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1.
Let ( t ) t0 be a -semistable convolution semigroup of probability measures on a Lie groupG whose idempotent 0 is the Haar measure on some compact subgroupK. Then all the measures 1 are supported by theK-contraction groupC K() of the topological automorphism ofG. We prove here the structure theoremC K()=C()K, whereC() is the contraction group of . Then it turns out that it is sufficient to study semistable convolution semigroups on simply connected nilpotent Lie groups that have Lie algebras with a positive graduation.  相似文献   

2.
In this paper we investigate both the contractivity and the asymptotic stability of the solutions of linear systems of delay differential equations of neutral type (NDDEs) of the form y(t) = Ly(t) + M(t)y(t – (t)) + N(t)y(t – (t)). Asymptotic stability properties of numerical methods applied to NDDEs have been recently studied by numerous authors. In particular, most of the obtained results refer to the constant coefficient version of the previous system and are based on algebraic analysis of the associated characteristic polynomials. In this work, instead, we play on the contractivity properties of the solutions and determine sufficient conditions for the asymptotic stability of the zero solution by considering a suitable reformulation of the given system. Furthermore, a class of numerical methods preserving the above-mentioned stability properties is also presented.  相似文献   

3.
This paper deals with adapting Runge-Kutta methods to differential equations with a lagging argument. A new interpolation procedure is introduced which leads to numerical processes that satisfy an important asymptotic stability condition related to the class of testproblemsU(t)=U(t)+U(t–) with , C, Re()<–||, and >0. Ifc i denotes theith abscissa of a given Runge-Kutta method, then in thenth stept n–1t n :=t n–1+h of the numerical process our interpolation procedure computes an approximation toU(t n–1+c i h–) from approximations that have already been generated by the process at pointst j–1+c i h(j=1,2,3,...). For two of these new processes and a standard process we shall consider the convergence behaviour in an actual application to a given, stiff problem.  相似文献   

4.
We shall develop a method to prove inequalities in a unified manner. The idea is as follows: It is quite often possible to find a continuous functional : n , such that the left- and the right-hand side of a given inequality can be written in the form (u)(v) for suitable points,v=v(u). If one now constructs a map n n , which is functional increasing (i.e. for each x n (which is not a fixed point of ) the inequality (x)<((x)) should hold) one specially gets the chain (u)( u))( 2(u))... n (u)). Under quite general conditions one finds that the sequence { n (u)} n converges tov=v(u). As a consequence one obtains the inequality (u)(v).  相似文献   

5.
We investigate the asymptotic behaviour of the summatory functions of z(n, ), k(n, ) z (n) and k(n, ) z (n).  相似文献   

6.
Summary Necessary and sufficient conditions are given in order that a sequence of probability measures, weakly convergent relative to a given topology 0 and associated -field ( 0), are weakly convergent (and satisfy a continuity theorem) relative to the ( 0)-measurable functions which are continuous in some finer topology 1, even if does not extend to ( 0). These conditions are shown to be applicable to a sequence of translated renewal measures. Alternate conditions (tightness, uniformity of weak convergence) are investigated and shown to be inappropriate.This research was partially supported by UMC Summer Faculty Research Fellowships  相似文献   

7.
Motivated by the known characterizations of equicontinuity in the dual of a Schwartz space, a nuclear space, or a strongly nuclear space,we introduce the concepts of a -sequence and of a ()-sequence in the dual of an arbitrary lcs [E,], and we investigate the corresponding topologies and () on E of uniform convergence on these sequences. Here is a normal sequence space such that . Under favorable enough conditions on , including the nuclearity of its normal topology , [,] acts as a universal generator for those lcs [E,] which satisfy =. Under somewhat weaker assumptions on , [,()] is a universal generator for the lcs [E,] with =(). These results cover e.g. the cases of -nuclear spaces and of nuclear spaces known from the recent literature. As an application we show that every non-trivial ultrabornological lcs is representable as an inductive limit of isomorphic copies of [, ( , )], where is any nuclear power series space of infinite type with stable exponent sequence.  相似文献   

8.
Stability analysis of numerical methods for delay differential equations   总被引:7,自引:0,他引:7  
Summary This paper deals with the stability analysis of step-by-step methods for the numerical solution of delay differential equations. We focus on the behaviour of such methods when they are applied to the linear testproblemU(t)=U(t)+U(t–) with >0 and , complex. A general theorem is presented which can be used to obtain complete characterizations of the stability regions of these methods.  相似文献   

9.
We present an explicit Runge-Kutta scheme devised for the numerical solution ofdelay differential equations (DDEs) where a delayed argument lies in the current Runge-Kutta interval. This can occur when the lag is small relative to the stepsize, and the more obvious extensions of the explicit Runge-Kutta method produce implicit equations. It transpires that the scheme is suitable forparallel implementation for solving both ODEs and more general DDEs. We associate our method with a Runge-Kutta tableau, from which the order of the method can be determined. Stability will affect the usefulness of the scheme and we derive the stability equations of the scheme when applied to the constant-coefficient test DDEu(t)=u(t) +u(t), where the lag and the Runge-Kutta stepsizeH n H are both constant. (The case=0 is treated separately.) In the case that 0, we consider the two distinct possibilities: (i) H and (ii)<H.In memory of Professor Leslie Fox, Balliol College, OxfordWork performed in part at The University of Auckland, New Zealand.This paper is presented as an outcome of the LMS Durham Symposium convened by Professor C.T.H. Baker on 4th–14th July 1992 with support from the SERC under Grant reference number GR/H03964.  相似文献   

10.
We generalize the well-known fact that for a pair of Morita equivalent ringsR andS their maximal rings of quotients are again Morita equivalent: If n (M) denotes the torsion theory cogenerated by the direct sum of the firstn+1 injective modules forming part of the minimal injective resolution ofM then n (R)= n (S) where is the category equivalenceR-ModS-Mod. Consequently the localized ringsR n (R) andS n (S) are Morita equivalent.  相似文献   

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