分数阶系统稳定性理论与控制研究

分数阶系统稳定性理论是分数阶非线性系统控制的基础. 针对分数阶非线性系统稳定性理论的讨论,本文从另一角度证明了该理论的正确性. 结果表明,分数阶非线性系统稳定性理论不仅适用于分数阶自治系统,也同样适用于分数阶非自治系统. 利用该理论分析了多个实例并进行了数值仿真,仿真结果验证了该理论的有效性. 关键词： 分数阶系统 稳定性理论 非自治 自治     

Who Proved Haag's Theorem?

In physics literature, there are several different characterizations of Haag's theorem and its consequences for quantum field theory. These different versions of Haag's theorem are due in part to various generalizations and more “rigorous” proofs of Haag's theorem as well as to the fact that many of these proofs were done using different formulations of quantum field theory. As a result, there is confusion about what Haag's theorem is and when it was proved. This paper clears up some of these confusions by examining the history and development of Haag's theorem up to 1959. It is argued that the question of who proved Haag's theorem is tied up with what the theorem is taken to show.     

Brillouin's theorem and the Hellmann-Feynman theorem for Hartree-Fock wave functions

It is shown that there is an intimate relation between the Hellmann-Feynman theorem and Brillouin's theorem. A more general form of Brillouin's theorem is provided, which applies to excited states of arbitrary symmetry and multiplicity. This new form leads to a simple proof of the Hellmann-Feynman theorem. This theorem is valid when all the orbitals that occur in the wave function are determined by a complete, and not a partial, variational procedure. Arguing in the opposite direction it is shown that the complete satisfaction of the generalized Brillouin's theorem provides an alternative scheme for obtaining the Hartree-Fock orbitals.     

分数阶系统的一种稳定性判定定理及在分数阶统一混沌系统同步中的应用

根据Lyapunov稳定定理及其逆定理和分数阶系统稳定定理,提出了如果整数阶系统稳定,其对应的阶次小于1的分数阶形式的系统也稳定的分数阶系统稳定的判定定理,并给出了详细的证明过程.并将该理论运用于分数阶混沌系统的同步,实现了未知参数分数阶统一混沌系统的自适应同步,仿真结果证实了该理论的正确性. 关键词： 分数阶系统 混沌 Lyapunov稳定定理 Lyapunov稳定逆定理     

An “optical” theorem for acoustic scattering by baffled flexible surfaces

The classical optical theorem for scattering by compact obstacles is a forward scattering theorem. That is, the total cross section of the obstacle is proportional to the imaginary part of the far field directivity factor evaluated in the forward scattering direction. An analogous theorem is derived in this paper for the scattering of acoustic waves by baffled membranes and plates. In this “optical” theorem the directivity factor is evaluated in the direction of the specularly reflected wave, so that it is a reflected scattering theorem.     

分数阶系统有限时间稳定性理论及分数阶超混沌Lorenz系统有限时间同步

研究了分数阶系统有限时间稳定性理论及分数阶混沌系统的同步问题.根据分数阶微分性质及分数阶系统稳定性理论,建立了分数阶系统有限时间稳定性理论并进行了证明.根据该理论设计控制器实现了分数阶超混沌Lorenz系统有限时间同步并运用数值仿真进行了验证. 关键词： 分数阶 超混沌Lorenz系统 稳定 有限时间同步     

No-Cloning Theorem,Kochen-Specker Theorem,and Quantum Measurement Theories

The usual no-cloning theorem implies that two quantum states are identical or orthogonal if we allow a cloning to be on the two quantum states. Here, we investigate a relation between the no-cloning theorem and the projective measurement theory that the results of measurements are either + 1 or − 1. We introduce the Kochen-Specker (KS) theorem with the projective measurement theory. We result in the fact that the two quantum states under consideration cannot be orthogonal if we avoid the KS contradiction. Thus the no-cloning theorem implies that the two quantum states under consideration are identical in that case. It turns out that the KS theorem with the projective measurement theory says a new version of the no-cloning theorem. Next, we investigate a relation between the no-cloning theorem and the measurement theory based on the truth values that the results of measurements are either + 1 or 0. We return to the usual no-cloning theorem that the two quantum states are identical or orthogonal in the case.

     

有导体存在时的唯一性定理的一种证明方法

提出一种用积分形式的高斯定理、环路定理（电场线的主要性质是它们的具体体现）和叠加原理来有有导体存在时的唯一性定理的方法。     

Generalized Noether's theorem. I. theory

This article is a theoretical investigation of generalized Noether's theorem, which, though unconcerned with considerations such as coordinate transformations, symmetry, and invariance, is the basic mechanism of conventional Noether's theorem, its extensions, and its inverse. The generalized theorem is a completely new approach to the subject—formally, conceptually, and practically. It is an association, for a set of field equations, of field variations with conserved currents. The theorem is stated from two points of view and analyzed with regard to its interpretation and its formal and conceptual relation to conventional Noether's theorem and extensions, transformation groups, and Hamilton's principle. The inverse theorem is also treated. The role of coordinate transformations in conventional Noether's theorem is analyzed.     

Generalization of classical rigorous theory of dispersion and Helmholtz-Kirchhoff integral theorem

New forms of the Ewald-Oseen extinction theorem and a diffraction formula are obtained by the generalization of the classical rigorous theory of dispersion. These theorem and formula reduce to the Helmholtz-Kirchhoff integral theorem in vector form under certain condition.     

Callias' index theorem,elliptic boundary conditions,and cutting and gluing

It is shown that elliptic boundary conditions play the same role in Callias' index theorem as spectral boundary conditions do in the Atiyah-Patodi-Singer index theorem. This is used to generalize Callias' index theorem to arbitrary complete spin-manifolds.     

Birkhoff theorem and matter

Birkhoff’s theorem for spherically symmetric vacuum spacetimes is a key theorem in studying local systems in general relativity theory. However realistic local systems are only approximately spherically symmetric and only approximately vacuum. In a previous paper, we showed the theorem remains approximately true in an approximately spherically symmetric vacuum space time. In this paper we prove the other case: the theorem remains approximately true in a spherically symmetric, approximately vacuum space time.     

格林互易定理在求解均匀带电圆环的静电势分布中的应用

对于静电场,由普遍的格林互易定理得出特殊情形下的格林互易定理.应用该定理推导出均匀带电圆环的数种在形式上互不相同的静电势分布解式.     

Lattice fermions in euclidean space-time

A very short proof of a no-go theorem for putting fermions on a lattice is given using the Poincaré-Hopf theorem. The no-go theorem forbids the lattice formulation of theories with handed fermions without species doubling. Examples of such theories are chiral invariant QCD and the Weinberg-Salam-Glashow model. We give arguments why it could be possible to circumvent the no-go theorem by relaxing one of the assumptions, viz. bilinearity of the action in the fermion fields.     

On the van Cittert-Zernike theorem

The van Cittert-Zernike theorem states that the spatial coherence over a space illuminated by an incoherent extended source is described by the Fourier transform of the intensity distribution over the source. The theorem is usually used in a restricted case of the spatial coherence in a plane parallel to the source plane and illuminated by an incoherent extended source of uniform intensity distribution. In this paper we re-examine the van Cittert-Zernike theorem by reviewing it in an original formulation and extend the theorem to the spatial coherence at any two points of a light field illuminated by an incoherent extended source having a non-uniform intensity distribution.     

留数定理在拓扑相变中的应用

留数定理是高校物理专业必修课程数学物理方法中的一个重要定理.传统教学中关于该定理的讲授着重于数学公式的推导和数学思想的传达,而对于其在具体物理问题上的应用鲜有涉及.本文以一维Su-Schrieffer-Heeger模型的拓扑相变问题为例,阐明了如何利用留数定理解析得到二阶位移量的表达式并用该物理量表征拓扑相变.在讲授留数定理的教学过程中引入具体物理问题的分析实例,可以使学生更深刻地理解数学定理中的物理内涵.     

Generalized Virial Theorem for Mixed State When Hamiltonians Include Coordinate-Momentum Couplings

The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this paper we discuss Virial theorem for mixed state for some Hamiltonians with coordinate-momentum couplings in order to know their contributions to internal energy.     

Spectral properties in a class of operators and group representations in nested Hilbert spaces

We characterize the spectrum of the elements of some operator algebras acting in a nested Hilbert space. In one of those algebras we prove the spectral theorem for Hermitian operators and the SNAG theorem for unitary representations of locally compact Abelian groups. Then we extend the SNAG theorem to representations in three more general classes of operators.     

Optical theorem detectors for active scatterers

We develop a new theory of the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. It applies to arbitrary lossless backgrounds and quite general probing fields. The derived formulation holds for arbitrary passive scatterers, which can be dissipative, as well as for the more general class of active scatterers which are composed of a (passive) scatterer component and an active, radiating (antenna) component. The generalization of the optical theorem to active scatterers is relevant to many applications such as surveillance of active targets including certain cloaks and invisible scatterers and wireless communications. The derived theoretical framework includes the familiar real power optical theorem describing power extinction due to both dissipation and scattering as well as a novel reactive optical theorem related to the reactive power changes. The developed approach naturally leads to three optical theorem indicators or statistics which can be used to detect changes or targets in unknown complex media. The paper includes numerical simulation results that illustrate the application of the derived optical theorem results to change detection in complex and random media.