Landscape of wave focusing and localization at low frequencies

High-contrast scattering problems are special among classical wave systems as they allow for strong wave focusing and localization at low frequencies. We use an asymptotic framework to develop a landscape theory for high-contrast systems that resonate in a subwavelength regime. Our from-first-principles asymptotic analysis yields a characterization in terms of the generalized capacitance matrix, giving a discrete approximation of the three-dimensional scattering problem. We develop landscape theory for the generalized capacitance matrix and use it to predict the positions of three-dimensional wave focusing and localization in random and non-periodic systems of subwavelength resonators.     

Convexity of the carrying simplex for discrete-time planar competitive Kolmogorov systems

We consider the geometry of carrying simplices of discrete-time competitive Kolmogorov systems. An existence theorem for the carrying simplex based upon the Hadamard graph transform is developed, and conditions for when the transform yields a sequence of convex or concave graphs are determined. As an application it is shown that the planar Leslie–Gower model has a carrying simplex that is convex or concave.     

Blow-up Mechanism of Classical Solutions to Quasilinear Hyperbolic Systems in the Critical Case

This paper deals with the blow-up phenomenon, particularly, the geometric blow-up mechanism, of classical solutions to the Cauchy problem for quasilinear hyperbolic systems in the critical case. We prove that it is still the envelope of the same family of characteristics which yields the blowup of classical solutions to the Cauchy problem in the critical case.     

Discrete equation on a square lattice with a nonstandard structure of generalized symmetries

We clarify the integrability nature of a recently found discrete equation on the square lattice with a nonstandard symmetry structure. We find its L-A pair and show that it is also nonstandard. For this discrete equation, we construct the hierarchies of both generalized symmetries and conservation laws. This equation yields two integrable systems of hyperbolic type. The hierarchies of generalized symmetries and conservation laws are also nonstandard compared with known equations in this class.     

Invariance results for linear,time-invariant,discrete-time systems

We establish a general invariance result for linear, time-invariant, discrete-time systems. This result, which constitutes necessary and sufficient conditions for asymptotic stability in the large is very general and yields several important variants. The results presented herein are in the same spirit as the authors’ earlier results for linear, time-invariant continuous-time systems. We demonstrate the applicability of the present results by means of a specific example.     

Continuous Markovian Model for Unexpected Shift in SPC

Various process models for discrete manufacturing systems (parts industry) can be treated as bounded discrete-space Markov chains, completely characterized by the original in-control state and a transition matrix for shifts to an out-of-control state. The present work extends these models by using a continuous-state Markov chain, incorporating non-random corrective actions. These actions are to be realized according to the statistical process control (SPC) technique and should substantially affect the model. The developed stochastic model yields Laplace distribution of a process mean. Real-data tests confirm its applicability for the parts industry and show that the distribution parameter is mainly controlled by the SPC sample size.     

Multigrid and M-Matrices in the Finite Pointset Method

We consider the Finite Pointset Method (FPM) for incompressible flows. In the classical FPM derivatives are approximated by a least squares approximation. In general this approach yields stencils with both positive and negative entries. We present how optimization routines can force the stencils to have only positive weights aside from the central point. This approach yields an M-matrix structure, which is of interest for various linear solvers. We investigate algebraic multigrid to solve the arising linear systems. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

时变仿射非线性系统的动态补偿线性化

用微分几何方法讨论了时变仿射非线性系统的动态补偿线性化问题，给出了系统动态的反馈线性化的条件，它是状态反馈线性化的推广。     

Coordination in decentralized assembly systems with uncertain component yields

The literature on assembly systems with random component yields has focused on centralized systems, where a single decision maker chooses all components’ production quantities and incurs all the costs. We consider a decentralized setting where the component suppliers choose their production quantities based solely on their own cost/reward structure, and the assembly firm makes ordering decisions based on its own cost/reward structure. When the suppliers control their inputs but the outputs exhibit random yields, coordination in such systems becomes quite complex. In such situations, incentive alignment control mechanisms are needed so that the suppliers will choose production quantities as in the centralized system case. One such mechanism is to penalize the supplier with the worse delivery performance. We analyze the conditions under which system coordination is achieved while respecting participation constraints. Further, we determine the optimal component ordering policy for the assembly firm and derive the optimal coordinating penalties.     

Methods for constructing observers for linear dynamical systems under uncertainty

We consider various methods for constructing asymptotic observers for linear stationary MIMO systems under an unknown external perturbation. Square systems (in which the number of measured outputs coincides with that of unknown inputs) are considered separately. For such systems we propose a method for constructing observers that yields either an asymptotic observer (for systems of maximal relative order) or an arbitrarily accurate observer. Hyperoutput systems (in which the number of measured outputs exceeds that of unknown inputs) are considered separately as well. For such systems we propose a method for synthesizing asymptotic observers of the phase vector.     

Geometric stable laws: Estimation and applications

Geometric stable laws constitute a class of limiting distributions of appropriately normalized random sums of i.i.d. random variables. We consider the problem of estimation of the parameters of univariate and multivariate geometric stable laws. Our estimation technique is based on the method of moments and yields consistent and asymptotically normal estimators. We apply our estimators to a currency exchange data and show that the geometric stable dominates Paretian stable and normal models.     

�������ŷֲ��Ķ��������̬����Ĺ�����ֵ����������Ĺ���

The log-normal distribution is a common choice for modeling positively skewed data arising from many practical applications.This article introduces a new method of constructing confidence interval for a common mean shared by several log-normal populations through confidence distributions, which combines all information from independent sources. We develop a non-trivial weighting approach by taking account of the sample variances of related quantities to enhance efficiency. Combined confidence distributions are used to construct confidence intervals for the common mean and a simplified version of one existing method is also proposed. We conduct simulation studies to evaluate the performance of the proposed methods in comparison with existing methods. Our simulation results show that the weighting approach yields shorter interval length than the non-weighting approach. The newly proposed confidence intervals perform very well in terms of empirical coverage probability and average interval length. Finally, applications of the proposed methodology is illustrated through three real data examples.     

Boundary regularity for nonlinear elliptic systems

We consider questions of boundary regularity for solutions of certain systems of second-order nonlinear elliptic equations. We obtain a general criterion for a weak solution to be regular in the neighbourhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighbourhood. This result is new for the situation under consideration (general nonlinear second order systems in divergence form, with inhomogeneity obeying the natural growth conditions). Received: 6 July 2001 / Accepted: 27 September 2001 / Published online: 28 February 2002     

On sparse countably infinite Steiner triple systems

We give a general construction for Steiner triple systems on a countably infinite point set and show that it yields 2 ${}^{\text{?}{}_{\text{0}}}$ nonisomorphic systems all of which are uniform and r‐sparse for all finite r?4. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 115–122, 2010     

Multigrid preconditioning for time-periodic Navier–Stokes problems

We propose to solve time-periodic Navier–Stokes problems by a discrete Fourier transform in time. Truncating the Fourier series yields a nonlinear system of equations for the unknown Fourier coefficients. Its solution by Picard iteration requires to solve a sequence of linear systems of equations. The focus of this work is on an efficient method to solve these linear systems. We employ GMRES, complemented by an optimal block triangular preconditioner. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global optimization of a quadratic functional with quadratic equality constraints

In this paper, we investigate a constrained optimization problem with a quadratic cost functional and two quadratic equality constraints. While it is obvious that, for a nonempty constraint set, there exists a global minimum cost, a method to determine if a given local solution yields the global minimum cost has not been established. We develop a necessary and sufficient condition that will guarantee that solutions of the optimization problem yield the global minimum cost. This constrained optimization problem occurs naturally in the computation of the phase margin for multivariable control systems. Our results guarantee that numerical routines can be developed that will converge to the global solution for the phase margin.     

Polynomial chaos for multirate partial differential algebraic equations with random parameters

In radio frequency applications, a multivariate model yields an efficient representation of signals with amplitude modulation and/or frequency modulation. Periodic boundary value problems of multirate partial differential algebraic equations (MPDAEs) have to be solved to reproduce the quasiperiodic signals. Typically, technical parameters appear in the system, which may exhibit some uncertainty. Substitution by random variables results in a corresponding stochastic model. We apply the technique of the generalised polynomial chaos to obtain according solutions. A Galerkin approach yields larger coupled systems of MPDAEs. We analyse the properties of the coupled systems with respect to the original formulations. Thereby, we focus on the case of frequency modulation, since the case of amplitude modulation alone is straightforward.     

Heteroclinic Transition Motions in Periodic Perturbations of Conservative Systems with an Application to Forced Rigid Body Dynamics

We consider periodic perturbations of conservative systems. The unperturbed systems are assumed to have two nonhyperbolic equilibria connected by a heteroclinic orbit on each level set of conservative quantities. These equilibria construct two normally hyperbolic invariant manifolds in the unperturbed phase space, and by invariant manifold theory there exist two normally hyperbolic, locally invariant manifolds in the perturbed phase space. We extend Melnikov’s method to give a condition under which the stable and unstable manifolds of these locally invariant manifolds intersect transversely. Moreover, when the locally invariant manifolds consist of nonhyperbolic periodic orbits, we show that there can exist heteroclinic orbits connecting periodic orbits near the unperturbed equilibria on distinct level sets. This behavior can occur even when the two unperturbed equilibria on each level set coincide and have a homoclinic orbit. In addition, it yields transition motions between neighborhoods of very distant periodic orbits, which are similar to Arnold diffusion for three or more degree of freedom Hamiltonian systems possessing a sequence of heteroclinic orbits to invariant tori, if there exists a sequence of heteroclinic orbits connecting periodic orbits successively.We illustrate our theory for rotational motions of a periodically forced rigid body. Numerical computations to support the theoretical results are also given.     

Chain spaces over Jordan systems

Strong Jordan systems are certain subspaces of associative algebras closed under inversion and with many units. Every strong Jordan system gives rise to a chain space. We show that every homotopism of Jordan systems yields a morphism between the associated chain spaces and vice versa. By this, we obtain an isomorphy of categories.