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The nontangential behavior of the Bergman metric near a smooth convex boundary point of a bounded pseudoconvex domain D n is studied in terms of its multitype.Received January 25, 2002; in revised form June 20, 2002 Published online November 18, 2002  相似文献   

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( « . III») - B p,q g(x) F p,q g(x) ( ) R n . --, . : , , , .  相似文献   

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It is proved that if D is a bounded open subset of a uniformly convex Banach space X and is a continuous mapping which is a local pseudo-contraction (e.g., locally nonexpansive) on D, then T has a fixed point in D if there exists xD such that z–Tz相似文献   

5.
We consider hypergroups associated with Jacobi functions () (x), (–1/2). We prove the existence of a dual convolution structure on [0,+[i(]0,s 0]{{) =++1,s 0=min(,–+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem.  相似文献   

6.
A. V. Pazhitnov 《K-Theory》1996,10(4):323-412
Let M be a closed connected smooth manifold with dim M=n6, and : 1(M) Z be an epimorphism. Denote by the group ring of 1(M) and let be its Novikov completion. Let D * be a free-based finitely generated chain complex over . Assume that D ii=0 for i1 and in–1 and that D * has the same simple homotopy type as the Novikov-completed simplicial chain complex of the universal covering M. Let N be an integer. We prove that D * can be realized, up to the terms of of degree N as the Novikov complex of a Morse map : M S 1, belonging to . Applications to Arnold's conjectures and to the theory of fibering of M over S 1 are given.  相似文献   

7.
Summary The Cahn-Hilliard model for phase separation in a binary alloy leads to the equations (I) ut=w, (II) w= (u)– u with an associated energy functional F(u)=f [(u)+ +¦u¦2/2] dx. In this paper we discuss the existence theory for initial bounday value problems arising from modifications to the Cahn-Hilliard model due to the addition of the non-differentiable term ¦u¦dx to the energy F(u).  相似文献   

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For families of processes with independent increments (t), 0tT, with frequent small jumps, limit theorems for expectations of the functionals F([0, T]) are proved of the form where diD, are positive numbers, A di are linear integro-differential or differential operators acting on functionals, and some differentiability conditions are imposed on the functional F. The case of power tails of the jump distribution is considered.Mathematics Subject Classification (2000):60F17  相似文献   

9.
The Brownian loop soup   总被引:6,自引:0,他引:6  
We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to chronologically add Brownian loops to simple curves in the plane.Cornell University; Research supported in part by the National Science FoundationUniversité Paris-Sud and IUFMathematics Subject Classification (2000):60J65, 81T40  相似文献   

10.
Summary We say that a curve C in P 3 has maximal rank if for every integer k the restriction map rc(k):H 0(P 3, OP3(k)) H0 (C, OC(k))has maximal rank. Here we prove the following results. Theorem 1Fix integers g, d with 0g3,dg+3.Fix a curve X of genus g and L Picd (X).If g=3and X is hyperelliptic, assume d8. Let L(X)be the image of X by the complete linear system H 0(X, L). Then a general projection of L(X)into P 3 has maximal rank. Theorem 2For every integer g0,there exists an integer d(g, 3)such that for every dd(g, 3),for every smooth curve X of genus g and every LPicd (X) the general projection of L(X)into P 3 has maximal rank.  相似文献   

11.
A minimization problem with convex and separable objective function subject to a separable convex inequality constraint and bounded variables is considered. A necessary and sufficient condition is proved for a feasible solution to be an optimal solution to this problem. Convex minimization problems subject to linear equality/linear inequality constraint, and bounds on the variables are also considered. A necessary and sufficient condition and a sufficient condition, respectively, are proved for a feasible solution to be an optimal solution to these two problems. Algorithms of polynomial complexity for solving the three problems are suggested and their convergence is proved. Some important forms of convex functions and computational results are given in the Appendix.  相似文献   

12.
We study the minimum number g(m,n) (respectively, p(m,n)) of pieces needed to dissect a regular m-gon into a regular n-gon of the same area using glass-cuts (respectively, polygonal cuts). First we study regular polygon-square dissections and show that n/2 -2 g(4,n) (n/2) + o(n) and n/4 g(n,4) (n/2) + o(n) hold for sufficiently large n. We also consider polygonal cuts, i.e., the minimum number p(4,n) of pieces needed to dissect a square into a regular n-gon of the same area using polygonal cuts and show that n/4 p(4,n) (n/2) + o(n) holds for sufficiently large n. We also consider regular polygon-polygon dissections and obtain similar bounds for g(m,n) and p(m,n).  相似文献   

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A set X of boundary points of a (possibly unbounded) convex body KE d illuminating K from within is called primitive if no proper subset of X still illuminates K from within. We prove that for such a primitive set X of an unbounded, convex set KE d (distinct from a cone) one has X=2 if d=2, X6 if d=3, and that there is no upper bound for X if d4.  相似文献   

14.
Let n be n-dimensional Euclidean space, and let : [0, L] n and : [0, L] n be closed rectifiable arcs in n of the same total length L which are parametrized via their arc length. is said to be a chord-stretched version of if for each 0s tL, |(t)–(s)| |(t)–(s)|. is said to be convex if is simple and if ([0, L]) is the frontier of some plane convex set. Individual work by Professors G. Choquet and G. T. Sallee demonstrated that if were simple then there existed a convex chord-stretched version of . This result led Professor Yang Lu to conjecture that if were convex and were a chord-stretched version of then and would be congruent, i.e. any chord-stretching map of a convex arc is an isometry. Professor Yang Lu has proved this conjecture in the case where and are C 2 curves. In this paper we prove the conjecture in general.  相似文献   

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In this paper, we give a complete characterization for the class of rational finite metrics with the property that the set () of primitive extensions of is finite. Here, for a metric on a setT, a positive extensionm of to a setV T is calledprimitive if none of the convex combinations of other extensions of toV is less than or equal tom. Our main theorem asserts that the following the properties are equivalent: (i) () is finite; (ii) Up to an integer factor, is a submetric of the path metric d H of a graphH with |(d H )=1; (iii) A certain bipartite graph associated with contains neither isometrick-cycles withk6 nor induced subgraphsK 3,3 . We then show that () is finite if and only if the dimension of the tight span of is at most two. We also present other results, discuss applications to multicommodity flows, and raise open problems.This research was supported by grant 97-01-00115 from the Russian Foundation of Basic Research and a grant from the Sonderforschungsbereich 343, Bielefeld Universität, Bielefeld, Germany.  相似文献   

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Let f C[a, b]. LetP be a subset ofC[a, b], L b – a be a given real number. We say thatp P is a best approximation tof fromP, with arc length constraintL, ifA[p] b a [1 + (p(x)) 2]dx L andp – f q – f for allq P withA[q] L. represents an arbitrary norm onC[a, b]. The constraintA[p] L might be interpreted physically as a materials constraint.In this paper we consider the questions of existence, uniqueness and characterization of constrained best approximations. In addition a bound, independent of degree, is found for the arc length of a best unconstrained Chebyshev polynomial approximation.The work of L. L. Keener is supported by the National Research Council of Canada Grant A8755.  相似文献   

17.
Summary The following theorem holds true. Theorem. Let X be a normed real vector space of dimension 3 and let k > 0 be a fixed real number. Suppose that f: X X and g: X × X are functions satisfying x – y = k f(x) – f(y) = g(x, y)(x – y) for all x, y X. Then there exist elements and t X such that f(x) = x + t for all x X and such that g(x, y) = for all x, y X with x – y = k.  相似文献   

18.
We give efficiency estimates for proximal bundle methods for finding f*minXf, where f and X are convex. We show that, for any accuracy <0, these methods find a point xkX such that f(xk)–f* after at most k=O(1/3) objective and subgradient evaluations.  相似文献   

19.
Summary The hydrodynamic limit for a Markov process of [0, )-valued spin fields on a periodic multidimensional lattice is studied. In the process a positive real number, called energy, is attached to each site of the lattice and each couple of adjacent sites exchange thier energy by random amounts at random times. The law of the exchange is such that the sum of the total energy is conserved, and that the process is reversible and of gradient type for the energy distribution. We show that under diffusion type scaling of space and time, the macroscopic energy distribution converges to a deterministic limit which is characterized by a non-linear diffusion equation /t=2–1P(), whereP is an increasing function which in a typical case equals const·2.  相似文献   

20.
By using the classical Hadamard theorem, we obtain an exact (in a certain sense) inequality for the best polynomial approximations of an analytic function f(z) from the Hardy space H p, p 1, in disks of radii , 1, and 2, 0 < 1 < < 2 < 1.  相似文献   

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