of the point symmetry group. For illustration purposes, the results obtained for the prismane (D _3h ) and adamantane (T _d ) structures are discussed. In the former case the numbers of substituted derivatives can be found for all subgroups of the D _3h group, whereas in the latter case these numbers can be determined for eight out of eleven subgroups of the T _d point symmetry group. This work is based on the text of the lecture presented by the authors at the 5th All-Russia Conference on Molecular Modeling (Moscow, April 2007). The paper deals with the methodology and detailed treatment of applied aspects related to solution of enumeration problems for substituted derivatives with prescribed symmetry groups. Unlike the known methods of symmetry specified enumeration, the technique suggested is simple enough and may be regarded as generalization of the Pólya methodology, which is widely used by chemists. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 227–245, February, 2008.     

A general Hsu-Robbins-Erdős Type estimate of tail probabilities of sums of independent identically distributed random variables

Periodica Mathematica Hungarica - Let X 1,X 2,... be a sequence of independent and identically distributed random variables, and put % MATHTYPE!MTEF!2!1!+-%...     

Information and asymptotic efficiency of the case-cohort sampling design in Cox's regression model

Efficiencies of the maximum pseudolikelihood estimator and a number of related estimators for the case-cohort sampling design in the proportional hazards regression model are studied. The asymptotic information and lower bound for estimating the parametric regression parameter are calculated based on the effective score, which is obtained by determining the component of the parametric score orthogonal to the space generated by the infinite-dimensional nuisance parameter. The asymptotic distributions of the maximum pseudolikelihood and related estimators in an i.i.d. setting show that these estimators do not achieve the computed asymptotic lower bound. Simple guidelines are provided to determine in which instances such estimators are close enough to efficient for practical purposes.     

Robust Output Tracking Control of an Uncertain Linear System via a Modified Optimal Linear-Quadratic Method

This study investigates the robust output tracking problem for a class of uncertain linear systems. The uncertainties are assumed to be time invariant and to satisfy the matching conditions. According to the selected nominal parameters, an optimal solution with a prescribed degree of stability is determined. Then, an auxiliary input via the use of an adapting factor, connected to the nominal optimal control, is introduced to guarantee the robustness and prescribed degree of stability for the output tracking control of the uncertain linear systems. This method is very simple and effective and can reject bounded uncertainties imposed on the states. A maglev vehicle model example is given to show its effectiveness.