三类边界条件下的贝塞尔-傅里叶矩的图像分析

提出了一种基于三类边界条件下贝塞尔函数的构造矩—贝塞尔-傅里叶矩,其定义在极坐标系下,可视为一种整体正交复数矩;该矩的正交多项式有较多零点,且多数呈均匀分布.通过对26个大写字母二值图像的重构及1260幅灰度蝴蝶图像的分类实验来验证所提出矩的有效性,同时提取三类边界条件下贝塞尔-傅里叶矩的不同阶矩作为图像分析的特征值(图像描述质)来表征图像.理论分析和实验结果表明:与正交傅里叶-梅林矩和泽尼克矩相比,三类边界条件下贝塞尔-傅里叶矩更适用于图像的分析和旋转不变性的目标识别,且图像重构准确度及不变性识别准确性均更优.     

曲边六面体矢量单元的改进与应用

改进了曲边六面体矢量基函数。简要回顾了原六面体矢量单元的定义之后，介绍了新的矢量基函数的构造方法，矢量基函数间的正交性因些有所改善，并有利于处理有限元Dirichlet边界条件。结合完全匹配层，将新单元应用于三维电磁散射问题，并进行了数值计算。     

非晶态Fe-P合金结构的计算机模拟(Ⅱ) Fe_(100-x)P_x结构与成分关系

本文以计算机制作的模拟非晶态Fe_(100-x)P_x(x分别取25,20,15)合金的无规密堆模型作为初始位形,应用准动态平衡边界条件、截尾Morse势对体系进行松弛(能量极小化)计算。得到了松弛前后三种不同成分模型的体系能量、简约径向分布函数、配位数分布、角分布函数及均匀度,讨论了非晶态Fe_(100x)P_x合金结构与成分的关系。     

透平转子的空气冷却和用有限元法计算枞树形榫头温度场的研究

稳定温度场的有限元法 对于边界为f的平面物体G,根据变分原理,可以证明满足拉普拉斯方程和第三类边界条件的温度函数t(x,y)是使如下泛函取极小的函数:文献[1]指出,根据不可逆过程热力学的昂色格理论和定态最小熵产生率原理,U(t)是与该物体系统熵产生率相联系的量,而该泛函取极小即是系统定态最小熵产生率原理。同样可以证明,相应于第二类边界条件的泛函为:     

电场强度的微分

一、电场强度微分的物理意义 从数学上我们知道: 函数f(x,y)的偏微分为: 现在我们来说明函数微分的物理意义。注意到(1)式的微分是对标量函数而进行的,所以对向量场必须进行向量分解。例如电场强度E,在直角坐标系就必须分解成平行x轴的Ex和垂道x轴的Ey。然后分别微分。我们以点电荷的电场强度为例进行说明。 设一正点电荷+q位于直角坐标系的原点0,它在场点(x,y)所产生的电场强度的两个分量为Ex、Ey。Ey在y=常数的直线上的变化曲线如图1中的曲线①所示。根据(1)式有:由上式可知:△x为Ey曲线上相距△x的两场值之差。如图1中的曲线③所示。…     

也谈不规范的斯特姆-刘维本征值问题

讨论了端点有集中载荷时弹性杆的纵振动问题．比较了现有的两种解法,分析了相关本征值问题的正交性问题．     

用雅可俾函数行列式指导热力学关系

一 、引言1.在本文提出的方法中要用到: 1.雅可俾函数行列式的三个主要性质[1]。设 x=x(u,v) y=y(u,v) u=u(s, t)v=v(s, t)雅可俾函数行列式定义为J的性质如下:令 2.对化学性质没有变化的均匀系,有下面四个麦克斯韦关系[2] 二、方法和例证 1、在热力学关系中只含有体系状态参量T、p、V、S时,首先将偏微分关系写成雅可俾函数行列式的形式,然后乘以D(x,y)/D(x,y),而其中变量(x,y)对绝热过程是o,V)或…。p)对共他过程是(T,D戍iT,P｝。最后利用雅可饶函数行列式的性质和麦克斯韦莱系,即可得到所需要的热力学关系。、_、;_-。。 例如,我们要…     

基于达朗贝尔公式对一端固定一端作受迫振动的有界弦振动问题的求解

通过延拓为奇函数和恰当的函数两种方式对弦的两端点进行延拓,运用达朗贝尔公式解决了一端固定,另一端作受迫振动Asin ωt的有界弦振动的定解问题,通过计算结果表达式直接得出了描述有界弦振动运动的物理量,直观分析出弦振动的运动过程.同时对该问题进行了拓展,运用行波法解决了一端为齐次的第一类或第二类边界条件另一端为非齐次边界条件的定解问题.     

稀疏正交联合约束多通道非负矩阵分解声信号分离算法

针对复杂环境下多通道声信号分离问题,提出稀疏正交联合约束多通道非负矩阵分解声信号分离方法。首先设计基于多通道扩展坂仓斋藤(Itakura-Saito,IS)散度的稀疏正交联合约束项构造代价函数,给出信号稀疏和信号正交约束辅助函数,实现代价函数最小化求解。然后通过迭代更新规则设计,得到稀疏正交优化的多通道非负矩阵分解基矩阵和系数矩阵,讨论了稀疏正交约束对基矩阵和系数矩阵稀疏性与连续性影响。最后基于多通道信号空间特性,进行了非负矩阵分解基聚类以获得多通道非负矩阵分解声信号的分离结果。双通道音频数据与四通道声学目标分离实验数据测试表明,对音频数据,所提算法在性能指标信号失真比(SDR)上提高了0.84 dB,对于直升机声源数据,所提算法在SDR上提高了4.53 dB。     

椭圆孔光子晶体光纤的本地正交函数模型

提出了一种用于分析椭圆孔光子晶体光纤的正交函数模型.发展了一种新型超格子的构造方法，将光子晶体光纤的横向介电常数表示为两种周期性结构叠加，这两种周期性结构分别用余弦函数展开；同时将横向电场以Hermite-Gaussian函数展开.利用正交函数的性质，将全矢量波动方程转化为矩阵本征值问题，求得两偏振模式传输常数.利用此模型可以研究圆孔及椭圆孔光子晶体光纤的模式特性、色散特性、偏振特性等. 关键词： 光子晶体光纤 超格子 正交函数 本征值问题     

Integrable Nonlinear Evolution Equations on the Half-Line

 A rigorous methodology for the analysis of initial-boundary value problems on the half-line, is applied to the nonlinear §(NLS), to the sine-Gordon (sG) in laboratory coordinates, and to the Korteweg-deVries (KdV) with dominant surface tension. Decaying initial conditions as well as a smooth subset of the boundary values are given, where n=2 for the NLS and the sG and n=3 for the KdV. For the NLS and the KdV equations, the initial condition q(x,0) = q ₀ (x) as well as one and two boundary conditions are given respectively; for the sG equation the initial conditions q(x,0) = q ₀ (x), q _t (x,0) = q ₁ (x), as well as one boundary condition are given. The construction of the solution q(x,t) of any of these problems involves two separate steps: (a) Given decaying initial conditions define the spectral (scattering) functions {a(k),b(k)}. Associated with the smooth functions , define the spectral functions {A(k),B(k)}. Define the function q(x,t) in terms of the solution of a matrix Riemann-Hilbert problem formulated in the complex k-plane and uniquely defined in terms of the spectral functions {a(k),b(k),A(k),B(k)}. Under the assumption that there exist functions such that the spectral functions satisfy a certain global algebraic relation, prove that the function q(x,t) is defined for all , it satisfies the given nonlinear PDE, and furthermore that . (b) Given a subset of the functions as boundary conditions, prove that the above algebraic relation characterizes the unknown part of this set. In general this involves the solution of a nonlinear Volterra integral equation which is shown to have a global solution. For a particular class of boundary conditions, called linearizable, this nonlinear equation can be bypassed and {A(k),B(k)} can be constructed using only the algebraic manipulation of the global relation. For the NLS, the sG, and the KdV, the following particular linearizable cases are solved: , respectively, where χ is a real constant. Received: 22 October 2001 / Accepted: 22 March 2002 Published online: 22 August 2002     

Diffusion in a symmetric bistable potential: A variational approach

An approximation procedure for the solution of stochastic nonlinear equations, which was derived from a variational principle in a previous paper, is applied to the problem of a particle that diffuses in a symmetric bistable potential starting from the point of unstable equilibrium. The second moment and variance for the particle's position are calculated as functions of the timet. Good agreement is found with results recently obtained by Baibuzet al. from an approximate evaluation of a path integral expression for the probability density.     

The Paraboson Fock Space and Unitary Irreducible Representations of the Lie Superalgebra {\mathfrak{osp}(1|2n)}

It is known that the defining relations of the orthosymplectic Lie superalgebra are equivalent to the defining (triple) relations of n pairs of paraboson operators . In particular, with the usual star conditions, this implies that the “parabosons of order p” correspond to a unitary irreducible (infinite-dimensional) lowest weight representation V(p) of . Apart from the simple cases p = 1 or n = 1, these representations had never been constructed due to computational difficulties, despite their importance. In the present paper we give an explicit and elegant construction of these representations V(p), and we present explicit actions or matrix elements of the generators. The orthogonal basis vectors of V(p) are written in terms of Gelfand-Zetlin patterns, where the subalgebra of plays a crucial role. Our results also lead to character formulas for these infinite-dimensional representations. Furthermore, by considering the branching , we find explicit infinite-dimensional unitary irreducible lowest weight representations of and their characters. NIS was supported by a project from the Fund for Scientific Research – Flanders (Belgium) and by project P6/02 of the Interuniversity Attraction Poles Programme (Belgian State – Belgian Science Policy). An erratum to this article can be found at     

The Spectral Gap of the Ferromagnetic XXZ-Chain

We prove that the spectral gap of the spin- ferromagnetic XXZ-chain with HamiltonianH=–_x S^{(1)}_xS^{(1)}_{x+1}+S^{(2)}_xS^{(2)}_{x+1}+\Delta S^{(3)}_xS^{(3)}_{x+1}, is given by -1 for all 1. This is the gap in the spectrum of the infinite chainin any of its ground states, the translation invariant ones as well asthe kink ground states, which contain an interface between an up and a down region.In particular, this shows that the lowest magnon energy is not affected by the presence of a domain wall. This surprising fact is a consequence of the SU _q (2)quantum group symmetry of the model.     

Calculation of superpropagators in non-linear quantum field theories

A new method of constructing the superpropagators, i.e. the Fourier transforms of the expressions of the form is suggested. The method makes it possible to derive by use of the same technique explicit analytic expressions for the superpropagators for a wide class of field theories — from strictly local up to essentially non-local. The essence of the method is the construction of a differential equation for the superpropagator which in general is of an infinite order. By use of the boundary condition atp ²=0 we find the solution of this equation depending on one arbitrary real parameter. Simple examples are given to illustrate the method.     

Hierarchy of Poisson brackets for elements of a scattering matrix

The infinite family of Poisson brackets between the elements of a scattering matrix is calculated for the linear matrix spectral problem.     

A nonlinear instability for 3×3 systems of conservation laws

The phenomenon of nonlinear resonance provides a mechanism for the unbounded amplification of small solutions of systems of conservation laws. We construct spatially 2-periodic solutionsu ^N C ([0,t _N ] × witht _N bounded, satisfying

On Dirichlet-to-Neumann Maps, Nonlocal Interactions, and Some Applications to Fredholm Determinants

We consider Dirichlet-to-Neumann maps associated with (not necessarily self-adjoint) Schrödinger operators describing nonlocal interactions in ${L^2(\Omega; d^n x)}$ , where ${\Omega \subset \mathbb{R}^n}$ , ${n\in\mathbb{N}}$ , ${n\geq 2}$ , are open sets with a compact, nonempty boundary ${\partial\Omega}$ satisfying certain regularity conditions. As an application we describe a reduction of a certain ratio of Fredholm perturbation determinants associated with operators in ${L^2(\Omega; d^{n} x)}$ to Fredholm perturbation determinants associated with operators in ${L^2(\partial\Omega; d^{n-1} \sigma)}$ , ${n\in\mathbb{N}}$ , ${n\geq 2}$ . This leads to an extension of a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with a Schrödinger operator on the half-line ${(0,\infty)}$ , in the case of local interactions, to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation.     

Nonlinear Schrödinger equations and sharp interpolation estimates

A sharp sufficient condition for global existence is obtained for the nonlinear Schrödinger equation $$\begin{array}{*{20}c} {(NLS)} & {2i\phi _t + \Delta \phi + \left| \phi \right|^{2\sigma } \phi = 0,} & {x \in \mathbb{R}^N } & {t \in \mathbb{R}^ + } \\ \end{array} $$ in the case σ=2/N. This condition is in terms of an exact stationary solution (nonlinear ground state) of (NLS). It is derived by solving a variational problem to obtain the “best constant” for classical interpolation estimates of Nirenberg and Gagliardo.