Binary functions,degeneracy, and alternating dimaps

This paper continues the study of combinatorial properties of binary functions — that is, functions $f:2^E\to ?$ such that $f(0?)=1$, where $E$ is a finite set. Binary functions have previously been shown to admit families of transforms that generalise duality, including a trinity transform, and families of associated minor operations that generalise deletion and contraction, with both these families parameterised by the complex numbers. Binary function representations exist for graphs (via the indicator functions of their cutset spaces) and indeed arbitrary matroids (as shown by the author previously). In this paper, we characterise degenerate elements – analogues of loops and coloops – in binary functions, with respect to any set of minor operations from our complex-parameterised family. We then apply this to study the relationship between binary functions and Tutte’s alternating dimaps, which also support a trinity transform and three associated minor operations. It is shown that only the simplest alternating dimaps have binary representations of the form we consider, which seems to be the most direct type of representation. The question of whether there exist other, more sophisticated types of binary function representations for alternating dimaps is left open.     

基于虚拟相位平面的相位展开方法

在基于相位分析的三维测量系统中,为了准确地得到物体的高度,相位展开扮演着很重要的角色。传统的相位展开方法常常需要额外的投影图,而傅里叶变换轮廓术只需要采集一幅或两幅变形条纹图就可以实现对物体轮廓的测量,其方法速度快,易于实现。针对傅里叶变换轮廓术方法计算得到的截断相位分布,本文提出了一种利用截断相位与参考平面相位差值2π的整数倍数获得截断相位的正确级次,辅助相位展开的方法。当被测物体较复杂,或者相位截断次数较多时,该方法在已有参考平面相位的基础上虚拟新的相位平面,依次比较截断相位和虚拟相位,进行多次分级相位展开,结合多个展开相位结果,最终得到正确的展开相位。该方法展开速度快,展开错误不会蔓延传递。仿真和实物实验结果证明了该方法的可行性,说明该方法可用于傅里叶变换轮廓术中进行截断相位的快速展开。     

Application of ‘Operational Quadrature Methods’ in Time Domain Boundary Element Methods

The usual time domain Boundary Element Method (BEM) contains fundamentalsolutions which are convoluted with time-dependent boundary data andintegrated over the boundary surface. Here, a new approach for theevaluation of the convolution integrals, the so-called OperationalQuadrature Methods developed by Lubich, is presented. In thisformulation, the convolution integral is numerically approximated by aquadrature formula whose weights are determined using the Laplacetransform of the fundamental solution and a linear multisep method. Tostudy the behaviour of the method, the numerical convolution of afundamental solution with a unit step function is compared with theanalytical result. Then, a time domain Boundary Element formulationapplying the Operational Quadrature Methods is derived. For thisformulation only the fundamental solutions in Laplace domain arenecessary. The properties of the new formulation are studied with anumerical example.     

Fourier Transform in Bounded Domains

The functional analysis, the concept of distributionsu in the sense of Schwartz [7] andtheir extension given by Gelfand and Shilov [5]to ultradistributions u ,enables us to find by the means of the Fourier transform a secondlanguage to characterize physical behaviour. Almost any expressionwith physical meaning can be transformed, even if it isformulated in domains with complicated boundaries and evenif it is not integrable.Numerical procedures in the transformed space can bedeveloped in analogy to those well known in engineeringmechanics like the methods of Finite or BoundaryElements (FEM or BEM). Basis of the approaches presentedhere is the analytical representation of characteristicdistribution of a domain and the theorem of Parseval whichstates the invariance of energy in respect to thetransformation. In addition, the concept of thecharacteristic distribution leads to a very simplederivation of the Green-Gauss formulas fundamental for theBoundary or Finite Elements (e.g. [6]).     

Linear Dynamical Identification: An Integral Transform seen as a Complex Wavelet Transform

This paper presents a technique that allows the direct linearidentification of frequency response functions from the computation ofa weighted integral transform. This transform allows toemphasize the influence of the poles and zeros of the frequencyresponse functions its formation is based on the Cauchy--Weierstrass theorem. It isthen shown that this transform is directly linked to a complex wavelettransform. This representation with a wavelet transform provides abetter understanding of the amplification effects of the weightedintegral transform and allows the singularities analysis.     

基于非对称漂移双gamma跳-扩散过程的创新幂型期权定价模型

针对假设股价的对数收益率布朗运动在期权定价时产生的无法解释股价对数收益率的尖峰厚尾和序列相关性的缺陷,采用了Zhang提出的非对称漂移双gamma跳-扩散过程来描述资产(股价)的对数收益率运动形态(该过程是kou提出的双指数跳-扩散过程的推广),并利用Esscher风险中性变换,研究了幂型期权的定价公式.还设计了两种创新的幂型期权,在非对称漂移双gamma跳-扩散过程下给出了相应的定价公式.     

多模跟踪技术在轮式侦察车图像处理器的应用

为解决目标旋转形变、遮挡、光照变化等目标跟踪的难题,对粒子滤波和尺度不变特征变换（SIFT）算法进行了改进,结合两种算法提出了决策主导模式的多模跟踪技术。该技术采用粒子滤波预测目标位置进行粗定位,SIFT特征匹配进行精定位的方法,在解决上述难题上有很好的鲁棒性。将该技术应用于轮式侦察车图像处理器,并进行了各种实验验证,结果证明了提出算法的有效性。     

基于时间响应函数的结构阻尼识别方法比较

研究了3种基于时间响应函数的结构阻尼识别方法, 包括对数衰减法、希尔 伯特方法和小波方法. 给出了3种方法的实现算法, 分析了对密集模态的识别能力. 构造仿真算例, 采用3种方法识别了5{\%}, 10{\%}和30{\%}噪声条件下的模态阻尼. 结果表明, 小波方法比对数衰减法和希尔伯特方法具有更好的噪声鲁棒性. 采用小波方法分析了润扬大桥结构健康监测系统获得的实测数据, 识别出了润扬大桥悬索桥前6阶模态参数, 第2阶和第3阶模态频率相差仅为0.015\,Hz. 研究表明, 小波方法具备噪声条件下密集模态的识别能力, 是工程中阻尼识别的优选方法.     

Hausdorff moment problem and fractional moments: A simplified procedure

The purpose of this paper is the recovering of a probability density function with support [0, 1] from the knowledge of its sequence of moments, i.e. the classical Hausdorff moment problem. To avoid the well-known ill-conditioning, firstly the moment curve is calculated from the assigned sequence of moments; next the unknown density is approximated by Maximum Entropy (MaxEnt) technique selecting some proper points on the moment curve. Exploiting convergence in entropy, a simplified quick procedure is suggested to recover the approximate density. An application to Laplace Transform inversion is illustrated.     

基于小波与齐次Besov空间的图像分割算法

从具有全局最优解的几何活动轮廓方法出发,分别提出了两种基于齐次Besov窄间与小波变换的图像分割算法,并给出了解的存在性证明.数值求解利用小波软阈值以及分裂Bregman方法,能够有效提高计算效率.由于小波变换具有多分辨特性,对于包含较多细节信息的图像,采用新算法能够得到更好的分割效果.数值实验表明采用新算法能够获得较...