Wigner functions and tomograms of the photon-depleted even and odd coherent states

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, this paper derives the Wigner functions for the photon-depleted even and odd coherent states （PDEOCSs）. Moreover, in terms of the Wigner functions with respect to the complex parameter a the nonclassical properties of the PDEOCSs are discussed. The results show that the nonclassicality for the state ｜β, m〉o （or ｜β,m〉e） is more pronounced when m is even （or odd）. According to the marginal distributions of the Wigner functions, the physical meaning of the Wigner functions is given. Further, the tomograms of the PDEOCSs are calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics.

New generating function formulae of even- and odd-Hermite polynomials obtained and applied in the context of quantum optics

By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.

The Odd Solutions of Equations Involving Euler-Like Function

φe(n) is a function similar to Euler function φ(n). We discussed and obtained all the odd solutions of the equations φe(xy) = φe(x) + 2φe(y), φe(xy) = 2φe(x) + 3φe(y) and φe(xyz) = φe(x) + φe(y) + φe(z) by using the methods and techniques of elementary number theory.

Wigner functions and tomograms of the even and odd binomial states

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, the Wigner functions of the even and odd binomial states （EOBSs） are obtained. The physical meaning of the Wigner functions for the EOBSs is given by means of their marginal distributions. Moreover, the tomograms of the EOBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.

基于两平晶三面互检的折射率均匀性测量方法

结合奇偶函数理论,提出了一种基于两平晶三面干涉测量平晶折射率均匀性的方法。该方法通过两块平晶3个表面之间的组合测量,对折射率均匀性引入的误差进行分部求解,生成4个随机波面作为初始3个表面面形和折射率均匀性误差,对其中的均匀性误差复原,结果与初始值仅相差0.6×10-6,残差与平晶表面面形的低频信息无关,仅取决于折射率均匀性本身的旋转不变项。在100 mm口径Zygo干涉仪上完成了两平晶折射率均匀性检测实验。同时通过三平晶透射法对同一块平晶的折射率均匀性进行检测,将两种方法的测量结果进行对比。结果表明两平晶方法获得的折射率均匀性结果与透射法获得的折射率均匀性波面形状相同,指标结果仅相差0.2×10-6,波面偏差峰谷值相差3 nm。分析了影响评估精度的误差项,旋转角度误差与对准误差的影响在实验精度条件下,均方根偏差均小于1 nm。实验结果表明所提出的两平晶三面互检方法能够有效地对平晶的折射率均匀性进行测量。

一种过零单边干涉图加权切趾函数对太阳观测中傅里叶变换光谱的影响分析

傅里叶变换光谱仪(FTS)因其出色的光谱分辨率而广泛用于太阳活动的观测。在使用过零单边干涉图进行光谱复原时,可能会出现频率泄漏、旁瓣效应以及对零光程差附近的采样数据重复利用,从而导致光谱线的平滑和畸变等问题。为了获得更准确的太阳光谱数据,必须对过零单边干涉图进行加权和切趾操作。对此,文章采用了一种奇次多项式非对称加权切趾函数来处理过零单边干涉图,并探讨了使用不同的切趾函数构建非对称加权切趾函数进行光谱恢复的效果。模拟数据实验的结果表明采用奇次多项式非对称加权切趾函数可以有效地恢复光谱。此外,与Griffiths、相里斌以及SP.Davis提出的加权切趾方法相比,文章中提出的方法表现出较小的误差。最后,将所提出的方法应用于Bruker IFS-125HR FTS采集的干涉图数据,与其他切趾方法相比,使用文中提出的方法可以有效地恢复光谱。

Convergence Phenomenon with Fourier Series of tg(x2)and Alike

The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .

DHL序列在奇特征域上的迹表示和线性复杂度

将DHL(Ding-Helleseth-Lam)序列看成是特征为奇素数的有限域Fq上的序列,利用经典四阶分圆的性质和迹函数基本理论,确定了DHL序列的Mattson-Solomon多项式,得到该序列在奇特征域上的迹函数表达式。在此基础上给出了计算该序列在Fq上线性复杂度的一般公式。

有关奇亏完全数的一些刻画

为探讨具有5个相异素因数的奇亏完全数的存在性问题,通过奇亏完全数的定义以及初等方法研究了具有5个相异素因数的奇正整数n是否是奇亏完全数的问题,给出3类具有5个相异素因数的奇正整数n不是奇亏完全数的几个结论.

Accelerated proportional degradation hazards-odds model in accelerated degradation test

An accelerated proportional degradation hazards-odds model is proposed. It is a non-parametric model and thus has path- free and distribution-free properties, avoiding the errors caused by faulty assumptions of degradation paths or distribution of degra- dation measurements. It is established based on a link function which combines the degradation cumulative hazard rate function and the degradation odds function through a transformation pa- rameter, and this makes the accelerated proportional degradation hazards model and the accelerated proportional degradation odds model special cases of it. Hypothesis tests are discussed, and the proposed model is applicable when some model assumptions are satisfied. This model is utilized to estimate the reliability of minia- ture bulbs under low stress levels based on the degradation data obtained under high stress levels to validate the effectiveness of this model.

The Odd Generalized Exponential Gompertz Distribution

In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution. We obtained some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher’s information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.

Factors Related to Functional Capacity and Quality of Life for Elderly People in a Middle-Sized City of São Paulo, Brazil

Introduction: It is a fact that the elderly population has been increasing all around the world and also in Brazil. This has been a challenge for governments and managers in the development of public policies to promote healthy and quality aging. And one of the conditions for healthy aging is to assess the functional capacity and quality of life of elderly people. Objective: The aim of the present study was to evaluate the factors that influence the loss of functional capacity and the worsening of the quality of life of a representative sample of elderly people from a medium-sized city in the inner of São Paulo State, Brazil. Methodology: Questionnaires about activities of daily living (ADL), instrumental activities of daily living (IADL), Flanagan quality of life scale (FQOLS), sociodemographic and morbidities aspects were applied to the elderly people. In order to assess associated factors to functional capacity and quality of life, chi-square tests and logistic regression models were fitted including variables: gender, age group, marital status, income, education level, body mass index, abdominal circumference and some morbidities reported by the elderly people. The level of significance adopted for the statistical tests was 5%. Results: Elderly with age over 75 years old and not married had more risk to be dependent on ADL, while elderly with more than 75 years old, not married, income below one minimal wage, cardiovascular disease and be diabetic had more risk to be dependent by IADL. Already, people with excess of weight had smallest risk to be dependent by IADL, paradoxically. The elderly not married and with an income below a minimum wage had the worst quality of life. Conclusions: Population aging in Brazil is an evident factor, so it is hoped that this study will contribute to the greatest diligence on the issues of the elderly and related social problems.

Quasiprobability distributions of new kinds of even and odd nonlinear coherent states

Using a numerical computational method, quasiprobability distributions of new kinds of even and odd nonlinear coherent states （EONLCS） are investigated. The results show that the distributions of the new even nonlinear coherent states （NLCS） are distinct from those of the new odd NLCS and imply that the new EONLCS always exhibit some different nonclassical effects. Finally, with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics, the tomograms of the new EONLCS are calculated. This is a new way of obtaining the tomogram function.

OR法在DIF检验中的应用——以英语学业能力测验为例

本文将比值比方法(odds ratios method,OR)这一DIF检验方法应用到某英语测验的DIF检验中,介绍OR法进行DIF检验的完整流程,并将其检验结果与应用较为广泛的Wald χ^(2)检验和似然比检验(likelihood ratio test,LRT)的检验结果进行比较,以进一步验证OR法在实证研究中的适用性。研究结果显示,OR法与LRT法结果差异较小且OR法步骤更简便,说明OR法与LRT法在DIF检验中的表现相似,LRT法适用于实证研究中,因此OR法同样适用于实证研究的DIF检验。

采用奇偶函数法的平面面形绝对测量技术仿真分析

随着现代工业和科学技术的飞速发展,特别是近代大规模集成电路技术的不断提高,对系统精度的要求日益提高。在光刻系统中,越来越短的特征尺寸要求我们使用更高精度的光刻物镜。在这之前我们需要更高精度的检测技术来满足加工及系统集成的需要。高精度移相干涉仪的测量结果包含了待测面和参考面的误差,移相干涉测量法的测量精度受限于参考面的精度。绝对测量方法通过移除参考面的误差,从而达到提高测量精度的目的。回顾了光学平面面形绝对测量方法,重点描述了基于奇偶函数的绝对测量方法。分析了旋转角度误差对测量结果的影响,通过旋转更小的角度求出了高阶面形拟合分量,给出了求高阶面形拟合分量的通项公式。

基于奇偶函数法的绝对检测实验研究

针对平面干涉检测技术的检测精度受限于参考面面形精度的问题,提出使用基于奇偶函数的高精度绝对检测方法消除干涉系统中参考面面形误差的影响。对旋转角度误差与旋转偏心误差对绝对检测方法测量精度的影响进行了仿真分析。利用商用菲索干涉仪,设计和分析了绝对检测精度实验及重复性实验。仿真结果显示:旋转角度误差在达到0.13°时,测量误差PV值为0.000 1λ;旋转偏心误差达到3pixel时,测量误差PV值为0.005λ。实验结果显示:测得实际样品的绝对检测精度PV_(10)值为0.041 5λ,RMS值为0.008 7λ,小于常规干涉检测所得结果;对同一平面两次独立的绝对检测结果进行点对点作差处理,从而获得残差图,其残差图PV_(10)值为0.004λRMS值为0.000 5λ。实验结果表明了该方法的高重复性和有效性。

共患对立违抗性障碍的注意缺陷多动障碍儿童的认知特点研究

目的 :探讨共患对立违抗性障碍 (ODD)的注意缺陷多动障碍 (ADHD)儿童的认知功能特点。方法 :以单纯ADHD +ODD、单纯ADHD和正常儿童各 3 6例 (性别、年龄与ADHD亚型组间匹配 )为研究对象 ,采用龚耀先修订的韦氏儿童智力量表、韦氏记忆量表、数字划消、Stroop测验和瑞文标准推理测验对其智力、记忆力、注意力水平及执行功能进行评定。结果 :两病例组的常识、类同、译码、言语智商、操作智商、全量表智商、A因子、C因子、经历定向、心智、再生、触觉、长时记忆、短时记忆、记忆商、瑞文标准推理测验标准分、Stroop测验A完成时间、C完成时间和总完成时间的测验成绩与正常对照组的差异具有显著性 ,两病例组间差异无显著性 ;正常组数字划消测验总分有显著高于两病例组 (F =2 5 2 1,P =0 0 93 )及平均失误率显著低于两病例组的趋势 (χ2 =5 15 0 ,P =0 0 76) ;ADHD组和正常对照组在算术、数字广度、积木、B因子、Stroop测验B完成时间和D完成时间上的差异具有显著性 ;ADHD +ODD组的瑞文标准推理测验标准分有优于ADHD组的趋势 (Z =-1 674,P =0 0 94)。结论 :伴或不伴ODD的ADHD儿童有着相似的认知模式 ,如扩大样本量 ,可能发现共患病组在某些认知功能上与纯ADHD组的差异。

连续系统单位冲激响应时域求解方法的研究

提出了连续系统单位冲激响应的3种时域求解方法:奇异函数平衡法、等效初始条件法和线性分析法。通过比较各自的特点,有助于全面掌握单位冲激响应时域求解方法。

定积分计算中的若干技巧

在微积分基本定理——计算定积分的基本公式——牛顿-莱布尼兹公式和计算定积分的2个常用积分公式:分部积分公式、换元积分公式基础之上,总结归纳了对具有某种性质的被积函数在某些特殊区间上的定积分的计算方法,以及在定积分的计算中常常被忽略的技巧。提出了在定积分计算中可以充分地利用被积函数的奇偶性、周期性、积分区间的对称性,以及定积分的几何意义(平面图形所围区域的面积)。也可以利用一些已经被证明的相关结论来计算定积分。这些方法的使用可以使定积分的计算量大大减少,从而提高运算效率,减少计算时间。

对称性在三重积分计算中的应用

将空间区域的对称性应用于三重积分的计算之中 ,归纳出了利用对称性计算三重积分的方法。