Pseudorandom properties of prime factors

In this paper we study some pseudo-random properties related to the prime factors of integers. We prove some results concerning the well distribution of the greatest prime factor modulo 4, and give some computational insight on the correlations, which seem to be beyond reach of proof.     

Compact Matrix Expressions for Generalized Wald Tests of Equality of Moment Vectors

Asymptotic chi-squared test statistics for testing the equality of moment vectors are developed. The test statistics proposed are generalized Wald test statistics that specialize for different settings by inserting an appropriate asymptotic variance matrix of sample moments. Scaled test statistics are also considered for dealing with nonstandard conditions. The specialization will be carried out for testing the equality of multinomial populations, and the equality of variance and correlation matrices for both normal and nonnormal data. When testing the equality of correlation matrices, a scaled version of the normal theory chi-squared statistic is proven to be an asymptotically exact chi-squared statistic in the case of elliptical data.     

Assessing the Error Probability of the Model Selection Test

The asymptotic error probability of Linhart's model selection test isevaluated, and compared with the nominal significance level. We examine thecase where the expected discrepancies of the candidate models from the truemodel are asymptotically equal. The local alternatives method is employed inthe limiting operation of the asymptotic evaluation. Although the errorprobability under the null hypothesis is actually shown to be equal to orless than the level for most situations, intolerable violations of the errorcontrol are observed for nested models: It is often erroneously concludedthat the smaller model is significantly better than the larger model. Toprevent this violation, a modification of Linhart's test statistic isproposed. The effectiveness of the proposed test is confirmed throughtheoretical analysis and numerical simulations.     

空间光通信指令传输的抗干扰设计

设计一种用归零码及多重相关解调技术的传输方案，并给了所需的几种抗干扰单元电路，最后结合实验说明了此方案可提高不良环境下传输数据的置信率。     

Individual and center-of-mass resonances in the motional spectrum of an electron cloud in a Penning trap

We have examined experimentally the motional spectrum of an electron cloud confined in a Penning trap. When the axial oscillation is excited by a radio frequency field the resonance exhibits a double structure. Both components depend differently on the number of trapped electrons and have different shape and width. We conclude that one of them corresponds to the excitation of the individual electrons while the other is the center-of-mass mode of the cloud. The threshold behaviour of the center-of-mass resonance suggests that it is a parametric instability of a Mathieu type equation of motion. Received 11 July 2001 and Received in final form 12 November 2001     

上海基础房价相关指标及走势的分析与研究

基础房价的相关指标及其走势一直是大众关心的热门话题．本文通过对上海基础房价相关指标的分析，建立了市场房价走势的两个数学模型．模型一：在相关性分析的基础上利用主成分分析消除指标间的共线性，再用回归拟合房价模型并进行预测；模型二：在相关性分析的基础上利用核估计方法预测出房价．继呵对2005年下半年的房价走势进行了预测，得出的结果与实际情况相吻合．     

Ion implantation induced by Cu ablation at high laser fluence

High energy laser plasma-produced Cu ions have been implanted in silicon substrates placed at different distances and angles with respect to the normal to the surface of the ablated target. The implanted samples have been produced using the iodine high power Prague Asterix Laser System (PALS) using 438 nm wavelength irradiating in vacuum a Cu target. The high laser pulse energy (up to 230 J) and the short pulse duration (400 ps) produced a non-equilibrium plasma expanding mainly along the normal to the Cu target surface. Time-of-flight (TOF) technique was employed, through an electrostatic ion energy analyzer (IEA) placed along the target normal, in order to measure the ion energy, the ion charge state, the energy distribution and the charge state distribution. Ions had a Boltzmann energy distributions with an energy increasing with the charge state. At a laser fluence of the order of 6 × 10⁶ J/cm², the maximum ion energy was about 600 keV and the maximum charge state was about 27+.In order to investigate the implantation processes, Cu depth profiles have been performed with Rutherford backscattering spectrometry (RBS) of 1.5 MeV helium ions, Auger electron spectroscopy (AES) with 3 keV electron beam and 1 keV Ar sputtering ions in combination with scanning electron microscopy (SEM). Surface analysis results indicate that Cu ions are implanted within the first surface layers and that the ion penetration ranges are in agreement with the ion energy measured with IEA analysis.     

类Kerr介质中双模SU(1,1)相干态场与Λ型三能级原子相互作用的量子统计性质

导出了类Kerr介质中双模SU(1,1)相干态场与Λ型三能级原子相互作用系统的态函数,研究了Kerr效应对Λ型三能级原子布居概率、双模SU(1,1)相干态场的互关联函数、Cauchy-Schwartz不等式及二阶相干度的影响.结果表明:Kerr效应使原子与光场的耦合减弱,原子布居的崩塌与复苏的周期缩短;在初始光场较弱和较强两种情况下,类Kerr介质对双模SU(1,1)相干态场两模间的相关性、相关程度以及光子的聚束与反聚束效应产生的作用有明显的区别.     

我国医疗费用增长与医疗设备投入的相关性研究

近年来我国卫生总费用占GDP的比例增长很快,而在卫生费用结构上则发生政府投入下降和个人支出的上升。本文采集了大量的统计数据,采用统计相关性研究的方法,论证了医疗设备规模的不断扩大是导致医疗费用上升的主要因素之一;医疗设备的快速增长与医院维修费用投入的增长直接相关,而引起医疗设备维修大量投入的主要原因则是故障期内医疗设备的非正常闲置。本文通过对个人卫生费用的上升、医疗设备规模的扩大及其医疗设备维修投入费用增加相关性的分析,说明了在这种关系下,十分有必要研究医院医疗设备维修体系,以在卫生投入和患者权益上达到平衡。     

Tests of quantum electrodynamics using ion traps

Experiments in ion traps on the g factors for the free and the bound electron in low-Z, hydrogen-like ions have provided the most accurate tests of quantum-electrodynamics calculations. Moreover they have been used to determine new and precise values for fundamental constants. Extensions to more stringent tests using ions of higher values of the nuclear charge Z are on the way. Also other QED tests such as Lamb shifts or hyperfine structures in H-like ions using traps will be feasible in the near future. The tests in bound systems, however, will be limited by nuclear structure effects which are difficult to calculate. Assuming the QED calculations as correct, the experimental results may be used to determine nuclear contributions and thus support nuclear models. Contribution presented at the TCP06, Vancouver Island, 2006.