Adaption of Collins formula to fractional Fourier transform studied in the entangled state representation of quantum optics

Adaption of Collins diffraction formula to the fractional Fourier transform in complex form (FFT-C) is demonstrated in entangled state |η? representation of quantum optics. The additivity property of FFT-C corresponding to Collins formula has been proved by using group multiplication of the Fresnel operator and the quantum mechanical version of the Collins formula.     

Multiplication rule for the Collins diffraction formula obtained by virtue of the Fresnel operator in quantum optics theory

By using the Fresnel operator we derive a multiplication rule for the Collins diffraction formula; the inverse of Collins diffraction integration can also be conveniently derived in this way in the context of quantum optics theory.     

New relation between input and output fields based on Collins diffraction formula and the Wigner function in entangled state representation

Based on the correspondence between the Collins diffraction formula (optical Fresnel transform) and the transform matrix element of a three-parameter two-mode squeezing operator in the entangled state representation 1 Fan, H-Y and Lu, H-L. 2006. Opt. Lett., 31: 2622–2624.  [Google Scholar] we further explore the relationship between output field intensity determined by the Collins formula and the input field's probability distribution along an infinitely thin phase space strip, both in the spatial domain and the frequency domain. The entangled Wigner function is introduced for recapitulating the result.     

Thermodynamic analysis of Collins helium liquefaction cycle

The present paper gives a thermodynamic analysis of the Collins helium liquefaction cycle with two reciprocating expanders. The results of the analysis make it clear that, for a given efficiency of expanders and effectiveness of heat exchangers, there exists an optimum mass flow fraction of total helium gas mass flow rate that should be diverted through the expanders for which liquid yield is maximum and net power input is minimum. The analysis quantitatively studies the effect of expander efficiency and heat exchanger effectiveness on the performance of the liquefier. It gives final steady state temperature distribution across the cycle, which is essential data for carrying out the preliminary design of various components in the cycle.     

反相色谱法在聚合物研究中的应用

本文介绍了近年来反相色谱法在无限稀溶液和定浓条件下对聚合物热力学性质的测定以及聚合物的微观结构、表面性能等的研究现状。     

An inverse gas chromatographic study of the adsorption of alkanes on hydroxyapatite

Saturated alkanes adsorption on synthetic well-crystallized hydroxyapatite was studied by the inverse gas chromatography method, at zero coverage. Hydroxyapatite was prepared from Ca(OH)₂ and H₃PO₄ aqueous solutions by a slow titration technique. The powder was characterized by XR diffraction, surface area measurement, and chemical analysis. Adsorption of saturated alkanes was investigated in the temperature range 338–353 K, using a flame ionization detector, and nitrogen as a carrier gas. The gas/solid partition coefficients were calculated from the retention data as well as the standard thermodynamic functions of adsorption, H⁰ _d, S⁰ _a and G⁰ _a. Linear relationships between lnK and 1/T and between G⁰ _a and the number of carbon atoms in saturated alkanes were observed. The dispersive component of the surface free energy was calculated for the investigated temperature region. A possible analytical application of hydroxyapatite to n-alkanes separation is given.     

Reliability analysis incorporating exponentiated inverse Weibull distribution and inverse power law

In reliability research, electronic devices are an important part of our lives and modelling their lives is the most difficult and fascinating area. To investigate the failure functioning of electronic equipments, reliability monitoring of systems is widely used. However, it is stated in the literature that one in five electronic system collapses are a consequence of degradation and saving energy and forecasting future losses, it is necessary to summarize the data through certain versatile models of probability . In current article, a model of reliability formed on inverse power law and generalized inverse Weibull model is suggested. This current distribution presents a clearer framework to modelling the efficiency and functionality lifespan of electronic equipments. In this article, an empirical analysis is discussed related to life cycle of a surface-mounted electrolytic capacitor (SMEC). In addition, it has noticed that evaluation of suggested distribution varies from classical model of inverse Weibull and that influences average time to failure (ATTF) of the studied capacitor.     

A numerical study of single source localization algorithms for phaseless inverse scattering problems

Optimization and Engineering - Phaseless inverse scattering problems appear often in practical applications since phaseless data are relatively easier to measure than the phased data, but they are...     

A comparative study of Domain Embedding Methods for regularized solutions of inverse Stefan problems

In this paper, various Domain Embedding Methods (DEMs) for an inverse Stefan problem are presented and compared. These DEMs extend the moving boundary domain to a larger, but simple and fixed domain. The original unknown interface position is then replaced by a new unknown, which can be a boundary temperature or heat flux, or an internal heat source. In this way, the non-linear identification problem is transformed into a linear one in the enlarged domain. Using different physical quantities as the new unknown leads to different DEMs. They are analysed from various points of view (accuracy, efficiency, etc.) through two test problems, by a comparison with a common Front-Tracking Method (FTM). The first test has a smooth temperature field and the second one has some singularities. The advantage of the DEMs in solving the inverse problem and in computing the corresponding direct mapping is shown. In the direct problem, high-order accurate schemes could be obtained more easily with the DEMs than with the FTM. In the inverse problem, an iterative regularization and a Tikhonov regularization have been employed. For the FTM, the iterative regularization is not efficient—the solution oscillates when the data are noisy. As for the Tikhonov regularization, it requests special care to choose an adequate penalty term. In contrast, both the regularizations give good results with all the considered DEMs, except for the second test problem at the beginning (t=0⁺) when the value of the heat flux and the heat source tends to ∞. Slightly different regularization effects have been obtained when using different DEMs. Finally, an automatic choice of the optimal regularization parameter is also discussed, using data with different noise levels. We propose the use of the curve of the residual norm against the regularization parameter. © 1997 John Wiley & Sons, Ltd.     

方解石晶体色散方程的研究

根据Sellmeir方程的系数在Lorentz模型中的意义所表明的数量关系,将该方程简化.对实验数据作适当的组合和变量替换,将修正的Sellmeir方程展开成多项式对实验数据进行拟合.根据对误差曲线的分析以及有关系数在Lorentz模型中作用,对该系数作进一步优化,最后确定修正的Sellmeir方程系数.得到在近紫外和近红外光谱区,方解石的修正的Sellmeir方程的系数分别为别为 Ao=2.6926,Bo=0.0192,Co=0.0195,Do=0.0143;和Ae=2.1846,Be=0.0085,Ce=.0143,De=0.0023,拟合结果的误差平方和分别为1.13×10-7和1.72×10-8.本结果可在计算方解石色散特性时使用,本方法可在拟合其它材料的色散方程时使用.     

A comparative study of controlled random search algorithms with application to inverse aerofoil design

This article presents a comparative study of some versions of the controlled random search algorithm (CRSA) in global optimization problems. The basic CRSA, originally proposed by Price in 1977 and improved by Ali et al. in 1997, is taken as a starting point. Then, some new modifications are proposed to improve the efficiency and reliability of this global optimization technique. The performance of the algorithms is assessed using traditional benchmark test problems commonly invoked in the literature. This comparative study points out the key features of the modified algorithm. Finally, a comparison is also made in a practical engineering application, namely the inverse aerofoil shape design.     

Identification of physical processes and inverse problems

General procedures of parametric and structural identification are considered as are inverse problems as their methodological basis.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 6, pp. 889–897, December, 1985.     

装配尺寸式的研究

 以装配体内零件要素特征和装配关系信息量最大为目标,对装配体内的各种要素用文字进行描述;提出目标尺寸和相关尺寸概念,以装配基准为线索探索目标尺寸形成的过程,从而建立目标尺寸与相关尺寸之间关系的文字表达式——装配尺寸式,为计算机自动建立装配尺寸关系提供一条新的途径.      

An inverse problem of carbonitriding

The problem of determining diffusion coefficients of carbon and nitrogen during carbonitriding has been stated and solved.M. V. Lomonosov Moscow State University, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 63, No. 3, pp. 462–467, October, 1992.     

平面多边形Newell公式的运用与推广

Newell公式在计算机图形学中常被用于计算多边形面积和平面法向量。论文主要讨论了Newell公式的运用与推广。首先将其推广三维空间中用于计算多面体体积的公式。其次讨论了在异面多边形的情况下,Newell公式的几何意义。最后,从数值计算的角度分析了Newell公式的计算方法。     

反设计的运用及现实意义

通过对实际产品设计的案例分析,初步阐述了反设计的运用规律,及反设计作为设计方法和设计观2个层面的现实意义.而其意义的考察,进一步凸现反设计对于目前物质世界的重要性,和人文层面的涵义.     

Collins formulae in both space and frequency domains for ABCD optical systems with small deformations

Abstract

Generalized Collins formulae for arbitrary imperfect ABCD optical systems with small deformations (misalignments and/or deviations from ideal optical operations) are obtained in both the space domain and the frequency domain. These formulae can provide a unified way to analyse the performance of a practical optical system in both domains, including the ideal as its special case. Particularly, it shows that a reciprocally symmetrical ABCD system with small deformations can implement so-called almost-fractional Fourier transformation (FRT) simultaneously in both domains with the same order. Some other applications in practice are also discussed to verify the effectiveness of our proposed method.     

Precise and versatile formula for birefringent filters

In an investigation of extraordinary- (E-) ray behavior and the index of refraction for E waves in a uniaxial crystal, a precise and versatile formula for birefringent filters, based on the exact construction of the optical path difference, is set up with neither the approximation Δn = n(o) - n(e) ≤ (or n(e)), nor the ambiguity sin(θ)sin(r(ω)) = n(e). The exact construction gives the correct variation of the position and the dimension in each path, yielding the path difference while the filter is tuning. The formula is applicable not only to a filter with its optical axis parallel to the entrance surface (PAPS) but also to a filter with its axis inclined to the surface (PAIS). Also, the formula indicates that a FAIS allows laser wavelengths to be tuned over a wider range than does a FAPS. The origin of the wider range is interpreted to be the greater variation in the index for the FAIS while the filter is tuning. With the help of the formula we design a FAIS for tuning a cw Ti:sapphire laser.