On O0-boundedness and -stability properties with perturbing Liapunov functional

In this paper we will extend the perturbing Liapunov functionmethod to systems of functional differential equations and discussØ₀-equiboundedness and Ø₀-equistability propertiesvia the concept of perturbing Liapunov functional.     

Fτ-Coherent 风险度量

该文提出了一个风险度量的新概念,即定义在任意停时 τ上的 F_τ-Coherent 风险度量. 对任一 满足Fatou 性质的F_τ-Coherent 风险调整值度量(即一个F_τCoherent风险度量的负值) ф_т: L^∞ (F) →L^∞ (F_τ) 我们都可以用一个 F_τ-凸概率测度集来给出它的显式表示.同时我们还证明了一个 F_τ-Coherent 风险调整值度量可以用它的可接受头寸集合来表示.     

Finiteness Properties of Certain Metabelian Arithmetic Groups in the Function Field Case

Consider the group scheme where R is an arbitrary commutative ring with 1 0 and a unitx R* acts on R by multiplication. We will study the finiteness properties of subgroups of G(O_S)where O_S is an S-arithmetic subring of a global function field.The subgroups we are interested in are of the form where Q is a subgroup of O_S*. The finiteness propertiesof these metabelian groups can be expressed in terms of the-invariant due to R. Bieri and R. Strebel. Theorem A. Let S be a finite set of places of a global functionfield (regarded as normalized discrete valuations) and O_S thecorresponding S-arithmetic ring. Let Q be a subgroup of O_S*.Then Q is finitely generated and for all integers n 1 the followingare equivalent:

(1) O_S Q is of type FP_n;

(2) O_S is n-tameas a ZQ-module;

(3) each p S restricts to a non-trivial homomorphism and the set is n-tame.

If these conditions hold for at least one n 1 then the identity holds.} Theorem B. Let r denote the rank of Q. Then the followinghold:

(1) the group O_S Q is not of type FP_r+1};

(2) if Qhas maximum rank r = |S| –1 then the group O_S Q is oftype FP_r.

In particular, is of type FP_{|S| –1} but not of type FP_|S|. 1991 Mathematics SubjectClassification: 20E08, 20F16, 20G30, 52A20.     

关于R0 -代数的公理系统

该文给出了R₀ -代数的一些简化公理系统,并证明了R₀ -代数等价于满足某些条件的BCK -代数.     

Hilbert空间上线性算子广义逆A(2)T,S的存在性及其表示式

设H₁和H₂是两个Hilbert空间, B(H₁,H₂)表示从H₁到H₂的所有有界线性算子的集合, T和S分别是H₁和H₂的两个闭子空间. 如果存在线性算子X ∈ B(H₂,H₁)满足XAX=X, R(X)=T, N(X)=S,则称X为线性算子$A$的具有指定像空间T和零空间S的外逆,记为A⁽²⁾_T,S. 该文进一步研究了线性算子广义逆A⁽²⁾_T,S存在的若干等价条件及其性质,建立了算子广义逆A⁽²⁾_T,S的表示形式.     

Exponential stability and maximal attractors for a one-dimensional nonlinear thermoviscoelasticity

This paper is concerned with the global existence, exponentialstability of solutions and associated nonlinear C₀-semigroupas well as the existence of maximal attractors in Hⁱ (i = 1,2, 4) for a nonlinear one-dimensional thermoviscoelasticitydescribing a kind of solid-like material. Some new ideas andmore delicated estimates are employed to prove the global existenceand exponential stability of solutions. The important featurefor the existence of maximal attractors in Hⁱ₊ (i = 1, 2, 4)is that the metric spaces H¹₊, H²₊ and H⁴₊ we work with arethree incomplete metric spaces, as can be seen from the physicalconstraints, i.e. > 0 and u > 0, with and u being absolutetemperature and deformation gradient (strain). For any positiveparameters ₁, ₂, ..., ₅ verifying some conditions, a sequenceof closed subspaces Hⁱ Hⁱ+ (i = 1, 2, 4) is found, and theexistence of maximal attractors in Hⁱ (i = 1, 2, 4) is established.     

∑e1型Banach空间上C0半群稳定性的谱特征

讨论一类不可分解的∑_e¹型Banach空间上有界线性算子的谱的特殊性质;给出了∑_e¹型Banach空间上一致有界C₀半群稳定性的一个谱特征,并给出稳定性定理的一个应用.     

Brownian运动连续模的拟必然收敛速率

在该文中, 作者得到了Brownian运动连续模在C_{r, p} - 容度意义下的泛函极限的收敛速率.     

Finite-dimensional H{infty} control of flexible beam equation systems

In this paper, we consider H control problem with measurementfeedback for flexible beam equation systems. The aim is to constructa finite-dimensional H controller with a given level for theflexible beam equation system. For that purpose, we first formulatethe system as an infinite-dimensional system in l² and derivea finite-dimensional reduced-order system for the infinite-dimensionalsystem. Then, an H controller with level d less than is constructedfor the reduced-order model. The finite-dimensional controllertogether with a residual mode filter plays a role of a finite-dimensionalH controller with level for the original flexible beam equationsystem, if the order of the residual mode filter is chosen sufficientlylarge.     

Arbitrary-norm hyperplane separation by variable neighbourhood search

^** Email: alejandro.karam{at}hec.ca^*** Email: gilles.caporossi{at}gerad.ca^**** Email: pierre.hansen{at}gerad.ca We consider the problem of separating two sets of points ina Euclidean space with a hyperplane that minimizes the sum ofp-norm distances to the plane of points lying on the ‘wrong’side of the plane. A variable neighbourhood search heuristicis used to determine the plane coefficients. For a set of exampleswith L₁-norm, L₂-norm and L-norm, for which the exact solutioncan be computed, we show that our algorithm finds it in mostcases and gets good approximations in the others. The use ofour heuristic solutions for problems in these norms can dramaticallyaccelerate exact algorithms. Our method can be applied on verylarge instances that are intractable by exact algorithms. Sincethe proposed approach works for truly arbitrary norms (otherthan the traditional 1, 2 and ), we can explore for the firsttime the effects of the choice of p on the generalization propertiesof p-norm hyperplane separation.     

A Calculation of the Culler-shalen Seminorms Associated to Small Seifert Dehn Fillings

We determine the relationship between the multiplicities ofthe zeros of certain rational functions defined on the SL₂(C)and PSL₂C character varieties of knot exteriors. This leadsto a formula for the Culler–Shalen seminorms associatedto small Seifert Dehn fillings of such manifolds. 2000 MathematicsSubject Classification: 57M05, 57M27, 57R65.     

Properties of Higher-Dimensional Shintani Generating Functions and Cocycles on Pgl3(Q)

In an earlier paper the second author used the formal, algebraicproperties of 2-dimensional Shintani generating functions toconstruct a 1-cocycle on PGL₂{Q}. We aim to generalise theseresults by using such functions in dimension n to obtain an(n–1)-cocycle on PGL_n{Q}, presumably related to the Bernoulliand Eisenstein cocycles of R. Sczech. By improving our methodswe achieve this goal for n=3. For n>3 we encounter obstaclesrelated to degenerate configurations of hyperplanes in n-space.Nevertheless, we obtain partial results closely connected toreciprocity laws for certain n-dimensional Dedekind sums. 1991Mathematics Subject Classification: 11F20, 11F75.     

A posteriori L2 error estimation on anisotropic tetrahedral finite element meshes

A new a posteriori L₂ norm error estimator is proposed for thePoisson equation. The error estimator can be applied to anisotropictetrahedral or triangular finite element meshes. The estimatoris rigorously analysed for Dirichlet and Neumann boundary conditions. The lower error bound relies on specifically designed anisotropicbubble functions and the corresponding inverse inequalities.The upper error bound utilizes non-standard anisotropic interpolationestimates. Its proof requires H² regularity of the Poisson problem,and its quality depends on how good the anisotropic mesh resolvesthe anisotropy of the problem. This is measured by a so-called‘matching function’. A numerical example supports the anisotropic error analysis.     

Observability and reachability for parallel-flow heat exchanger equations

^** Email: sano{at}cc.kagoshima-u.ac.jp This paper is concerned with the dynamical analysis of parallel-flowheat exchanger equations with observation at the outlet of tube/controlat the inlet of tube. The parallel-flow heat exchanger equationis super-stable under zero boundary condition. The system canbe described by an unbounded operator of lower triangular formthrough a variable transformation. By calculating a C₀-semigroupgenerated by the operator, it is shown that the system is observableif both fluid temperatures are measured at the outlet, and thatthe system is observable with respect to the non-negative coneof the state space if either of them is measured at the outlet.Moreover, it is shown that the system is reachable if both fluidtemperatures are controlled at the inlet, and that the systemis reachable with respect to the non-negative cone of the statespace if either of them is controlled at the inlet.     

On the Gauss-Newton method for l1 orthogonal distance regression

The problem of fitting a curve or surface to data has many applications.There are also many fitting criteria which can be used, andone which is widely used in metrology, for example, is thatof minimizing the least squares norm of the orthogonal distancesfrom the data points to the curve or surface. The Gauss–Newtonmethod, in correct separated form, is a popular method for solvingthis problem. There is also interest in alternatives to leastsquares, and here we focus on the use of the l₁ norm, whichis traditionally regarded as important when the data containwild points. The effectiveness of the Gauss–Newton methodin this case is studied, with particular attention given tothe influence of zero distances. Different aspects of the computationare illustrated by consideration of two particular fitting problems.     

H{infty} filtering for linear continuous-time systems with sampled measurements

The problem of H filtering of continuous-time systems with sampledmeasurements has been investigated. Both finite-and infinite-horizoncases have been considered. It has bas been shown that the sampled-dataH filtering problem can be solved in terms of a differentialRiccati equation with finite discrete jumps. When the systemis time-invariant with zero initial condition, and an infinitehorizon is concerned, the solution to the above problem is equivalentto a solution to a discrete-time algebraic Riccati equation.     

On approximation theorems for controllability of non-linear parabolic problems

^** Email: anil{at}math.iitb.ac.in^*** Email: mcj{at}math.iitb.ac.in^**** Email: akp{at}math.iitb.ac.in In this paper, we consider the following control system governedby the non-linear parabolic differential equation of the form: [graphic: see PDF] where A is a linear operator with dense domain and f(t, y)is a non-linear function. We have proved that under Lipschitzcontinuity assumption on the non-linear function f(t, y), theset of admissible controls is non-empty. The optimal pair (u^*,y^*) is then obtained as the limit of the optimal pair sequence{(u_n^*, y_n^*)}, where u_n^* is a minimizer of the unconstrainedproblem involving a penalty function arising from the controllabilityconstraint and y_n^* is the solution of the parabolic non-linearsystem defined above. Subsequently, we give approximation theoremswhich guarantee the convergence of the numerical schemes tooptimal pair sequence. We also present numerical experimentwhich shows the applicability of our result.     

Robust disturbance attenuation of fluid dynamic systems with norm-bounded uncertainties

In this paper, we consider the problem of robust control of fluid dynamic systems in an Hsense. The system under studyis nonlinear in state and linear in inputs with parameter uncertaintiesin all entries. The controller is designed, via Hamilton–Jacobiequation and Riccati equation approaches, such that the resultingclosed-loop systems is robust stable and has a robust Hperformance.In particular, it is shown that the robust Hcontrol problemis solvable for a nonlinear system (governed by Navier–Stokes equation) in the neighbourhood of the origin if a robust Hcontrolproblem is solvable for a corresponding linearized system.     

Robust H{infty} control of uncertain systems with time-varying state and control input delays

In this paper, a new method for robust H controller of uncertainsystems with time-varying state and control input delays isproposed. A sufficient condition, which is dependent on themaximum value of the time derivative of time-varying delay,is also presented for the existence of H controller. The proposedcontroller not only stabilizes closed-loop uncertain systemsbut also guarantees a prescribed H norm bound of the closed-looptransfer matrix from the disturbance to controlled output. Furthermore,we propose a new robust stability criterion to decide the allowedmaximum bound of plant uncertainty which still can be stabilizedby proposed robust controller. An example given illustratesthe availability of the proposed design method.     

The global linear and local quadratic convergence of a non-interior continuation algorithm for the LCP

^** Email: zhenghaihuang{at}yahoo.com.cn; huangzhenghai{at}hotmail.com In this paper, we propose a non-interior continuation algorithmfor solving the P₀-matrix linear complementarity problem (LCP),which is conceptually simpler than most existing non-interiorcontinuation algorithms in the sense that the proposed algorithmonly needs to solve at most one linear system of equations ateach iteration. We show that the proposed algorithm is globallyconvergent under a common assumption. In particular, we showthat the proposed algorithm is globally linearly and locallyquadratically convergent under some assumptions which are weakerthan those required in many existing non-interior continuationalgorithms. It should be pointed out that the assumptions usedin our analysis of both global linear and local quadratic convergencedo not imply the uniqueness of the solution to the LCP concerned.To the best of our knowledge, such a convergence result hasnot been reported in the literature.