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1.
G.E. Farr 《Discrete Mathematics》2019,342(5):1510-1519
This paper continues the study of combinatorial properties of binary functions — that is, functions such that , where 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. 相似文献
2.
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。 相似文献
3.
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. 相似文献
4.
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]). 相似文献
5.
6.
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. 相似文献
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8.
The classical Discrete Fourier Transform (DFT) satisfies a duality property that transforms a discrete time signal to the frequency domain and back to the original domain. In doing so, the original signal is reversed to within a multiplicative factor, namely the dimension of the transformation matrix. In this paper, we prove that the DFT based on Simpson's method satisfies a similar property and illustrate its effect on a real discrete signal. The duality property is particularly useful in determining the components of the transformation matrix as well as components of its positive integral powers. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
9.
10.
多模跟踪技术在轮式侦察车图像处理器的应用 总被引:1,自引:0,他引:1
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。 相似文献