生命周期个人拓展消费的优化研究

随着我国经济社会的发展,人们的消费水平和消费层次也在逐步提高,消费领域在不断扩展,因而提出拓展消费这一新的概念。同时改变现有的在研究消费效用最大化时对周期阶段划分的方法,把拓展消费的生命周期划分为三个阶段。借以引入各阶段倾向的效用模型,并运用多阶段最优动态规划和变分法原理来探讨完全行为个人整个生命周期谋求拓展消费效用最大化时各阶段的最优消费解。通过研究,得出了在次优消费解的选择下,得以实现现实最优构成的结论。     

On a new class of multiplicative pseudo-random number generators

In the computing literature, there are few detailed analytical studies of the global statistical characteristics of a class of multiplicative pseudo-random number generators.We comment briefly on normal numbers and study analytically the approximately uniform discrete distribution or (j,)-normality in the sense of Besicovitch for complete periods of fractional parts {x _{0 1} ⁱ /p} on [0, 1] fori=0, 1,..., (p–1)p^–1–1, i.e. in current terminology, generators given byx _{n+1 1} x _n mod p wheren=0, 1,..., (p–1)p ^–1–1,p is any odd prime, (x ₀,p)=1, ₁ is a primitive root modp ², and 1 is any positive integer.We derive the expectationsE(X, ),E(X ², ),E(X _nX_n+k); the varianceV(X, ), and the serial correlation coefficient k. By means of Dedekind sums and some results of H. Rademacher, we investigate the asymptotic properties of k for various lagsk and integers 1 and give numerical illustrations. For the frequently used case =1, we find comparable results to estimates of Coveyou and Jansson as well as a mathematical demonstration of a so-called rule of thumb related to the choice of ₁ for small k.Due to the number of parameters in this class of generators, it may be possible to obtain increased control over the statistical behavior of these pseudo-random sequences both analytically as well as computationally.     

Photoinduced non-linear optical diagnostic of SiNxOy/Si111 interfaces

Anisotropic (elliptically polarized) photoinduced second harmonic generation (PISHG) in SiN_xO_y/Si1 1 1 films was proposed for contact-less monitoring of specimens with different nitrogen to oxygen (N/O) ratios. As a source for the photoinducing light, we used a nitrogen Q-switched pulse laser at wavelengths of 315, 337 and 354 nm as well as doubled frequency YAG–Nd laser wavelength (λ=530 nm). The YAG : Nd pulse laser (λ=1.06 μm; W=30 MW; τ=10–50 ps) was used to measure the PISHG. All measurements were done in a reflected light regime. We found that the output PISHG signal was sensitive to the N/O ratio and the film thickness. Measurements of the PISHG versus pumping wavelengths, powers, incident angles as well as independent measurements of the DC-electric field induced second harmonic generation indicate the major role played in this process by axially symmetric photoexcited electron–phonon states. The SiN_xO_y films were synthesized using a technique of chemical evaporation at low pressures. Films with thickness varying between 10 and 30 nm and with an N/O ratio between 0 and 1 were obtained. Electrostatic potential distribution at the Si1 1 1–SiN_xO_y interfaces was calculated. Comparison of the experimentally obtained and quantum chemically calculated PISHG data are presented. High sensitivity of anisotropic PISHG to the N/O ratio and film thickness is revealed. The role of the electron–phonon interactions in the dependencies observed is discussed. We have shown that the PISHG method has higher sensitivity than the traditional extended X-ray absorption fine structure spectroscopic and linear optical method for films with the N/O ratio higher than 0.50.     

四元Heisenberg群上次拉普拉斯算子的m幂次的基本解

本文研究了四元Heisenberg群上次拉普拉斯算子的m幂次的基本解,该结论是Heisenberg群上结果的推广.本文利用了四元Heisenberg群上的Fourier变换理论构造了该群上次拉普拉斯算子的m幂次的基本解,并且给出了基本解的积分表示.     

Enhanced Compression of Fundamental Solitons in Dispersion Decreasing Fibers with Negative Third-order Dispersion Ⅱ. Effects of Fiber Characteristics and Initial Soliton Width

Previous work have shown that the combined effects of negative third-order dispersion (TOD) and Raman self-scattering (RSS) can significantly enhance soliton compression in dispersion decreasing fibers (DDFs). In this paper, the effects of the negative TOD coefficient and the effective amplification of DDF′s on the performance of soliton compression are investigated. It is shown that for a given initial soliton width and a given effective amplification, there exists an optimum value of the negative TOD coefficient of the DDF at which the enhancement in soliton compression is maximum. It is also shown that the compression enhancement saturates when the effective amplification exceeds a certain value, which has been explained as a compromise between the higher-order effects induced increase of the ratio of input to output group-velocity dispersion coefficients of the DDF and the TOD induced non-adiabatic compression characteristics. The dependence of the compression enhancement on the initial soliton width have also be studied and the scheme is found works well for solitons with initial widths less than 3 ps.     

Perturbation models

A Markov chain (with a discrete state space and a continuous parameter) is perturbed by forcing a chain to return to “permissible” states whenever it happens to enter “forbidden” states, with returns governed by a replacement distribution.The compensation method is employed to obtain the distribution for the modified chain, in terms of the original chain and the perturbation mechanism.Emphasis is placed on ergodic chains, and interpretation of results in terms of perturbation theory of semi-groups and the ergodic potential theory (based on the fundamental matrix of a chain) is mentioned.     

Boundary integral equation method in micropolar elasticity

This paper presents the integral representations of the displacement and rotation fields of the micropolar continuum, and the regularized integral representations of the traction and couple vector. Thus the boundary integral equations and the boundary integro-differential equations are derived. In addition, the formulation for crack problems is given by both the boundary integral equations and the boundary integro-differential equations.     

二阶广义分布参数系统的谱分布

应用泛函分析算子理论的方法研究了Hilbert空间中二阶广义分布参数系统的谱分布问题,利用有界线性算子的广义逆给出了所讨论问题的解及解的构造性表达式。这对研究二阶广义分布参数系统的镇定及渐进稳定性问题都有重要的理论价值。     

On the transfer matrix of a MIMO system

We develop a deterministic ab initio model for the input–output relationship of a multiple‐input multiple‐output (MIMO) wireless channel, starting from the Maxwell equations combined with Ohm's law. The main technical tools are scattering and geometric perturbation theories. The derived relationship can lead us to a deep understanding of how the propagation conditions and the coupling effects between the elements of multiple‐element arrays affect the properties of an MIMO channel, e.g. its capacity and its number of degrees of freedom. Copyright © 2011 John Wiley & Sons, Ltd.     

用蓝色光二极管测量掺钛蓝宝石飞秒激光脉冲宽度

用蓝色光二极管双光子跃迁光电流信号测量掺钛蓝玉石飞秒激光脉冲宽度，实验高精度地记录了二阶干涉自相关曲线及其精细结构，由于用蓝色二极管双光子跃迁代替了常用的二次谐波，而且光信号直接转化为电信号，从而使飞秒激光脉冲宽度的测量大为简化。