Basis Problem for Turbulent Actions II: c0-Equalities

Let (Xⁿ,dⁿ) be a sequence of finite metric spaces of uniformlybounded diameter. An equivalence relation D on the product defined by if and only if is a c₀-equality.A systematic study is made of c₀-equalities and Borel reductionsbetween them. Necessary and sufficient conditions, expressedin terms of combinatorial properties of metrics d_n, are obtainedfor a c₀-equality to be effectively reducible to the isomorphismrelation of countable structures. It is proved that every Borelequivalence relation E reducible to a c₀-equality D either reducesa c₀-equality D' additively reducible to D, or is Borel-reducibleto the equality relation on countable sets of reals. An appropriatelydefined sequence of metrics provides a c₀-equality which isa turbulent orbit equivalence relation with no minimum turbulentequivalence relation reducible to it. This answers a questionof Hjorth. It is also shown that, whenever E is an F-equivalencerelation and D is a c₀-equality, every Borel equivalence relationreducible to both D and to E has to be essentially countable.2000 Mathematics Subject Classification: 03E15.     

Elements with generalized bounded conjugation orbits

For a pair of linear bounded operators and on a complex Banach space , if commutes with then the orbits of under are uniformly bounded. The study of the converse implication was started in the 1970s by J. A. Deddens. In this paper, we present a new approach to this type of question using two localization theorems; one is an operator version of a theorem of tauberian type given by Katznelson-Tzafriri and the second one is on power-bounded operators by Gelfand-Hille. This improves former results of Deddens-Stampfli-Williams.     

Bi-Invariant Domains in Semisimple Groups: Nonprincipal Orbits and Boundaries

Let G be a complex semisimple group with real form G . For the action of G × G on G by left and right translation, we define and study an orbit-type stratification of G. In particular, we compute the dimension of an arbitrary stratum; we identify certain strata of low codimension in G, the union of whose closures contains every nonprincipal stratum; and we describe the boundaries and adjacency relations of the maximal connected domains in G that contain only principal orbits.     

Higher order symmetric spaces and the roots of the identity in a Lie group

Let denote the set of all -roots of the identity in a Lie group . We show that is always an embedded submanifold of , having the conjugacy classes of its elements as open submanifolds. These conjugacy classes are examples of -symmetric spaces and we show, more generally, that every -symmetric space of a Lie group is a covering manifold of an embedded submanifold of . We compute also the Hessian of the inclusions of and into , relative to the natural connection on the domain and to the symmetric connection on .

     

Gibbs光学双稳系统的状态反馈控制

基于稳定性理论,提出了一种状态反馈控制混沌的方法。介绍了该方法的控制原理以及各个预期的周期轨道反馈系数的选取原则。以Gibbs光学双稳系统为例,验证了该方法的有效性。数值结果表明,通过调节反馈系数,可以将系统控制在所需的目标轨道上。     

Long-memory in an order-driven market

This paper introduces an order-driven market with heterogeneous investors, who submit limit or market orders according to their own trading rules. The trading rules are repeatedly updated via simple learning and adaptation of the investors. We analyze markets with and without learning and adaptation. The simulation results show that our model with learning and adaptation successfully replicates long-memories in trading volume, stock return volatility, and signs of market orders in an informationally efficient market. We also discuss why evolutionary dynamics are important in generating these features.     

Algorithm of orbit determination using one or two GPS satellites

The problem of orbit determination using one or two GPS satellites is discussed. Methods of getting initial values based on linear translation is presented; the Secant method and the descend Newton iterative procedure and the continuation algorithm are used synthetically to solve the nonlinear equations. Computer simulation shows that this algorithm can give preliminary state of satellite orbit with a certain precision in short time.     

Induced and coinduced Banach Lie–Poisson spaces and integrability

The Poisson induction and coinduction procedures are used to construct Banach Lie–Poisson spaces as well as related systems of integrals in involution. This general method applied to the Banach Lie–Poisson space of trace class operators leads to infinite Hamiltonian systems of k-diagonal trace class operators which have infinitely many integrals. The bidiagonal case is investigated in detail.     

Methods of rapid orbit forecasting after maneuvers for geostationary satellites

A geostationary (GEO) satellite may serve as a navigation satellite, but there is a problem that maneuvers frequently occur and the forces are difficult to model. Based on the technique of determining satellite orbits by transfer, a predicted orbit with high accuracy may be achieved by the method of statistical orbit determination in case of no maneuver force. The predicted orbit will soon be invalid after the maneuver starts, and it takes a long time to get a valid orbit after the maneuver ends. In order to improve ephemeris usability, the method of rapid orbit forecasting after maneuvers is studied. First, GEO satellite movement is analyzed in case of maneuvers based on the observation from the orbit measurement system by transfer. Then when a GEO satellite is in the free status just after maneuvers, the short arc observation is used to forecast the orbit. It is assumed that the common system bias and biases of each station are constant, which can be obtained from orbit determination with long arc observations. In this way, only 6 orbit elements would be solved by the method of statistical orbit determination, and the ephemeris with high accuracy may be soon obtained. Actual orbit forecasting with short arc observation for SINOSAT-1 satellite shows that, with the tracking network available, the precision of the predicted orbit (RMS of O-C) can reach about 5 m with 15 min arc observation, and about 3 m with 30 min arc observation. Supported by the National High Technology Research and Development Program of China (Grant No. 2006AA12Z322), the National Basic Research Program of China (Grant No. 2007CB815503), and the West Light Program of Chinese Academy of Sciences (Grant No. 2007LH01)     

Bessel functions of third order and the distribution of cyclic planar motions with three directions

The exact distribution of a cyclic planar motion with three directions is explicitly derived in terms of Bessel functions of order three (suitably combined). The absolutely continuous part of the distribution is proved to satisfy suitable boundary conditions and some of its properties are analyzed. The transformations converting the governing equations of order three is presented and its solutions (used here) derived by applying the Frobenius method.