量子光学中新的广义P-表示

本文利用谐振子产生算符的围道积分δ函数形式的本征态和Glanber相干态所构造的双重围道积分型完备性条件,建立了新的广义P-表示,其特点是当密度矩阵为正规乘积时,这种表示极易导出,而且即使当Glauber P-表示是奇异函数,新的广义P-表示仍为好函数。     

含时弱耦合玻色气体的时间演化及准粒子表象

本文用不变量理论精确求解了弱耦合玻色气体含时SchrSdinger方程并研究了其时间演化问题．由于含时系统的Bogoliubov变换会导致弱耦合玻色气体准粒子表象完备基矢组存在无法自定的含时相位因子，本文通过计算玻色气体微扰前粒子数表象与准粒子表象间的变换系数，获得了弱耦合玻色气体准粒子表象的完备基矢组从而解决了这一困难．     

双模场中Susskind-Glogower相算符的对偶本征矢

找到了双模场中Susskind-Glogower相算符eiφ态矢|(S),q〉的对偶本征矢|(S),q〉*,运用围道积分证明了|(S),q〉*是e-iφ和光子数差算符的共同本征矢.研究了|(S),q〉*的性质,结果是|(S),q〉*及其对偶〈(S),q |构成围道积分形式的完备性,给出了双模场的相态表象.     

从几何角度看指数形式的傅里叶级数

本文利用正交向量,从几何视角研究周期序列的分解和表示。通过内积运算,推导离散傅里叶级数公式。与传统教学方法相比,本文提出的授课方法避免了对完备正交函数集和最小均方误差准则下线性逼近的分析,使学生更为直观地理解周期序列的分解方法和指数形式的傅立叶级数的含义。     

非圆孔径离散采样点正交多项式波前拟合

Zernike多项式拟合是一种在光学领域中广泛应用的分析技术.由于现代光学工程中采集数据的离散性和非圆孔径系统的大量使用,Zernike多项式拟合不能完全满足分析需要.提出了一种基于Zernike多项式的非圆孔径离散采样点的正交多项式.通过矩阵的QR分解方法得到在离散采样点上的正交多项式基底.分别使用Zernike多项式和正交多项式对150 mm90 mm的矩形光栅反射波前进行拟合,结果表明两种方法残差波前的PV和RMS值分别相差0.013波长和小于0.001波长.对比不同项数拟合的正交多项式和Zernike多项式系数表明,正交多项式系数之间彼此独立,并由正交多项式系数计算得到了对应的Seidel像差.正交多项式各项系数可以逐项求解,该方法可以显著提高求解速度.     

三维非谐势阱中BEC混沌动力学研究

玻色一爱园斯坦凝聚（BEC）是一种新的物质形态,一个宏观量子系统。本文在平均场理论和双模近似的框架下,推导出研究玻色一爱因斯坦凝聚体动力学行为及其性质的数学模型Gross—Pitaevskii方程,用数值方法通过Fortran语言和Madab程序模拟研究了该系统基态波函数和化学势随非线性项的变化,并对其混沌特征和吸引子等非线性动力学参数做了分析,并从模拟数据发现了在临界值处直接由周期态进入混沌态,没有经历准周期行为,而且状态随初始条件的变化而变化,从瞬态混沌到定态混沌经过了一系列的分岔的现象。     

基于Karhunen-Loeve变换的正交椭圆球面波脉冲波形设计

针对正交椭圆球面波函数(PSWF)脉冲硬件实现复杂度高和难以实时产生的问题,通过对PSWF脉冲求解和正交化两个过程的优化整合,该文提出了一种基于Karhunen-Loeve变换的正交PSWF脉冲波形设计方法。该方法首先将PSWF脉冲表示为Legendre多项式加权求和的形式,通过对原脉冲互相关矩阵进行Karhunen-Loeve变换,得到正交系数矩阵,从而实现PSWF脉冲的正交化。以此为基础,设计了一种高效快捷的正交PSWF脉冲实现方案,建立了正交PSWF脉冲与Legendre多项式系数向量的对应关系,能够通过改变特征多项式的系数来快速设计正交PSWF脉冲,同时具有实时性好和实现复杂度低的优点,为正交PSWF脉冲的工程化实现提供了一种高效快捷的新方案。     

基于矢量波函数空间算子理论的波导系统有限元分析

该文介绍了一种能够消除非物理模的波导系统的有限元分析方法,从矢量波函数空间的偏微分算子理论出发,推导出具有简洁而自洽数学形式的完备的电磁波基本方程组,将电场矢量用两个标量函数表示,并用有限元法对这两个标量函数进行数值求解,从而得到了波导系统的有关参数,文中以加载膜片波导和E面矩形波导阶梯为例说明了这一分析及计算过程。     

非对称单脊波导的特性计算

从矢量波函数空间的偏微分算子理论出发,给出完备的旋量波函数空间的本征函数系及电磁波基本方程组,由此推导出数学形式简洁的并矢格林函数及基于旋量波算子空间本征函数系的电磁场量,在脊波导的耦合边界上模式匹配,推导出计算公式,给出了两个分析脊波导的实例,得到主模和第一个高阶模的截止频率,非对称脊波导的电中心线偏移量.     

Bessel-Legendre不等式在时滞系统稳定性分析中的新结果

本文主要研究了时变时滞线性系统的时滞相关稳定性问题。首先,本文基于Bessel-Legendre积分不等式推导出三阶Bessel-Legendre积分不等式的一般形式,它与Wirtinger-based积分不等式和Jensen不等式相比,能够让系统产生更少的保守性;其次,本文在构建Lyapunov-Krasovskii泛函时,充分结合了二阶与三阶Bessel-Legendre不等式一般形式的所有特征,量体裁衣地构造出一个含增广项的Lyapunov-Krasovskii泛函;再次,为了让泛函具有更精确的下界,本文对Lyapunov-Krasovskii泛函中的部分项进行整体正定处理,以至于放松了正定条件;最后,一个新的稳定判据以线性矩阵不等式的形式被推导出来,并通过数值实例仿真来表明本文方法的有效性与优越性。     

Mathematical representation of 2D image boundary contour using fractional implicit polynomial

Implicit polynomial (IP) fitting is an effective method to quickly represent two-dimensional (2D) image boundary contour in the form of mathematical function. Under the same maximum degree, the fractional implicit polynomial (FIP) can express more curve details than IP and has obvious advantages for the representation of complex boundary contours. In existing studies, algebraic distance is mainly used as the fitting objective of the polynomial. Although the time cost is reduced, there are problems of low fitting accuracy and spurious zero set. In this paper, we propose a two-stage neural network with differentiable geometric distance, which uses FIP to achieve mathematical representation, called TSEncoder. In the first stage, the continuity constraint is used to obtain a rough outline of the fitting target. In the second stage, differentiable geometric distance is gradually added to fine-tune the polynomial coefficients to obtain a contour representation with higher accuracy. Experimental results show that TSEncoder can achieve mathematical representation of 2D image boundary contour with high accuracy.     

Fourier transforms in propagation and scattering problems

Three-dimensional Fourier transforms are applied to electromagnetic wave propagation problems. After obtaining functions in transform space, inversion and contour integration yield a plane wave integral representation.     

Construction of biological surface models from cross-sections imageprocessing

An approach improving on existing techniques is presented for blending cross-sections of biological objects to produce a polynomial surface model. As intermediate steps to the final surface skinning, representative data points on the cross-sections are selected for defining piecewise cubic B-splines providing an immediate reduction in storage and computational requirements for the contour representation of the objects. A mesh of quadrilateral patches is subsequently formed over adjacent cross-sections using bicubic B-spline surfaces which exhibit second parametric derivative continuity. The surface model provides a complete and robust representation with significant data reduction. The resulting algorithm is demonstrated using bone data for a human hand     

Closed form and infinite series solutions for the MGF of a dual-diversity selection combiner output in bivariate Nakagami fading

Using a circular contour integral representation for the generalized Marcum-Q function, Q/sub m/(a,b), we derive a new closed-form formula for the moment generating function (MGF) of the output signal power of a dual-diversity selection combiner (SC) in bivariate (correlated) Nakagami-m fading with positive integer fading severity index. This result involves only elementary functions and holds for any value of the ratio a/b in Q/sub m/(a,b). As an aside, we show that previous integral representations for Q/sub m/(a,b) can be obtained from a contour integral and also derive a new, single finite-range integral representation for Q/sub m/(a,b). A new infinite series expression for the MGF with arbitrary m is also derived. These MGFs can be readily used to unify the evaluation of average error performance of the dual-branch SC for coherent, differentially coherent, and noncoherent communications systems.     

Vector quantization of pitch information in Mandarin speech

A method of quantizing the shape of pitch contour segments of Mandarin speech by using orthogonal polynomial representation and vector quantization techniques is proposed. Only a very limited number of representative pitch contour patterns of words can be found in Mandarin conversation; therefore, pitch information can be represented by the shape and the length of the pitch contour segment word by word instead of frame by frame. An average bit rate of 0.78 b/frame (34.67 b/s) for voiced sounds was achieved. The method is a variable-rate coding scheme with an average delay of 317 ms     

Computer Analysis of Short-Boundary Planar Circuits

A method of computer analysis of planar (two-dimensional) circuits having an arbitrarily shaped short boundary is proposed. The proposed method is based upon the contour integral representation of the two-dimensional wave equation. Results of the computer analyses for simple circuits are compared with analytical solutions to show the validlty and accuracy of the proposed method. Some examples of analyses of practical circuits are also presented.     

Analytical simplification of the 2-D method of moments impedance integral

The elements of the two-dimensional (2-D), method of moments (MoM) impedance matrix are analytically reduced by way of an integral transform. The resulting impedance expression is a single integral with an analytic integrand for nearly arbitary shape and weight function sets. The reduced expression requires fewer computations, thereby reducing the matrix fill time. This moments via integral transform method (MITM) is based on an integral representation of the Green's function (Hankel function) and utilizes a special integral transform. The method is developed for 2-D perfectly electrically conducting bodies subjected to a transverse magnetic field. A comparison between brute force and MITM is presented for polynomial shape and weight functions.     

Orthogonal functionals of the Poisson process

In analogy to the orthogonal functionals of the Brownian-motion process developed by Wiener, ltô, and others, a theory of the orthogonal functionals of the Poisson process is presented making use of the concept of multivariate orthogonal polynomials. Following a brief discussion of Charlier polynomials of a single variable, multivariate Charlier polynomials are introduced. An explicit representation as well as an orthogonality property are given. A multiple stochastic integral of a multivariate function with respect to the Poisson process, called the multiple Poisson-Wiener integral, is defined using the multivariate Charlier polynomials. A multiple Poisson-Wiener integral, which gives a polynomial functional of the Poisson process, is orthogonal to any other of different degree. Several explicit forms are given for the sake of application. It is shown that any nonlinear functional of the Poisson process with finite variance can be developed in terms of these orthogonal functionals, corresponding to the Cameron-Martin theorem in the case of the Brownian-motion process. Finally, some possible applications to nonlinear problems associated with the Poisson process are briefly discussed.     

Solutions of the damped oscillator Fokker-Planck equation

The quantum theory of damping is presented and illustrated by means of a driven damped harmonic oscillator. The theory is formulated in the coherent state representation which illustrates very vividly the nearly classical nature of the problem. In this representation the reduced system density operator equation becomes a Fokker-Planck equation. Green's function solutions are found for the damped oscillator in closed form and as an eigenfunction expansion. In addition, a quantum regression theorem due to Lax is derived in the coherent state representation. The theorem allows two-time averages to be computed from one-time averages.     

A hybrid formulation for the probe-to-patch attachment-mode currentfor rectangular microstrip antennas

We present a hybrid representation for the attachment-mode current existing on the surface of a coaxially fed rectangular microstrip patch antenna. The hybrid representation consists of a one- or two-term residue and an eigenfunction series which gives the attachment-mode current at all points on the patch surface, including the probe-to-patch junction. It is numerically demonstrated that the residue and eigenfunction series blend smoothly in the close vicinity of the Stokes region which includes the probe-to-patch junction. The Stokes region is a very narrow region over which the attachment-mode current changes rapidly. The residue and eigenfunction series are used outside and within this Stokes region, respectively. This hybrid representation can be used in either spectral- or space-domain techniques for a full-wave solution to the microstrip antenna problem. The residue series is obtained by using an equivalent contour integral representation of the infinite eigenfunction series, which subsequently reduces to the Watson transform under the assumption of a slightly lossy substrate. At or near the Stokes regions the residue series is inadequate, as it cannot model the rapidly varying junction currents there. Examination of the residue series shows that the attachment mode is a superposition of exponentially attenuated, leaky, surface-traveling modes. This hybrid representation is expected to provide the optimum trade-off between speed and accuracy for computations involving electrically large finite arrays