A Comparative analysis of Green’s functions of 1D matching equations for motion synthesis

When filtering an input image, the Green’s functions of matching equations are capable of inducing a broad class of motions, a property that has led to their use in several computer graphics and computer vision applications. In all such applications, the Green’s functions of second-order differential equations have been considered, even though no justification has been given for their preference over simpler, first-order equations. Here we present a study of first-order one-dimensional matching equations, both in the uniform and in the affine motion models. Comparing their Green’s functions with those of the corresponding second-order cases, we find evidence for the latter’s superiority in motion synthesis. We also propose and discuss a general discretization scheme for Green’s functions of one-dimensional matching equations, showing that the affine motion model is particularly sensitive to the sampling frequency. In this case, we advocate the use of area sampling, for allowing realistic motion simulations.     

A semi-local convergence theorem for a robust revised Newton’s method

It is well known that Newton’s iteration will abort due to the overflow if the derivative of the function at an iterate is singular or almost singular. In this paper, we study a robust revised Newton’s method for solving nonlinear equations, which can be carried out with a starting point with a degenerate derivative at an iterative step. It is proved that the method is convergent under the conditions of the Newton–Kantorovich theorem, which implies a larger convergence domain of the method. We also show that our method inherits the fast convergence of Newton’s method. Numerical experiments are performed to show the robustness of the proposed method in comparison with the standard Newton’s method.     

Efficient approach and application of the Green’s functions in spatial domain in multilayered media

Based on the dipole source method, all components of the Green＇s functions in spectral domain are restructured concisely by four basis functions, and in terms of the two-level discrete complex image method （DCIM） with the high order Sommerfeld identities, an efficient algorithm for closed-form Green＇s functions in spatial domain in multilayered media is presented. This new work enjoys the advantages of the surface wave pole extraction directly carried out by the generalized integral path without troubles of that all components of Green＇s function in spectral domain should be reformed respectively in transmission line network analogy, and then the Green＇s functions for mixed-potential integral equation （MPIE） analysis in both near-field and far-field in multilayered media are obtained. In addition, the curl operator for coupled field in MPIE is avoided conveniently. It is especially applicable and useful to characterize the electromagnetic scattering by, and radiation in the presence of, the electrically large 3-D objects in multilayered media. The numerical results of the S-parameters of a microstrip periodic bandgap （PBG） filter, the radar cross section （RCS） of a large microstrip antenna array, the characteristics of scattering, and radiation from the three-dimensional （3-D） targets in multilayered media are obtained, to demonstrate better effectiveness and accuracy of this technique.     

A boundary integral method applied to plates of arbitrary plan form

An integral equation method for the solution of thin elastic plates of arbitrary plan form has been presented. The method involves embedding the real plate in a fictitious plate for which the Green's function is known. An unknown load vector is then introduced on the boundary of the real plate (line load and line normal moment). The deflection field due to both known transverse and unknown boundary loads can then be found everywhere by superposition. Satisfaction of the boundary conditions on the real plate results in a vector integral equation in the unknown boundary vector.In concept, any consistent set of boundary conditions will yield a solution. Practically, boundary conditions requiring higher derivatives of the deflection are both very cumbersome and yield singularities in the integral equations which cause numerical difficulties. For these reasons only clamped boundary conditions are treated numerically in the present paper.For interior bending moments and deflections (greater than distances of the order of one boundary subdivision from the boundary) the method is both highly accurate and inexpensive. Errors right on the boundary, e.g. the clamping moment in the clamped boundary condition case, can be appreciable, however. While this can be improved by a more sophisticated treatment of the unknown boundary vector in the numerical solution (increased expense) it is shown in the paper that a simple boundary extrapolation procedure gives excellent accuracy there.     

Accurate evaluation of Green’s functions in a layered medium by SDP-FLAM

Based on local Taylor expansions on the complex plane, a method for fast locating all modes (FLAM) of spectral-domain Green’s Functions in a planar layered medium is developed in this paper. SDP-FLAM, a combination of FLAM with the steepest descent path algorithm (SDP), is employed to accurately evaluate the spatial-domain Green’s functions in a layered medium. According to the theory of complex analysis, the relationship among the poles, branch points and Riemann sheets is also analyzed rigorously. To inverse the Green’s functions from spectral to spatial domain, SDP-FLAM method and discrete complex image method (DCIM) are applied to the non-near field region and the near filed region, respectively. The significant advantage of SDP-FLAM lies in its capability of calculating Green’s functions in a layered medium of moderate thickness with loss or without loss. Some numerical examples are presented to validate SDP-FLAM method. Supported by the National Natural Science Foundation of China (Grant No. 60621002), and the State Key Development Program for Basic Research of China (Grant No. 2009CB320200)     

An integral equation method for the numerical solution of Laplace's equation without Green's function

The common way to establish an integral equation for the solution of Laplace's equation uses the Green's function of the given equation. It will be shown in this paper that an integral equation can also be constructed by using a particular solution of the Laplace equation as the Kernel of the integral equation.     

An efficient numerical technique for the solution of nonlinear singular boundary value problems

In this work, a new technique based on Green’s function and the Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems (SBVPs) is proposed. The technique relies on constructing Green’s function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on the ADM, the proposed technique avoids solving a sequence of transcendental equations for the undetermined coefficients. It approximates the solution in the form of a series with easily computable components. Additionally, the convergence analysis and the error estimate of the proposed method are supplemented. The reliability and efficiency of the proposed method are demonstrated by several numerical examples. The numerical results reveal that the proposed method is very efficient and accurate.     

Numerical convergence and physical fidelity analysis for Maxwell’s equations in metamaterials

In this paper, we develop a leap-frog mixed finite element method for solving Maxwell’s equations resulting from metamaterials. Our scheme is similar to the popular Yee’s FDTD scheme used in electrical engineering community, and is preferable for three dimensional large scale modeling since no storage of the large coefficient matrix is needed. Our scheme is proved to obey the Gauss’s law automatically if the initial fields satisfy that. Furthermore, the conditional stability and optimal error estimate for the proposed scheme are proved. To our best knowledge, we are unaware of any other publications devoted to the convergence analysis of this leap-frog explicit scheme for Maxwell’s equations even in a simple medium, while our results for metamaterials automatically reduce to the standard Maxwell’s equations in vacuum by dropping some terms resulting from the constitutive equations. Numerical results confirming our analysis are presented.     

A new algorithm for the extraction of the surface waves for the Green’s function in layered dielectrics

There exist the complicated waveguide modes as well as the surface waves in the electromagnetic field induced by a horizontal electric dipole in layered lossless dielectrics between two ground planes. In spectral domain, all these modes can be characterized by the rational parts with the real poles of the vector and scalar potentials. The accurate extraction of these modes plays an important role in the evaluation of the Green’s function in spatial domain. In this paper, a new algorithm based on rational approximation is presented, which can accurately extract all the real poles and the residues of each pole simultaneously. Thus, we can get all the surface wave modes and waveguide modes, which is of great help to the calculation of the spatial domain Green’s function. The numerical results demonstrated the accuracy and efficiency of the proposed method.     

Spectral stability based event localizing temporal decomposition

In this paper a new approach to Temporal Decomposition (TD) of speech, called Spectral Stability Based Event Localizing Temporal Decomposition (S²BEL-TD), is presented. The original method of TD proposed by Atal (1983, Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, 81–84) is known to have the drawbacks of high computational cost, and the high parameter sensitivity of the number and locations of events. In S²BEL-TD, the event localization is performed based on a maximum spectral stability criterion. This overcomes the high parameter sensitivity of events of Atal’s method. Also, S²BEL-TD avoids the use of the computationally costly singular value decomposition routine used in Atal’s method, thus resulting in a computationally simpler algorithm for TD. Simulation results show that an average spectral distortion of about 1.5 dB can be achieved with line spectral frequencies as the spectral parameter. It is shown that the temporal pattern of the speech excitation parameters can also be well described using the S²BEL-TD technique.     

A modified particle swarm optimization via particle visual modeling analysis

A particle is treated as a whole individual in all researches on particle swarm optimization (PSO) currently, these are not concerned with the information of every particle’s dimensional vector. A visual modeling method describing particle’s dimensional vector behavior is presented in this paper. Based on the analysis of visual modeling, the reason for premature convergence and diversity loss in PSO is explained, and a new modified algorithm is proposed to ensure the rational flight of every particle’s dimensional component. Meanwhile, two parameters of particle-distribution-degree and particle-dimension-distance are introduced into the proposed algorithm in order to avoid premature convergence. Simulation results of the new PSO algorithm show that it has a better ability of finding the global optimum, and still keeps a rapid convergence as with the standard PSO.     

Stability of PID-controlled second-order time-delay feedback systems

In the previous papers, the stability of PID-controlled first-order time-delay systems has been investigated by means of several methods, of which the Nyquist criterion, a generalization of the Hermite–Biehler Theorem, and the root location method are well known. Explicit expressions of the boundaries of the stability region, which is the set of controller parameters that give stable closed-loop systems, have been determined. From these studies, one can verify that not all plants can be made stable and then obtain the set of process parameters that allow stable closed-loop systems. With this set, one can implement the stability region of the process parameters. In a recent paper the stability conditions based on Pontryagin’s studies and valid for arbitrary-order plants have been presented. The procedure deduced for the controller parameters is exhaustive, but that deduced for the process parameters requires further mathematical evaluations, whose complexity is proportional to the number of process time constants. In the aforementioned recent paper these evaluations have been performed for a second-order time-delay plant whose transfer function has no zero. The aim of this paper is to execute these calculations for a second-order plant whose transfer function has one zero and to provide the related stability region.     

A rubber sheeting algorithm for non-rectangular maps

Inherent errors in the conversion process (from maps to digital information) cause variations in the location of common boundary lines between adjacent maps. In order to eliminate these discrepancies and define a continuous database, the popular practice is to adjust the map’s boundaries. Preventing relative distortions between the map boundaries (which get altered) and the content of the map necessitates correcting and geometrically improving the map’s contents — a process known as “rubber sheeting”.The paper presents a new method for rubber sheeting, which is not dependent on the shape of the closed polygon circumscribing the map (to be improved), or on the number of points defining its perimeter. The method also covers the various possible relations between maps, such as adjacent maps, a map included completely within another map, a group of maps, etc.The algorithm is based on a non-rectangular bilinear interpolation over the entire area of the map. It determines systematic and random corrections, and subdivides the maps into separate influencing zones as a function of the map perimeter’s shape. The process ensures homogeneity in each map by itself, and, therefore, continuity over an entire database.     

Abnormal condition detection in a cement rotary kiln with system identification methods

In this paper, we use system identification methods for abnormal condition detection in a cement rotary kiln. After selecting proper inputs and output, an input–output model is identified for the plant’s normal conditions. A novel approach is used in order to estimate the delays of the input channels of the kiln before identification part. This method eases the identification since with determining the input channels delays, the dimension of search space in the identification part reduces. Afterward, to identify the kiln’s model, Locally Linear Neuro-Fuzzy (LLNF) model is used. This model is trained by LOcally LInear MOdel Tree (LOLIMOT) algorithm which is an incremental tree-structure algorithm. Finally, with the model for normal condition of the kiln, the incident of abnormalities in output are detected based on the length of duration and magnitude of difference between the real output and model’s output. We distinguished three abnormal conditions in the kiln, two of which are known as common abnormal conditions and another one which was not characteristically known for cement experts either.     

A comparative study of heuristic algorithms on Economic Lot Scheduling Problem

The Economic Lot Scheduling Problem (ELSP) has been well-researched for more than 40 years. As the ELSP has been generally seen as NP-hard, researchers have focused on the development of efficient heuristic approaches. In this paper, we consider the time-varying lot size approach to solve the ELSP. A computational study of the existing solution algorithms, Dobson’s heuristic, Hybrid Genetic algorithm, Neighborhood Search heuristics, Tabu Search and the newly proposed Simulated Annealing algorithm are presented. The reviewed methods are first tested on two well-known problems, those of Bomberger’s [Bomberger, E. E. (1966). A dynamic programming approach to a lot size scheduling problem. Management Science 12, 778–784] and Mallya’s [Mallya, R (1992). Multi-product scheduling on a single machine: A case study. OMEGA: International Journal of Management Science 20, 529–534] problems. We show the Simulated Annealing algorithm finds the best known solution to these problems. A similar comparison study is performed on various problem sets previously suggested in the literature. The results show that the Simulated Annealing algorithm outperforms Dobson’s heuristic, Hybrid Genetic algorithm and Neighborhood search heuristics on these problem sets. The Simulated Annealing algorithm also shows faster convergence than the best known Tabu Search algorithm, yet results in solutions of a similar quality. Finally, we report the results of the design of experiment study which compares the robustness of the mentioned meta-heuristic techniques.     

An extension of LaSalle’s Invariance Principle for a class of switched linear systems

In this paper LaSalle’s Invariance Principle for switched linear systems is studied. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, in this paper the switching modes are allowed to be only Lyapunov stable. Under certain ergodicity assumptions, an extension of LaSalle’s Invariance Principle for global asymptotic stability of switched linear systems is proposed provided that the kernels of derivatives of a common quadratic Lyapunov function with respect to the switching modes are disjoint (except the origin).     

Effect of numerical integration on meshless methods

In this paper, we present the effect of numerical integration on meshless methods with shape functions that reproduce polynomials of degree k1. The meshless method was used on a second order Neumann problem and we derived an estimate for the energy norm of the error between the exact solution and the approximate solution from the meshless method under the presence of numerical integration. This estimate was obtained under the assumption that the numerical integration scheme satisfied a form of Green’s formula. We also indicated how to obtain numerical integration schemes satisfying this property.     

Efficient linear-scaling quantum transport calculations on graphics processing units and applications on electron transport in graphene

We implement, optimize, and validate the linear-scaling Kubo–Greenwood quantum transport simulation on graphics processing units by examining resonant scattering in graphene. We consider two practical representations of the Kubo–Greenwood formula: a Green–Kubo formula based on the velocity auto-correlation and an Einstein formula based on the mean square displacement. The code is fully implemented on graphics processing units with a speedup factor of up to 16 (using double-precision) relative to our CPU implementation. We compare the kernel polynomial method and the Fourier transform method for the approximation of the Dirac delta function and conclude that the former is more efficient. In the ballistic regime, the Einstein formula can produce the correct quantized conductance of one-dimensional graphene nanoribbons except for an overshoot near the band edges. In the diffusive regime, the Green–Kubo and the Einstein formalisms are demonstrated to be equivalent. A comparison of the length-dependence of the conductance in the localization regime obtained by the Einstein formula with that obtained by the non-equilibrium Green’s function method reveals the challenges in defining the length in the Kubo–Greenwood formalism at the strongly localized regime.     

Toward Symbolic Integration of Elliptic Integrals

A method is proposed by which elliptic integrals can be integrated symbolically without information regarding limits of integration and branch points of the integrand that is required in integral tables using Legendre’s integrals. However, it is assumed that when all polynomials in the integrand have been factored symbolically into linear factors, the exponents of all distinct linear factors are known. The recurrence relations are one-parameter relations, all formulas are given explicitly, and the integral is eventually expressed in terms of canonicalR-functions, with no increase in their number if neither limit of integration is a branch point of the integrand. It is the use ofR-functions rather than Legendre’s integrals that makes it possible to carry out the whole process symbolically. If (possibly complex) numerical values of the symbols are known, there are published algorithms for numerical computation of theR-functions.     

Synchronous generator modelling and parameters estimation using least squares method

In this paper, a technique for estimating the synchronous machine’s parameters using sudden short circuit test, is proposed. Before implementing estimation algorithms, a special method of the machine modelling is given. This last one allows to perform tests such as short-circuit, load impact and shedding test, in an easier way than the models usually developed in the literature. Thanks to the well known electrical equivalent circuit of the generator, the relationships between parameters generally used in the industry (i.e., reactances and time constants) and those used in researcher’s domains will be given. Finally, simulation results of the proposed method, allows to show that the algorithm is capable of providing very good estimated parameters fitting with the actual parameters.