From finitary to infinitary second‐order logic

A back and forth condition on interpretations for those second‐order languages without functional variables whose non‐logical vocabulary is finite and excludes functional constants is presented. It is shown that this condition is necessary and sufficient for the interpretations to be equivalent in the language. When applied to second‐order languages with an infinite non‐logical vocabulary, excluding functional constants, the back and forth condition is sufficient but not necessary. It is shown that there is a class of infinitary second‐order languages whose non‐logical vocabulary is infinite for which the back and forth condition is both necessary and sufficient. It is also shown that some applications of the back and forth construction for second‐order languages can be extended to the infinitary second‐order languages. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

利用光子统计概率测量单分子光子源的信号背景比

理论上研究了基于Hanbury Brown Twiss 探测方式，利用单光子和双光子统计概率P RS(1),PRS(2),直接测量单分子光子源的信号背景比.在研究过程中同时考 虑到单分子布居于暂稳态和探测器量子效率对测量结果的影响.在满足PRS(1)2 PRS(2)-3PRS(2)的条件时，研究给出了一种有效测量信号背景比的方 法SBR=P2RS(1)/2PRS(2).另外，分析讨论了Mandel参数Q 与信号背景比之间的关系. 关键词： 单分子光子源 信号背景比 光子统计 暂稳态 Mandel参数     

Molecular field theory for nematic liquid crystal film with finite layers

The nematic liquid crystal film composed of n molecular layers is studied based upon a spatially anisotropic pair potential, which reproduces approximately the elastic free energy density. On condition that the system has perfect nematic order, as in the Lebwohl—Lasher model, the director in the film is isotropic. The effect of the temperature is investigated by means of molecular field theory. Some new results are obtained. Firstly, symmetry breaking takes place when taking account of the temperature, and the state with the director along the normal of the film has the lowest free energy. Secondly, the N—I phase transition temperature increases as an effect of finite sizes instead of decreasing as in the Lebwohl—Lasher model. Thirdly, the nematic order is induced in the layers near the surface in the isotropic phase.     

Precision of neural timing: The small ? limit

We explore the precision of neural timing in a model neural system with n identical input neurons whose firing time in response to stimulation is chosen from a density f. These input neurons stimulate a target cell which fires when it receives m hits within ? msec. We prove that the density of the firing time of the target cell converges as ?→0 to the input density f raised to the mth and normalized. We give conditions for convergence of the density in L¹, pointwise, and uniformly as well as conditions for the convergence of the standard deviations.     

Liapunov-type inequality for delay-differential equations of third order

A Liapunov-type inequality for a class of third order delay-differential equations is derived.     

Order Determination for Multivariate Autoregressive Processes Using Resampling Methods

LetX₁, …, X_nbe observations from a multivariate AR(p) model with unknown orderp. A resampling procedure is proposed for estimating the orderp. The classical criteria, such as AIC and BIC, estimate the orderpas the minimizer of the function[formula]wherenis the sample size,kis the order of the fitted model, Σ²_kis an estimate of the white noise covariance matrix, andC_nis a sequence of specified constants (for AIC,C_n=2m²/n, for Hannan and Quinn's modification of BIC,C_n=2m²(ln ln n)/n, wheremis the dimension of the data vector). A resampling scheme is proposed to estimate an improved penalty factorC_n. Conditional on the data, this procedure produces a consistent estimate ofp. Simulation results support the effectiveness of this procedure when compared with some of the traditional order selection criteria. Comments are also made on the use of Yule–Walker as opposed to conditional least squares estimations for order selection.     

Magnetic susceptibility, heat capacity, and optical conductivity of LiPc and LiPcI

The magnetic susceptibility, using dc and electron spin resonance (ESR) methods, the specific heat, and the infrared properties of the one-dimensional molecular semiconductors lithium phthalocyanine (LiPc) and the iodinated compound LiPcI have been investigated for temperatures K. LiPc has a half-filled conduction band and is expected to be an organic metal. However, due to the strong Coulomb repulsion the system is a one-dimensional Mott-Hubbard insulator with a Hubbard gap of 0.75 eV as inferred from optical measurements. The localized electrons along the molecular stacks behave like a S = 1/2 antiferromagnetic spin chain. The spin susceptibility, as determined by ESR experiments, and the magnetic contribution to the heat capacity show a Bonner-Fisher type of behavior with an exchange constant K. LiPcI is an intrinsic narrow-gap semiconductor with an optical gap of 0.43 eV. In ESR experiments it is silent, indicating that all the unpaired electrons have been removed from the macrocycle via doping with iodine. Received: 16 June 1998 / Accepted: 14 July 1998     

OSCILLATION OF SECOND ORDER NONLINEAR IMPULSIVE DIFFERENCE EQUATION

Sufficient conditions to guarantee all solutions to be oscillatory of a second order nonlinear impulsive difference equation are obtained by using Riccati transformation.     

1996～2000年《武汉大学学报(自然科学版)》引文分析

以1996-2000年《武汉大学学报（自然科学版）》上发表的917篇科技论文为统计样本，据义献计量学的方法对其引文进行了统计分析．结果表明：《武汉大学学报（自然科学版）》篇均引文节为7．83，引文主要类型为期刊。占76．6％。外文文献占引文总数的66．77％，最大中文引文年限为2年，半哀期为7年，衰减系数为31．30％．最大外义引文年限为3年，半哀期为10年，哀减系数为17．08％．刊载论文的总被引量和总影响因子在逐年增加。     

具有“弱积分小”系数的二阶椭圆型偏微分方程解的振动性质

本文考虑二阶非线性椭圆型偏微分方程解的振动性质，得到了在具有“弱积分小”系数条件下，所有解均振动的充分准则，这些结果在很大程度上改进和推广了具有“积分小”系数的二阶常微分方程的振动结果．