On the Renormalization of Feynman Integrals

An arbitrary Feynman integral is considered for external momenta in the Euclidean region, the usual rotation of energy contours having been used to write the integral as an integral over Euclidean internal momenta. A compactification of the space of internal momenta is defined, and the Feynman integral is written as the integral of a current on this compact manifold. This presentation of the integral is used to give a proof of the convergence criterion for Feynman integrals, and to show that a well-defined renormalized integral may be obtained by a subtraction operation or by analytic renormalization.     

遥感相机中时间延时积分电荷耦合器件积分级数的最优选择

针对时间延时积分电荷耦合器件积分级数对成像质量的影响,提出了一种航天遥感相机中时间延时积分电荷耦合器件积分级数的最优选择方法.构造了典型成像系统的信噪比与积分级数关系模型和调制传递函数与卫星姿态角和积分级数的函数模型;以信噪比和调制传递函数的容许值为约束条件,推导出了任意条件下时间延时积分电荷耦合器件的可选积分级数区间并给出了最优的积分级数解,给出了对应的增益设置指导函数.运用仿真实验对该方法进行验证,并与传统方法进行比较,结果表明:该方法能够选取最优的积分级数,从而获得满足信噪比和调制传递函数指标的最佳成像质量;若该值不存在,依然能获取相对最佳的折中值和视觉效果;同时,本文成像效果优于传统方法.     

遥感相机中时间延时积分电荷耦合器件 积分级数的最优选择

针对时间延时积分电荷耦合器件积分级数对成像质量的影响,提出了一种航天遥感相机中时间延时积分电荷耦合器件积分级数的最优选择方法.构造了典型成像系统的信噪比与积分级数关系模型和调制传递函数与卫星姿态角和积分级数的函数模型;以信噪比和调制传递函数的容许值为约束条件,推导出了任意条件下时间延时积分电荷耦合器件的可选积分级数区间并给出了最优的积分级数解,给出了对应的增益设置指导函数.运用仿真实验对该方法进行验证,并与传统方法进行比较,结果表明:该方法能够选取最优的积分级数,从而获得满足信噪比和调制传递函数指标的最佳成像质量;若该值不存在,依然能获取相对最佳的折中值和视觉效果;同时,本文成像效果优于传统方法.     

Rubinowicz transform of the MTPO surface integrals

The surface integral of the modified theory of physical optics is reduced to a line integral by using the Rubinowicz transform for the incident scattered fields by an arbitrary aperture in a black surface. The integral theorem of Kirchhoff is applied to the scattering geometry and the diffracted fields are expressed in terms of a line integral along the contour of the diffracting edge.     

The cross-correlation integral: Its features and application to nonstationarity detection in time series

A generalization of the correlation integral, called the cross-correlation integral, is suggested. Features of the cross-correlation integral are studied, and a new attribute of a time series is defined. It is viewed as some kind of dimension and is associated with the fill rate of the attractor. It is demonstrated that the cross-correlation integral is calculated in much the same way as the wavelet transform of the density of points in the attractor. The cross-correlation integral is applied to detection of nonstationarity in time series. A comparison with statistical methods is made.     

New framework for the Feynman path integral

The well-known Fourier integral solution of the free diffusion equation in an arbitrary Euclidean space is reduced to Feynmannian integrals using the method partly contained in the formulation of the Fresnelian integral. By replacing the standard Hilbert space underlying the present mathematical formulation of the Feynman path integral by a new Hilbert space, the space of classical paths on the tangent bundle to the Euclidean space (and more general to an arbitrary Riemannian manifold) equipped with a natural inner product, we show that our Feynmannian integral is in better agreement with the qualitative features of the original Feynman path integral than the previous formulations of the integral.     

First Integrals and Integral Invariants of Relativistic Birkhoffian Systems

For a relativistic Birkhoflan system, the first integrals and the construction of integral invariants are studied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the perfect differential method. Secondly, the equations of nonsimultaneous variation of the system are established by using the relation between the simultaneous variation and the nonsimultaneous variation. Thirdly, the relation between the first integral and the integral invariant of the system is studied, and it is proved that, using a t~rst integral, we can construct an integral invarlant of the system. Finally, the relation between the relativistic Birkhoflan dynamics and the relativistic Hamilton;an dynamics is discussed, and the first integrals and the integral invariants of the relativistic Hamiltonian system are obtained. Two examples are given to illustrate the application of the results.     

广义Birkhoff系统的积分不变量

研究广义Birkhoff系统的积分不变量.给出系统存在积分不变量的条件,在此条件下导出系统的线性积分不变量、通用积分不变量和二阶绝对积分不变量.举例说明结果的应用. 关键词： 广义Birkhoff方程 线性积分不变量 通用积分不变量 二阶绝对积分不变量     

高功率光纤啁啾脉冲放大光源中的B积分受限

基于金斯堡-朗道方程模型,针对100kHz光纤啁啾脉冲放大系统中的B积分受限问题进行了理论分析,包含群速色散、增益色散、平均功率饱和和能量饱和效应及自相位调制效应。给出了典型放大器构型下脉冲可压缩性随B积分的变化关系。得到了展宽脉冲宽度为1ns条件下,亚ps压缩脉冲对系统总的B积分限值约为40rad。对短间隔脉冲串放大特性和B积分进行了理论研究,验证了在单脉冲B积分受限不变的情况下可以实现总脉冲能量倍增。     

超短脉冲在光学介质中传输的B积分特性

 从非线性薛定谔方程出发,利用分步傅里叶算法对其进行求解,数值模拟了在超短脉冲激光系统中几种光学介质中的B积分传输规律,并对其特性进行了简要分析。数值计算结果表明,初始脉冲的输入光强与光学介质的增益系数的增大会使B积分值增加。脉冲形状对B积分值有一定影响,与飞秒高斯脉冲比较,当输入为ps级的啁啾脉冲时,B积分较小。针对所选计算模型,适当的群速色散与高阶色散可以减小B积分值。这对超短脉冲放大系统的设计有参考意义。     

A solution of radiative transfer in isotropic plane-parallel atmosphere by integrating Milne equation

In this paper we solve the inversion problem of the radiative transfer process in the isotropic plane-parallel atmosphere by iterative integrations of the Milne integral equation. As a result, we obtain the scattering function in the form of a cubic polynomial in optical thickness. The author has already solved the same problem by iterative integrations of Chandrasekhar's integral equation. In the Milne integral equation, both the cosines of the viewing angles and the optical thickness are integral variables, while in Chandrasekhar's integral equation the cosines of the viewing angles are variables but the optical thickness is not. We derive several series of exponential-like functions as intermediate derivations. Their convergences are evaluated by the author's previous work in the solution of Chandrasekhar's integral equation. The truncated scattering function up to the third order in optical thickness thus obtained is identical to that obtained from Chandrasekhar's integral equation, though their apparent forms are different. Chandrasekhar pointed out that the solution of Chandrasekhar's integral equation does not have a uniqueness of solution. The Milne equation, in contrast, has been proven to have a unique solution. We discuss the uniqueness of the solution by these two methods.     

自旋为任意整数的传播子

以自旋为任意整数的自由粒子的波函数(Bargmann-Wigner方程的解)为基础，进一步研究了 自旋为任意整数的投影算符和传播子.证明了Behrends和Fronsdal所构造的投影算符是正确 的.导出了自旋为任意整数的场的一般对易规则和费恩曼传播子的一般表达式. 关键词： 整数自旋 投影算符 对易规则 费恩曼传播子     

基于积分图像的人体肢体检测算法

 为了实现视频序列图像中运动人体肢体的检测,提出了一种基于积分图像和类哈尔特征的检测方法,类哈尔特征(Haar like feature)因其固有的特点,适用于检测矩形或类矩形的图像区域,积分图像的特点是可以利用类哈尔特征快速定位人体肢体在图像中的位置。积分图像用于表示视频中的原始图像,边缘检测模板与原始视频每一帧进行卷积之后,通过累加计算可以得到该图像的积分图像,然后利用类哈尔算子,根据设定的阈值,即可以准确定位人体肢体位置。实验结果表明：该方法较背景减除法检测人体肢体准确。     

导体表面电荷不均匀分布的数值计算

用积分法分析了被屏蔽导体表面的电荷分布,提出了一种具有特殊场域的求解电场 方法,为了求解在奇异点的积分,提出了一系列解析公式,可以避免复杂的数学处理,还分析了一个具体实例的临近效应,讨论了积分法的计算精度 。     

Measures for Fermionic Integration

The formal Berezin integral for anticommuting variables is modified to a functional which can be applied directly to an infinite dimensional Grassmann algebra. Then a Gaussian measure is constructed on an extended Grassmann algebra and the functional integral is realized as integral on this measure space.     

An annular superposition integral for axisymmetric radiators

A fast integral expression for computing the nearfield pressure is derived for axisymmetric radiators. This method replaces the sum of contributions from concentric annuli with an exact double integral that converges much faster than methods that evaluate the Rayleigh-Sommerfeld integral or the generalized King integral. Expressions are derived for plane circular pistons using both continuous wave and pulsed excitations. Several commonly used apodization schemes for the surface velocity distribution are considered, including polynomial functions and a "smooth piston" function. The effect of different apodization functions on the spectral content of the wave field is explored. Quantitative error and time comparisons between the new method, the Rayleigh-Sommerfeld integral, and the generalized King integral are discussed. At all error levels considered, the annular superposition method achieves a speed-up of at least a factor of 4 relative to the point-source method and a factor of 3 relative to the generalized King integral without increasing the computational complexity.     

Contour integration on super-Riemann surfaces

Super contours are defined to be superconformal maps of real (1,1)-dimensional superspace into complex (1,1)-dimensional superspace. A method for integration along supercontours is defined in terms of a modified Berezin integral on (1,1)-dimensional real superspace. The natural transformation properties of this modified Berezin integral are inherited by the contour integral, so that the contour integral of a half form on a general super-Riemann surface is defined.     

Voiceless affricate/fricative distinction by frication duration and amplitude rise slope

Previous psychophysical studies have shown that the perceptual distinction between voiceless fricatives and affricates in consonant-vowel syllables depends primarily on frication duration, whereas amplitude rise slope was suggested as the cue in automatic classification experiments. The effects of both cues on the manner of articulation between /integral of/ and /t integral of/ were investigated. Subjects performed a forced-choice task (/integral of/ or /t integral of) in response to edited waveforms of Japanese fricatives /integral of i/, /integral of u/, and /integral of a/. We found that frication duration, onset slope, and the interaction between duration and onset slope influenced the perceptual distinction. That is, the percent of /integral of/ responses increased with an increase in frication duration (experiments 1-3). The percent of /integral of/ responses also increased with a decrease in slope steepness (experiment 3), and the relative importance between slope portions was not even but weighted at onset (experiments 1 and 2). There was an interaction between the two cues of frication duration and steepness. The relative importance of the slope cue was maximum at a frication duration of 150 ms (experiment 3). It is concluded that the frication duration and amplitude rise slope at frication onset are acoustic cues that discriminate between /integral of/ and /t integral of/, and that the two cues interact with each other.     

Path integration in conical space

Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of the conical surface embedded in Euclidean space. The path integral calculation is compatible with the Schrödinger equation modified with the Gaussian and the mean curvature.