Banach空间中线性系统精确零可控性

本文研究了状态空间为一般 Banach空间的线性系统的精确零可控性问题 .首先建立了一个同对偶半群有关的映射的可测性 .然后利用此可测性和 Banach空间中闭凸集的强分离定理导出了精确零可控性的充分必要条件     

Banach格上的b-AM-紧算子(英文)

本文对Banach格上的b-AM-紧算子进行了描述,得到了如下三个结论:1)如果Banach格F是无限维的,则E是KB-空间当且仅当每个从E到F的AM-紧算子是b-AM-紧算子。2)Banach格E是离散的KB-空间当且仅当每个从E到F的连续算子是b-AM-紧算子。3)如果E是离散的,则每个从E到F的b-弱紧算子是b-AM-紧算子。其次给出了b-AM-紧算子的控制性质,得到如下两个结论:1)如果E和F是两个Banach格,算子S,T:E→F满足0≤S≤T且T是b-AM-紧算子,则算子S是b-AM-紧算子当且仅当F具有序连续范数或者E是离散空间。2)如果S,T是从E到F的算子满足0≤S≤T,如果T是b-AM-紧算子,则S2也是b-AM-紧算子。     

Mixed finite element approximations based on 3‐D hp‐adaptive curved meshes with two types of H(div)‐conforming spaces

Two stable approximation space configurations are treated for the mixed finite element method for elliptic problems based on curved meshes. Their choices are guided by the property that, in the master element, the image of the flux space by the divergence operator coincides with the potential space. By using static condensation, the sizes of global condensed matrices, which are proportional to the dimension of border fluxes, are the same in both configurations. The meshes are composed of different topologies (tetrahedra, hexahedra, or prisms). Simulations using asymptotically affine uniform meshes, exactly fitting a spherical‐like region, and constant polynomial degree distribution k, show L² errors of order k+1 or k+2 for the potential variable, while keeping order k+1 for the flux in both configurations. The first case corresponds to RT(k) and BDFM(k+1) spaces for hexahedral and tetrahedral meshes, respectively, but holding for prismatic elements as well. The second case, further incrementing the order of approximation of the potential variable, holds for the three element topologies. The case of hp‐adaptive meshes is considered for a problem modelling a porous media flow around a cylindrical horizontal well with elliptical drainage area. The effect of parallelism and static condensation in CPU time reduction is illustrated.     

Dense distribution of chaotic maps in continuous map spaces

This article is concerned with distribution of several kinds of chaotic maps in a continuous map space, in which the maps are defined in a closed bounded set of a Banach space. It is shown that the map space contains a dense set of maps that are strictly coupled-expanding, have nondegenerate and regular snap-back repellers, have nondegenerate and regular homoclinic orbits to repellers, and consequently that are chaotic in the sense of Devaney as well as in the original sense of Li–Yorke, and have the topological entropy larger than any given positive constant. Further, in the finite-dimensional case, there exists a dense residual set of the map space such that every map?f in the set is strictly coupled-expanding in k pairwise disjoint compact sets for any given integer k?≥?2, is chaotic in the sense of Li–Yorke and has the infinite topological entropy and a nontrivial invariant measure.     

Hierarchic finite element bases on unstructured tetrahedral meshes

The problem of constructing hierarchic bases for finite element discretization of the spaces H¹, H ( curl ), H ( div ) and L₂ on tetrahedral elements is addressed. A simple and efficient approach to ensuring conformity of the approximations across element interfaces is described. Hierarchic bases of arbitrary polynomial order are presented. It is shown how these may be used to construct finite element approximations of arbitrary, non‐uniform, local order approximation on unstructured meshes of curvilinear tetrahedral elements. Copyright © 2003 John Wiley & Sons, Ltd.     

Banach空间二阶非线性微分方程的终值问题

本文利用半序理论研究Banach空间中二阶非线性微分方程终值问题最小解和最大解的存在性,并将所得结果应用于无穷维微分方程的终值问题。     

Stochastic uniform observability of general linear differential equations

The aim of this article is to discuss the uniform observability property of general linear differential equations with multiplicative white noise in Hilbert spaces. Based on perturbation theory for evolution operators on Hilbert Schmidt spaces and on the space of nuclear operators, new representations of the covariance operators associated to the mild solutions of the investigated stochastic differential equations are given. Using these results we obtain deterministic characterizations of the stochastic uniform observability property. We also identify an entire class of stochastic differential equations which are never stochastic uniformly observable. Some examples will illustrate the theory.     

Design spaces,measures and metrics for evaluating quality of time operators and consequences leading to improved algorithms by design—illustration to structural dynamics

For the first time, for time discretized operators, we describe and articulate the importance and notion of design spaces and algorithmic measures that not only can provide new avenues for improved algorithms by design, but also can distinguish in general, the quality of computational algorithms for time‐dependent problems; the particular emphasis is on structural dynamics applications for the purpose of illustration and demonstration of the basic concepts (the underlying concepts can be extended to other disciplines as well). For further developments in time discretized operators and/or for evaluating existing methods, from the established measures for computational algorithms, the conclusion that the most effective (in the sense of convergence, namely, the stability and accuracy, and complexity, namely, the algorithmic formulation and algorithmic structure) computational algorithm should appear in a certain algorithmic structure of the design space amongst comparable algorithms is drawn. With this conclusion, and also with the notion of providing new avenues leading to improved algorithms by design, as an illustration, a novel computational algorithm which departs from the traditional paradigm (in the sense of LMS methods with which we are mostly familiar with and widely used in commercial software) is particularly designed into the perspective design space representation of comparable algorithms, and is termed here as the forward displacement non‐linearly explicit L‐stable (FDEL) algorithm which is unconditionally consistent and does not require non‐linear iterations within each time step. From the established measures for comparable algorithms, simply for illustration purposes, the resulting design of the FDEL formulation is then compared with the commonly advocated explicit central difference method and the implicit Newmark average acceleration method (alternately, the same conclusion holds true against controllable numerically dissipative algorithms) which pertain to the class of linear multi‐step (LMS) methods for assessing both linear and non‐linear dynamic cases. The conclusions that the proposed new design of the FDEL algorithm which is a direct consequence of the present notion of design spaces and measures, is the most effective algorithm to‐date to our knowledge in comparison to the class of second‐order accurate algorithms pertaining to LMS methods for routine and general non‐linear dynamic situations is finally drawn through rigorous numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd.     

Flow equivalence and isotopy for subshifts

We study basic properties of flow equivalence on one-dimensional compact metric spaces with a particular emphasis on isotopy in the group of (self-) flow equivalences on such a space. In particular, we show that such an orbit-preserving map is not always an isotopy, but that this always is the case for suspension flows of irreducible shifts of finite type. We also provide a version of the fundamental discretization result of Parry and Sullivan which does not require that the flow maps are either injective or surjective. Our work is motivated by applications in the classification theory of sofic shift spaces, but has been formulated to supply a solid and accessible foundation for other purposes.     

Pseudo-orbits,stationary measures and metastability

We characterize absolutely continuous stationary measures (acsms) of randomly perturbed dynamical systems in terms of pseudo-orbits linking the ergodic components of absolutely continuous invariant measures (acims) of the unperturbed system. We focus on those components, called least elements, which attract pseudo-orbits. Under the assumption that the transfer operators of both systems, the random and the unperturbed, satisfy a uniform Lasota–Yorke inequality on a suitable Banach space, we show that each least element is in a one-to-one correspondence with an ergodic acsm of the random system.     

无穷维线性系统可控性的一个注记

设x和u是Banach空间．U*具有Radon-Nikodym性质［3］本文研究无穷维线性系统X(t)_=AX(t)=AX(t)十BU(t)的可控性．其中A和B是有界线性算子，我们证明：此系统在［O，T］上精确可控性的充要条件是存在正整教n，使得：其中，这是著名的有限线性系统可控性条件对无穷维系统的推广．     

Asymptotically efficient order selection in nonstationary AR processes

In this paper we investigate the issue of asymptotic efficiency in nonstationary AR(∞) processes. Since the inverse of the autocovariance matrix of the underlying process cannot be evaluated due to the fact that the matrix is singular, traditional methods and techniques (Karagrigoriou 1995, 1997; Bhansali 1996) cannot be applied. Here we attempt to reduce the nonstationary case to a stationary one so that known results can then be applied to the reduced process. Asymptotic results regarding the overestimation of the order of an AR process with several unit roots are presented and the asymptotic efficiency of the order selected is established in the case whered (d>0) unit roots are present.     

Coherent States of a Harmonic Oscillator in a Finite-dimensional Hilbert Space and Their Squeezing Properties

Abstract

New coherent states of a harmonic oscillator in a finite-dimensional Fock space are introduced. Some properties of these coherent states are discussed. The second-order squeezing of these coherent states with respect to the quadrature operators is studied in detail. In particular, for a two-state system the arbitrary higher-order squeezing of these states is investigated. It is shown that these coherent states exhibit much richer squeezing properties than the coherent states of a usual harmonic oscillator in an infinite-dimensional Fock space. It is found that these coherent states have not only second-order squeezing but also higher-order squeezing with respect to the quadrature operators of the field under consideration.     

Petrov–Galerkin finite element methods with a hinged test space for singularly perturbed problems

In this paper we introduce finite element methods of Petrov–Galerkin type for the approximate solution of two-point boundary-value problems for singularly perturbed, second-order, ordinary, linear differential equations. We write down Petrov–Galerkin methods on a uniform mesh which have asymptotic error estimates, as the mesh size tends to zero, whose magnitude is independent of the singular perturbation parameter. This is in marked contrast to standard finite element methods which do not possess such a property on a uniform mesh. For these, typically, the error on a fixed uniform mesh blows up as the singular perturbation parameter tends to zero. This robust behaviour of these Petrov–Galerkin methods for singularly perturbed problems is achieved by choosing trial spaces of standard piecewise polynomial type, while the test spaces consist of hinged piecewise polynomials. We consider self-adjoint and non-self-adjoint two-point boundary-value problems with Dirichlet boundary conditions. We define hinged test spaces for both types of problem. We then introduce a number of sample problems and we present numerical solutions of these sample problems using a Petrov–Galerkin method with the appropriate hinged test space.     

增生算子方程的具误差的Ishikawa迭代序列的收敛率估计

设X是一实的Banach空间,T：X→Y是一Lipschitz的增生算子。本文证明了具误差的Ishikawa迭代序列强收敛到方程x Tx=f的唯一解：并得一个一般的收敛估计式。若T：X→X是一Lipschitz的强增生算子,则具误差的Ishikawa迭代序列强收敛到方程Tx=f的唯一解。本文结果推广和发展了现有的相应结果。     

A note on the Gauss-Jacobi quadrature formulae for singular integral equations of the second kind

A fast and efficient numerical method based on the Gauss-Jacobi quadrature is described that is suitable for solving Fredholm singular integral equations of the second kind that are frequently encountered in fracture and contact mechanics. Here we concentrate on the case when the unknown function is singular at both ends of the interval. Quadrature formulae involve fixed nodal points and provide exact results for polynomials of degree 2n − 1, where n is the number of nodes. Finally, an application of the method to a plane problem involving complete contact is presented.     

Thermodynamic aspects of transverse wave propagation in an incompressible hyperelastic solid

Summary Thermodynamic considerations in the propagation of finite amplitude plane shear waves in an incompressible isotropic hyperelastic solid are examined, in particular the validity of the assumption of zero thermal conductivity which results in the adiabatic approximation. Two problems are considered for a solid withdc/d|F|>0, wherec is the transverse wave speed andF is the shear component of the deformation gradient tensor for simple shear. These problems, which are used to illustrate thermodynamic effects, are the sudden application of a spatially uniform shearing stress to the free surface of an unstressed half space at rest and the sudden removal of the spatially uniform shearing stress on the surface of a half space at rest and in a state of simple shear.With 2 Figures     

Modification of the procedure for measuring space-time observables when introducing supplementary fundamental constants

The problem of measuring space-time quantities when introducing supplementary fundamental constants is considered. A certain modification of the standard measurement procedure is proposed which involves the dependence of the right-hand side of the commutation relations between the space-time observables on both the supplementary physical constant H and the angular momentum operator. Relationships between the operators of the physical quantities are given for the case when the wave function of the system is transformed in accordance with the simplest finite-dimensional concepts of generalized algebra. A lower limit is obtained for the product of the dispersions of the coordinate and momentum operators which enables the value of the supplementary constant H to be estimated when the experimental data are of high accuracy.Translated from Izmeritel'naya Tekhnika, No. 7, pp. 3–4, July, 1994.     

Impurities in d-Wave Superconductors: Effect of Singular Density of States

We analyzed the effect of nonmagnetic impurities in d-wave superconductors with an energy dependent density of states. Two singular forms for the density of states have been considered. The strength of singularity affect the degradation of the critical temperature and reduces the pair-breaking effect.