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1.
We construct a homology transfer *H*(B) H*(E) for a certain class of proper simplicial maps pE B. Roughly, the important hypothesis is that there is a compact space F, so that all fibres Fx>=p–1(x), xB, are quotient spaces of F, in a certain locally controlled manner. The composition p** H*(B)H*(E)H*(B) is multiplication by the Euler characteristic of F.  相似文献   

2.
. , BMO VMO.

This paper is a part of the author's Ph.D. thesis written under the supervision of Prof. F. Schipp, Eötvös L. University, Budapest.  相似文献   

3.
We consider the heat equation on ={(x,t) R 2;t<0, ¦x¦<(–t)} and give the uniqueness of kernel functions at the infinity (see Theorem 5). For the proof, we examine the continuity of the density of the parabolic measure onD ={(x,t);t>x}, closely related to . By this theorem, we can decide the Martin boundary of (<1) with respect to the heat equation.  相似文献   

4.
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   

5.
Summary Letu h be the finite element solution to–u=f with zero boundary conditions in a convex polyhedral domain . Fromu h we calculate for eachz and ||1 an approximationu h (z) toD u(z) with |D u(z)u h (z)|=O(h 2k–2) wherek is the order of the finite elements. The same superconvergence order estimates are obtained also for the boundary flux. We need not work on a regular mesh but we have to compute averages ofu h where the diameter of the domain of integration must not depend onh.  相似文献   

6.
We present a characterization of the normal optimal solution of the linear program given in canonical form max{c tx: Ax = b, x 0}. (P) We show thatx * is the optimal solution of (P), of minimal norm, if and only if there exists anR > 0 such that, for eachr R, we havex * = (rc – Atr)+. Thus, we can findx * by solving the following equation for r A(rc – Atr)+ = b. Moreover,(1/r) r then converges to a solution of the dual program.On leave from The University of Alberta, Edmonton, Canada. Research partially supported by the National Science and Engineering Research Council of Canada.  相似文献   

7.
Summary The inverse Sturm-Liouville problem is the problem of finding a good approximation of a potential functionq such that the eigenvalue problem (*)–y +qy=y holds on (0, ) fory(0)=y()=0 and a set of given eigenvalues . Since this problem has to be solved numerically by discretization and since the higher discrete eigenvalues strongly deviate from the corresponding Sturm-Liouville eigenvalues , asymptotic corrections for the 's serve to get better estimates forq. Let k (1kn) be the first eigenvalues of (*), let k be the corresponding discrete eigenvalues obtained by the finite element method for (*) and let k k for the special caseq=0. Then, starting from an asymptotic correction technique proposed by Paine, de Hoog and Anderssen, new estimates for the errors of the corrected discrete eigenvalues are obtained and confirm and improve the knownO(kh 2)(h:=/(n+1)) behaviour. The estimates are based on new Sobolev inequalities and on Fourier analysis and it is shown that for 4+c 2 k(n+1)/2, wherec 1 andc 2 are constants depending onq which tend to 0 for vanishingq.  相似文献   

8.
In this paper we prove that the moduli spaces MI 2n+1(k) of mathematical instanton bundles on 2n+1 with quantum number k are singular for n 2 and k 3 ,giving a positive answer to a conjecture made by Ancona and Ottaviani in 1993.  相似文献   

9.
In this paper, we study (real) eigenvalues and eigenvectors of convex processes, and provide conditions for the existence of eigenvectors in a given convex coneK n . It is established that the maximal eigenvalue ofG(·) inK is expressed by (whereK 0 is the polar cone ofK) provided that the minimum is attained in intK 0. This result is applied to study the asymptotic behaviour of certain differential inclusions{G(x(t)). We extend some known results for the von Neumann-Gale model to our more general framework. We prove that ifx 0 is the unique eigenvector corresponding to the maximal eigenvalue 0 ofG(·) inK, then the nonexistence of solutions of a certain special trigonometric form is necessary and sufficient for every viable solutionx(·) to satisfy- 0 t x(t)cx 0 ast for somec0. Our method is to study the family of convex conesW =cl{vx :xK,vG(x) where is any real number. We characterize the maximal eigenvalue 0 as the minimal for whichW can be separated fromK.The research was supported in part by a grant from the ministry of science and the Maagara special project for the absorption of new immigrants in the Department of Mathematics at Technion.  相似文献   

10.
A quasilinear equation u -x·u/2+f(u)=0 is studied, wheref(u)=–u+u , > 0, 0<. <1, >1 andx R n. The equation arises from the study of blow-up self-similar solutions of the heat equation t =+. We prove the existence and non-existence of ground state for various combination of , and . In particular, we prove that when / < forn=1,2 or / < (n + 2) /(n – 2) forn 3 there exists no non-constant positive radial self-similar solution of the parabolic equation, but for many cases where / > (n + 2)/(n – 2) there exists an infinite number of non-constant positive radial self-similar solutions.  相似文献   

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