Topological inverse semigroups

That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Hom (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory, all these results generalize the corresponding ones related to topological semigroups or topological groups.

Delay-Dependent Absolute Stability ofUncertain Lur′e Systems with Time-Delays^1）

This paper is concerned with delay dependent absolute stability for a class of uncertain Lur′e systems with multiple time-delays. By using a descriptor model transformation of the sys-tem and by applying a recent result on bounding of cross products of vectors, a new type of Lya-punov-Krasovskii functional is constructed. Based on the new functional, delay-dependent suffi-cient conditions for absolute stability are derived in terms of linear matrix inequalities. These con-ditions do not require any parameter tuning, and can be solved numerically using the software LMI Lab. A numerical example is presented which shows that the proposed method can substantiallyimprove the delay bound for absolute stability of Lur′e system with time-delays, compared to theexisting ones.

The Reduced-order Design of Robust Adaptive Backstepping Controller

For a class of systems with unmodeled dynamics, robust adaptive stabilization problemis considered in this paper. Firstly, by a series of coordinate changes, the original system is re-parameterized. Then, by introducing a reduced-order observer, an error system is obtained. Basedon the system, a reduced-order adaptive backstepping controller design scheme is given. It is provedthat all the signals in the adaptive control system are globally uniformly bounded, and the regulationerror converges to zero asymptotically. Due to the order deduction of the controller, the design schemein this paper has more practical values. A simulation example further demonstrates the e?ciency ofthe control scheme.

CAVITY FORMATION AND ITS VIBRATION FOR A CLASS OF GENERALIZED INCOMPRESSIBLE HYPER-ELASTIC MATERIALS

The problem of radial symmetric motion for a solid sphere composed of a class of generalized incompressible neo-Hookean materials, subjected to a suddenly applied surface tensile dead load, is examined.The analytic solutions for this problem and the motion equation of cavity that describes cavity formation and growth with time are obtained. The e?ect of radial perturbation of the materials on cavity formation and its motion is discussed. The plane of the perturbation parameters of the materials is divided into four regions. The existential conditions and qualitative properties of solutions of the motion equation of the cavity are studied in di?erent parameters’ regions in detail. It is proved that the cavity motion with time is a nonlinear periodic vibration. The vibration center is then determined.

The Asymptotic Property of Generalized Taylor Remainder "Mean Value Point"

This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f(n+i)(x0)h(n+i) = 0(i = 1, 2,..., p - 1) and f(n+p)(x0)h(h+p) don't exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.

LEAST-SQUARES SOLUTION OF AXB = DOVER SYMMETRIC POSITIVE SEMIDEFINITE MATRICES X

Least-squares solution of AXB = D with respect to symmetric positive semidefinite matrix X is considered. By making use of the generalized singular value decomposition, we derive general analytic formulas, and present necessary and sufficient conditions for guaranteeing the existence of the solution. By applying MATLAB 5.2, we give some numerical examples to show the feasibility and accuracy of this construction technique in the finite precision arithmetic.

Ruin Probabilities under a Markovian Risk Model

In this paper, a Markovian risk model is developed, in which the occurrence of the claims is described by a point process {N(t)} t≥0 with N(t) being the number of jumps of a Markov chain during the interval [0, t]. For the model, the explicit form of the ruin probability Ψ(0) and the bound for the convergence rate of the ruin probability Ψ(u) are given by using the generalized renewal technique developed in this paper. Finally, we prove that the ruin probability Ψ(u) is a linear combination of some negative exponential functions in a special case when the claims are exponentially distributed and the Markov chain has an intensity matrix (q ij ) i,j∈E such that q m = q m1 and q i = q i(i+1), 1 ≤ i ≤ m−1.

Asymptotic Behaviors of the Solutions to Scalar Viscous Conservation Laws on Bounded Interval

Abstract This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value problem for scalar viscous conservations laws ut + f(u)x = ux,x on [0,1], with the boundary condition u(0,t)=um,u(1t)=u+ and the initial data u(x,0)= u0(x, where um p u+ and f is a given function satisfying f'(u>0 for u under consideration. By means of energy estimates method and under some more regular conditions on the initial data, both the global existence and the asymptotic behavior are obtained. When um < u+, which corresponds to rarefaction waves in inviscid conservation laws, no smallness conditions are needed. While for um > u+, which corresponds to shock waves in inviscid conservation laws, it is established for weak shock waves, which means that |um m u+| is small. Moreover, exponential decay rates are both given.

A Linear Time Algorithm for the Minimum-weight Feedback Vertex Set Problem in Series-parallel Graphs

A feedback vertex set is a subset of vertices in a graph, whose deletion from the graph makes the resulting graph acyclic. In this paper, we study the minimum-weight feedback vertex set problem in series-parallel graphs and present a linear-time exact algorithm to solve it.