伴随阵的若干性质探讨

运用摄动法，简化了jin L X在2000年提出的“对于幂等阵和幂零阵的伴随矩阵分别是幂等阵与幂零阵”结论的证明，并对给定的方阵给出了伴随矩阵的一些性质．     

Riccati inequality and other results for discrete symplectic systems

In this paper we establish several new results regarding the positivity and nonnegativity of discrete quadratic functionals F associated with discrete symplectic systems. In particular, we derive (i) the Riccati inequality for the positivity of F with separated endpoints, (ii) a characterization of the nonnegativity of F for the case of general (jointly varying) endpoints, and (iii) several perturbation-type inequalities regarding the nonnegativity of F with zero endpoints. Some of these results are new even for the special case of discrete Hamiltonian systems.     

Fedosov supermanifolds

We study the properties of the symplectic curvature tensor on supermanifolds. Using the method of normal coordinates, we establish higher-order relations between affine extensions of the curvature tensor and of the symplectic structure tensor. We find a generating function for higher-order relations. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 2, pp. 202–227, November, 2006.     

随机环境中的一类非线性时间序列的伴随几何遍历性分析

本文将AR(m)-ARCH(m)模型推广为REAR(m)-ARCH(m)模型,并给出了REAR(m)-ARCH(m)具有伴随几何遍历性的一个充分条件。     

On the existence of potential landscape in the evolution of complex systems

A recently developed treatment of stochastic processes leads to the construction of a potential landscape for the dynamical evolution of complex systems. Since the existence of a potential function in generic settings has been frequently questioned in literature, here we study several related theoretical issues that lie at core of the construction. We show that the novel treatment, via a transformation, is closely related to the symplectic structure that is central in many branches of theoretical physics. Using this insight, we demonstrate an invariant under the transformation. We further explicitly demonstrate, in one‐dimensional case, the contradistinction among the new treatment to those of Ito and Stratonovich, as well as others. Our results strongly suggest that the method from statistical physics can be useful in studying stochastic, complex systems in general. © 2007 Wiley Periodicals, Inc. Complexity 12: 19–27, 2007     

Second-order necessary conditions for domain optimization problems in elastic structures,part 1: Surface traction given as a field

In this paper, domain optimization problems for both linear and nonlinear elastic structures are studied. The first variation and the second variation of the objective function are calculated in terms of the solution, of the first variation of the solution for the primal elastic system, and of the adjoint variables introduced. The adjoint variables obey a (fictitious) linear elastic system in contrast with the nonlinear adjoint systems introduced by Dems and Mróz, and by Dems and Haftka. From these results, the first-order and the second-order necessary conditions that an optimal domain should satisfy are immediately derived.Portions of this paper were presented at the 5th IFAC Symposium on Control of Distributed Parameter Systems, Perpignan, France, 1989. The authors would like to express their sincere thanks to the referees for their critical readings.     

POINCARE-CARTAN INTEGRAL INVARIANTS OF BIRKHOFFIAN SYSTEMS

Based on modern differential geometry, the symplectic structure of a Birkhoffiansystem which is an extension of conservative and nonconservative systems is analyz ed. Anone-dimensional damped vibration is taken as an ilhustrative example and an integralinvariant of Poincaré's type is found.     

Squeezing in Representation by Quadratic Combinations of Canonical Operators

The technique of integration within an ordered product of operators and the coherent-state representationare used to convert exponential operators of basis operators (p2, Q2, pQ + Qp) to those of the basis operators (a2, a+2,ara). The coherent state representation of unitary squeezing operators in the factorized form and their normal productform are thus derived. The squeezing engendered by operators of the general form exp{-i[αP2 + βQ2 + γ/2 (QP + PQ)] }is also obtained.