无心型曲线的规范方程及作图

在一定的条件下利用不变量对无心型曲线方程进行化简,得到两种不同形式的规范方程。本文则在相同的条件下,给出使规范方程唯一的规则,从而进一步解决了中断言的不能利用规范方程作无心型二次曲线的图形的问题。

对“湍流通用物理方程”等两篇文章的意见

本文以均匀不可压情况为例,系统地分析“湍流通用物理方程”和“湍流通用物理方程的推导及讨论”等两篇文章所提出的理论,指出“第二种平均”(“第二次平均”)的系综不存在,“湍流力假设”和“有效湍流力假设”不成立,文章采用的封闭手断也不合理,因此所推得的“湍流通用物理方程”及其一维简化,即“规范方程”均不成立;文[2]从这些方程出发,对湍流特性所作的一切分析都失去依据;文中还存在大量不应有的其他错误。

湍流通用物理方程的推导及讨论

湍流的通用方程已经获得。利用变形率张量与摄动变形位移的点积分解湍流脉动速度,并使用密度加权的侧偏系综平均方法取代Reynolds平均方法,对Navier-Stokes方程进行平均。在二阶精度上没有出现未知相关量,从而获得了具有二阶精度的封闭的湍流通用物理方程。方程中无相关量,不引入任何经验系数,无需构造任何湍流模型,即可描述任意复杂湍流场并解释湍流物理本质。方程在长时标上描述湍流平均行为,在短时标上描述相应尺度层次的湍流结构现象,从而统一了湍流的统计及结构二大学派。方程简化后得到湍流的规范方程,是混合的Burgers-Korteweg-de Vries方程,对该方程的分析给出了湍流转捩准则。文中对湍流的间歇性、拟序结构、各向异性、湍流能量逆转等现象的物理本质进行了初步讨论。

Kdv-Burgers方程的三角变换法求解

Kdv-Burgers方程(1) 其中σ和δ分别代表耗散系数和色散系数。由于方程(1)结合耗散项和色散项于一个方程,因此能说明较只有耗散项的Burgers方程和只有色散项的kdv方程更多的物理现象,引起了国内外学者的很大兴趣,它不仅作为含气泡的液体流动[1]和弹性管道中的液体流动[2]的模型方程,而且还被推荐地湍流的规范方程[3-5]。对于方程(1)的行波解,不同的作者已采用不同的方法给出研究[6-12]。本文我们进一步采用三角变换法求解方程(1)的行波解,不仅得到了已有一个孤波解,而且给出了更多的信息。

基于规范化LoG的尺度不变性兴趣点检测子

在图像匹配、目标识别、视频检索等应用领域中,当尺度发生变化的时候,现有灰度检测子的检测效果会明显下降。为了克服上述缺点,构建了一种尺度不变性检测子:迭代的Harris-Laplace检测子(Ite-HL-Det).首先在多尺度的情况下使用Harris角点检测子提取初始点;然后,在整个尺度空间内使用迭代法,根据规范化拉普拉斯方程的局部极值确定某局部结构的特征尺度,并使用Harris度量来最终确定兴趣点的空间位置;同时,比较全面的给出了特征尺度的有关定义和性质。实验结果表明,当存在尺度改变和旋转变化的时候,该检测子所提取的兴趣点邻域能较好地覆盖内容相同的局部图像结构。

三阶常系数线性齐次微分方程组新探

本文给出了三阶常系数线性齐次微分方程组可化成与之等价的三阶常系数线性齐次微分方程的充要条件及几个有益的结果,并获得了三阶常系数线性齐次微分方程组的一种简便解法.

任意大气层折射误差的实用修正方法

本文利用差分方法求解任意大气层中的射线规范方程，对单脉冲雷达定位与三基地雷达定位测速的折射误差实用地进行了修正．

粒子的相互作用、极限环和相变

从各种相互作用的规范理论出发，讨论了规范场方程的某些新的解，并引入了势，然后探讨了它们与极限环、各种奇异点的关系，最后论述了这些结果可能具有的粒子性质和相变等物理意义．

R-函数理论在梯形截面柱弹性扭转问题中的应用

将弹性扭转问题看成为泊松方程的边值问题,利用泊松方程的基本解构造了一个函数,推导出第二类Fredholm积分方程.应用R-函数理论,构建了一个规范化方程.通过寻找适当的规范化方程,来表示问题的边界,并证明积分方程核的奇异性被克服了.通过研究梯形截面弹性体的扭转问题,表明结果与有限元数值计算结果很接近,该方法具有较高的精度,为边值问题的研究和求解提供了一种新的数学方法.该方法同样可以解决位势问题,还可以用来讨论其他更为复杂的算子,并且适用于其他形状的情形.

再论二次曲面的圆截线

本文讨论二次曲面上存在圆截线的充要条件 ,若其特征根 t1≥ t2 ≥ t3 ,且 t2 ≠ 0 。

张量扩散滤波在极化SAR图像降噪中的应用

为完成对全极化SAR图像相干斑噪声的有效抑制,引入了张量扩散模型。分析并引入了规范化的张量扩散模型,并对扩散张量的设计进行了分析。结合全极化SAR图像数据的格式,对扩散方程进行了改造,提出了适用于协方差矩阵数据格式的滤波方程,并给出了算法的实施步骤。对AIRSAR数据集中的样本图像Flevoland进行了定性的、定量的实验,实验结果表明,新的算法能够有效的提高等效视数并保持图像的空间分辨率和SAR数据的极化属性。

A Secondary Operator Ordering Problem for a Charged Rigid Planar Rotator in Uniform Magnetic Field

When the motion of a particle is constrained, an excess term exists using hermitian form of Cartesian momentum pi (i = 1, 2, 3) in usual kinetic energy (1/2μ)∑p2i, and the correct kinetic energy turns out to be (1/2μ) ∑(1/ fi)pifipi, where the fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions fi is given for a charged rigid planar rotator in the uniform magnetic field.

Canonical Formalism for Lagrangians of Maximal Nonlocality

A canonical formalism for Lagrangians of maximal nonlocality is established. The method is based on the familiar Legendre transformation to a new function, which can be derived from the maximally nonlocal Lagrangian.The corresponding canonical equations are derived through the standard procedure in local theory and appear much like those local ones, though the implication of the equations is largely expanded.

Coupled-channel cavity QED model and Semi-classical solution

A semi-classical scheme is presented to solve the coupled-channel cavity QED (CQED) model. Such model exhibits remarkable characteristics as shown by numerical calculations. A relation between the swing or angular velocity of the detuning and the motion of the atoms is discussed. With the augmentation of the optical field intensity or frequency, the atoms are trapped firstly and then they move stochastically and finally chaos sets in.

New Multiple Soliton-like and Periodic Solutions for （2＋l）-Dimensional Canonical Generalized KP Equation with Variable Coefficients

In this paper, the generalized ranch function method is extended to （2＋1）-dimensianal canonical generalized KP （CGKP） equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the （2＋1）-dimensional OGKP equation with variable coetffcients.

A Test for the Local Intrinsic Lorentz Symmetry

Basing on a generalization of Wong＇s equations, the problem of motions for particles in the Lorentz gauge field configuration, which is Schwarzschild-like solution of Yang-Mills equations, is studied. The picture of interaction between particles with the Lorentz gauge field is described in an analogous manner to that between isotopic-spin-carrying particles and Yang-Mills field. By examining the effective potential and the equations of orbits for particles, it is found that the considered motions possess some qualitative features resembling to motions of particles in a centrally symmetric gravitational field.

Numerical Simulation of Antennae by Discrete Exterior Calculus

Numerical simulation of antennae is a topic in computational electromagnetism,which is concerned withthe numerical study of Maxwell equations.By discrete exterior calculus and the lattice gauge theory with coefficient R,we obtain the Bianchi identity on prism lattice.By defining an inner product of discrete differential forms,we derivethe source equation and continuity equation.Those equations compose the discrete Maxwell equations in vacuum caseon discrete manifold,which are implemented on Java development platform to simulate the Gaussian pulse radiation onantennaes.

湍流的KdV-Burgers方程模型

本文在求得KdV-Burgers方程鞍-焦异宿轨道行波解析解的基础上,证实了高歌提出的把KdV-Burgers方程作为湍流规范方程的想法是有深刻意义的。文中分析了湍流涡旋的串级散裂过程,指出:由于湍流的间隙性,这种串级散裂过程是按等比数列进行的;其次,由行波解的扰动速度场求得了湍流能谱,在双对数坐标系中,其斜率在-1.76—-1.97之间,并用Frisch的间隙湍流模型,求得它的分数维在2.09—2.72之间,从而进一步论证了湍流的间隙性。最后,以大气动力学力例,简要地分析了湍流的耗散和色散效应的物理机制。

An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications

We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix triplet. As applications, we present necessary and suficient conditions for the existence of the generalsolutions to the system of matrix equations DXA = C1, EXB = C2, F XC = C3 and the matrix equation AXD + BY E + CZF = Gover F. We give the expressions of the general solutions to the system and the matrix equation when thesolvability conditions are satisfied. Moreover, we present numerical examples to illustrate the results of thispaper. We also mention the other applications of the equivalence canonical form, for instance, for the compressionof color images.

Picard–Fuchs Equation for Glueball Superfield for the SO(N) Gauge Group

In this paper, by using the factorization equation of the N= 2 supersymmetric gauge theory, we study N= 1 theory in Argyres–Douglas points. We suppose that all monopoles become massive. We derive general Picard–Fuchs equations for glueball superfields. These equations are hypergeometric equations and have regular singular points corresponding to Argyres–Douglas points. Furthermore, we obtain the solution of these differential equations.