摘要:

AbstractWe consider motion on the circle, possibly with friction and external forces, the initial velocity being a large random variable. We prove that under various assumptions the probability law of the stopping position of the motion converges to a distribution depending only on the motion equation. Here the time of stopping is either a constant or the first time instant at which the velocity vanishes, and the initial velocity is of the form αU+ β, whereUis a fixed random variable and α and/or β tend to infin

ISSN:0025-584X    

DOI:10.1002/mana.19981890102

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractIn this paper we focus on three fixed point theorems and an integral equation. Schaefer's fixed point theorem will yield a T‐periodic solution of(0.1)x(t)= a(t)+tt‐hD(t,s)g(s,x(s))dsifDandgsatisfy certain sign conditions independent of their magnitude. A combination of the contraction mapping theorem and Schauder's theorem (known as Krasnoselskii's theorem) will yield a T‐periodic solution of(0.2)x(t)= f(t,x(t)) +tt‐hD(t,s)g(s,x(s))dsiffdefines a contraction and ifDandgare small enough.We prove a fixed point theorem which is a combination of the contraction mapping theorem and Schaefer's theorem which yields a T‐periodic solution of (0.2) when / defines a contraction mapping, whileDandgsatisfy the aforementioned sign c

ISSN:0025-584X    

DOI:10.1002/mana.19981890103

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractA system of functions satisfies Descartes' rule of signs if the number of zeros (with multiplicities) of a linear combination of these functions is less than or equal to the number of variations of strict sign in the sequence of the coefficients. In this paper we characterize the systems of functions satisfying a stronger property than the above mentioned Descartes' rule: The difference between the number of zeros and the changes of sign in the sequence of coefficients must be always a nonnegative even number. We show that the approximation to the number of zeros given by these systems of functions is better than the approximation provided by any other systems of functions satisfying a Descartes' rule of signs. This last result improves, in the particular case of polynomials, the main theorem of [14].

ISSN:0025-584X    

DOI:10.1002/mana.19981890104

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractLetEbe a realq‐uniformly smooth Banach space. SupposeTis a strongly pseudo‐contractive map with open domainD(T) inE.Suppose further that T has a fixed point inD(T).Under various continuity assumptions onTit is proved that each of the Mann iteration process or the Ishikawa iteration method converges strongly to the unique fixed point of T. Related results deal with iterative solutions of nonlinear operator equations involving strongly accretive maps. Explicit error estimates are also provi

ISSN:0025-584X    

DOI:10.1002/mana.19981890105

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractThe Dirichlet, Neumann and mixed problems of statics of the theory of elasticity for anisotropic homogeneous media are studied inn‐dimensional (n≧ 2) domains with boundaries containing closed cuspidal edges. Theorems of the existence and uniqueness of solutions of these problems in the Besov and Bessel potential spaces are obtained. Smoothness of solutions in a closed domain occupied by elastic medium is investiga

ISSN:0025-584X    

DOI:10.1002/mana.19981890106

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractSuppose G is a connected reductive algebraic group,Pis a parabolic subgroup of G,Lis a Levi factor ofP, and e is a regular nilpotent element in Lie L. We assume that the characteristic of the underlying field is good for G. Choose a maximal torus,T, and a Borel subgroup,B, of G, so that T⊆B∩L,B ⊆ Pande ∈LieB.Let β be the variety of Borel subgroups ofGand let

ISSN:0025-584X    

DOI:10.1002/mana.19981890107

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractWe prove a natural generalization of Kneser's oscillation and Hardy's inequality for Sturm‐Liouville differential expressions. In Particular, assuming − d/dxp0(x)+q0(x), x ∈ a, b), −∞≦a

ISSN:0025-584X    

DOI:10.1002/mana.19981890108

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractSupposeGis a Lie group acting as a group of holomorphic automorphisms on a holomorphic principal bundleP→X.We show that if there is a holomorphic action of the complexificationGCof G on. X, this lifts to a holomorphic action ofGCon the bundleP→X.Two applications are presented. We prove that given any connected homogeneous complex manifoldG/Hwith more than one end, the complexificationGCofGacts holomorphically and transitively onG/H.We also show that the ends of a homogeneous complex manifoldG/Hwith more than two ends essentially come from a space of the formS/Γ, where Γ is a Zariski dense discrete subgroup of a semisimple complex Lie group S with S and Γ being explicitly constructed in terms o

ISSN:0025-584X    

DOI:10.1002/mana.19981890109

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractA nonlinear spectral problem for a Sturm‐Liouville equation‐(p(x, λ)y'(x, λ))' +q(x, λ)y(x, λ) = 0 on a finite interval [a,b] with λ‐dependent boundary conditions is considered. The spectral parameter λ is varying in an interval ∧ andp(x, λ),q(x, A) are real, continuous functions on [a,b] × ∧ Some criteria to the eigenvalue accumulation at the endpoints of A will be established. The results are applied to concrete problems arising in mag

ISSN:0025-584X    

DOI:10.1002/mana.19981890110

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractWe first study the asymptotic behavior of nonlinear semigroups with holomorphic generators, and then use our results, inter alia, to construct holomorphic retractions onto the fixed point sets of holomorphic self‐mappings of bounded convex domains in a complex Banach spac

ISSN:0025-584X    

DOI:10.1002/mana.19981890111

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY