共查询到20条相似文献,搜索用时 31 毫秒
1.
Rumen Tsanev Marinov 《Rendiconti del Circolo Matematico di Palermo》2009,58(1):11-27
In this article, we study an iterative procedure of the following form
, where f is a function and F is a set valued map acting from a Banach space X to a linear normed space Y, for solving generalized equations.
We show that this method is locally Q-linearly convergent to a solution x* of the generalized equation
if the set-valued map
is Aubin continuous at (0, x*) with a constant M for growth, f: X → Y is a function, whose Fréchet derivative is L-Lipschitz and A ∈ L(X,Y) is such that 2M∥Δf(x*) − A∥ < 1. We also study the stability of this method.
The research of this paper is partially supported by a Technical University of Varna internal research grant number 487/2008. 相似文献
2.
Marc Coppens 《Arkiv f?r Matematik》2008,46(1):31-41
Let X be a smooth n-dimensional projective variety embedded in some projective space ℙ
N
over the field ℂ of the complex numbers. Associated with the general projection of X to a space ℙ
N-m
(N-m>n+1) one defines an extended Gauss map (in case N-m>2n-1 this is the Gauss map of the image of X under the projection). We prove that is smooth. In case any two different points of X do have disjoint tangent spaces then we prove that is injective. 相似文献
3.
Johnson William B. Lindenstrauss Joram Schechtman Gideon 《Israel Journal of Mathematics》1986,54(2):129-138
It is proved that ifY ⊂X are metric spaces withY havingn≧2 points then any mapf fromY into a Banach spaceZ can be extended to a map
fromX intoZ so that
wherec is an absolute constant. A related result is obtained for the case whereX is assumed to be a finite-dimensional normed space andY is an arbitrary subset ofX.
Supported in part by US-Israel Binational Science Foundation and by NSF MCS-7903042.
Supported in part by NSF MCS-8102714. 相似文献
4.
Let X be a Lévy process in, , obtained by subordinating Brownian motion with a subordinator with a positive drift. Such a process has the same law as the sum of an independent Brownian motion and a Lévy process with no continuous component. We study the asymptotic behavior of the Green function of X near zero. Under the assumption that the Laplace exponent of the subordinator is a complete Bernstein function we also describe the asymptotic behavior of the Green function at infinity. With an additional assumption on the Lévy measure of the subordinator we prove that the Harnack inequality is valid for the nonnegative harmonic functions of X. 相似文献
5.
María J. Carro 《Mathematische Zeitschrift》2007,255(4):813-825
Given a sublinear operator T such that is bounded, it can be shown that is bounded, with constant C/(1−q), for every 0 < q < 1. In this paper, we study the converse result, not only for sequence spaces, but for general measure spaces proving that,
if T : L
q
(μ) → X is bounded, with constant C/(1−q), for every and X is Banach, then T : L log (1/L)(μ) → X is bounded. Moreover, this result is optimal. We also show that things are quite different if the Banach condition on X is dropped.
This work has been partially supported by MTM2004-02299 and by 2005SGR00556. 相似文献
6.
Rasul Shafikov 《Mathematische Zeitschrift》2007,256(4):757-767
If R is a real analytic set in (viewed as ), then for any point p∈R there is a uniquely defined germ X
p
of the smallest complex analytic variety which contains R
p
, the germ of R at p. It is shown that if R is irreducible of constant dimension, then the function p→ dim X
p
is constant on a dense open subset of R. As an application it is proved that a continuous map from a real analytic CR manifold M into which is CR on some open subset of M and whose graph is a real analytic set in is necessarily CR everywhere on M. 相似文献
7.
Abstract A classical result of A. D. Alexandrov states that a connected compact smooth n-dimensional manifold without boundary, embedded in ℝn+1, and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of M in a hyperplane Xn+1 =constant in case M satisfies: for any two points (X′,Xn+1),
on M, with
, the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper,
we establish it under some additional conditions. Some variations of the Hopf Lemma are also presented. Several open problems
are described. Part I dealt with corresponding one dimensional problems.
(Dedicated to the memory of Shiing-Shen Chern)
* Partially supported by NSF grant DMS-0401118. 相似文献
8.
Melanie Rupflin 《Calculus of Variations and Partial Differential Equations》2008,33(3):329-341
Generalizing a result of Freire regarding the uniqueness of the harmonic map flow from surfaces to an arbitrary closed target
manifold N, we show uniqueness of weak solutions u ∈ H
1 under the assumption that any upwards jumps of the energy function are smaller than a geometrical constant , thus establishing a conjecture of Topping, under the sole additional condition that the variation of the energy is locally
finite. 相似文献
9.
Kameswarrao S. Casukhela 《Journal of Theoretical Probability》1997,10(3):759-771
An infinite sequence of random variables X=(X
1, X
2,...) is said to be spreadable if all subsequences of X have the same distribution. Ryll-Nardzewski showed that X is spreadable iff it is exchangeable. This result has been generalized to various discrete parameter and higher dimensional settings. In this paper we show that a random measure on the tetrahedral space
is spreadable, iff it can be extended to an exchangeable random measure on
. The result is a continuous parameter version of a theorem by Kallenberg. 相似文献
10.
We prove a local variational principle of pressure for any given open cover. More precisely, for a given dynamical system
(X, T), an open cover
of X, and a continuous, real-valued function f on X, we show that the corresponding local pressure P(T, f;
) satisfies
, moreover, the supremum can be attained by a T-invariant ergodic measure. By establishing the upper semi-continuity and affinity of the entropy map relative to an open
cover, we further show that
for any T-invariant measure μ of (X, T), i.e., local pressures determine local measure-theoretic entropies. As applications, properties of both local and global
equilibrium states for a continuous, real-valued function are studied.
The first author is partially supported by NSFC Grants 10531010 and 10401031, program of new century excellent talents in
universities, special foundation on excellent Ph.D thesis, and presidential award of the Chinese Academy of Sciences.
The second author is partially supported by NSF grant DMS0204119 and NSFC grant 10428101. 相似文献
11.
12.
A. Languasco 《Monatshefte für Mathematik》2004,141(2):147-169
Denote by E[X,X+H] the set of even integers in [X,X+H] that are not a sum of two primes (i.e. that are not Goldbach numbers). Here we prove that there exists a (small) positive constant such that for
we have
. 相似文献
13.
Let X and Y be reduced complex spaces with countable topology. Let
be a locally semi-finite holomorphic map such that the analytic set
is nowhere dense in X. If Y is complete Kähler, then we prove that X is also complete Kähler. Especially if
is a (not necessarily finitely sheeted) ramified covering over a complete Kähler space Y, then X is also complete Kähler.
Received: 2 August 2002 相似文献
14.
Let X be a compact metric space and let Lip(X) be the Banach algebra of all scalar- valued Lipschitz functions on X, endowed with a natural norm. For each f ∈ Lip(X), σπ(f) denotes the peripheral spectrum of f. We state that any map Φ from Lip(X) onto Lip(Y) which preserves multiplicatively the peripheral spectrum:
σπ(Φ(f)Φ(g)) = σπ(fg), A↓f, g ∈ Lip(X)
is a weighted composition operator of the form Φ(f) = τ· (f °φ) for all f ∈ Lip(X), where τ : Y → {-1, 1} is a Lipschitz function and φ : Y→ X is a Lipschitz homeomorphism. As a consequence of this result, any multiplicatively spectrum-preserving surjective map between Lip(X)-algebras is of the form above. 相似文献
σπ(Φ(f)Φ(g)) = σπ(fg), A↓f, g ∈ Lip(X)
is a weighted composition operator of the form Φ(f) = τ· (f °φ) for all f ∈ Lip(X), where τ : Y → {-1, 1} is a Lipschitz function and φ : Y→ X is a Lipschitz homeomorphism. As a consequence of this result, any multiplicatively spectrum-preserving surjective map between Lip(X)-algebras is of the form above. 相似文献
15.
We devise a new embedding technique, which we call measured descent, based on decomposing a metric space locally, at varying speeds, according to the density of some probability measure. This
provides a refined and unified framework for the two primary methods of constructing Fréchet embeddings for finite metrics,
due to Bourgain (1985) and Rao (1999). We prove that any n-point metric space (X, d) embeds in Hilbert space with distortion
where αX is a geometric estimate on the decomposability of X. As an immediate corollary, we obtain an
distortion embedding, where λX is the doubling constant of X. Since λX ≤ n, this result recovers Bourgain’s theorem, but when the metric X is, in a sense, “low-dimensional,” improved bounds are achieved.
Our embeddings are volume-respecting for subsets of arbitrary size. One consequence is the existence of (k, O(log n)) volume-respecting embeddings for all 1 ≤ k ≤ n, which is the best possible, and answers positively a question posed by U. Feige. Our techniques are also used to answer
positively a question of Y. Rabinovich, showing that any weighted n-point planar graph embeds in
with O(1) distortion. The O(log n) bound on the dimension is optimal, and improves upon the previously known bound of O((log n)2).
Received: April 2004 Accepted: August 2004 Revision: December 2004
J.R.L. Supported by NSF grant CCR-0121555 and an NSF Graduate Research Fellowship. 相似文献
16.
Let X be a nonempty measurable subset of and consider the restriction of the usual Lebesgue measure σ of to X. Under the assumption that the intersection of X with every open ball of has positive measure, we find necessary and sufficient conditions on a L2(X)-positive definite kernel in order that the associated integral operator be nuclear. Taken nuclearity for granted, formulas for the trace of the operator are derived. Some of the results are re-analyzed
when K is just an element of .
相似文献
17.
Peter Raith 《Journal d'Analyse Mathématique》1999,78(1):117-142
Assume thatX is a finite union of closed intervals and consider aC
1-mapX→ℝ for which {c∈X: T′c=0} is finite. Set
. Fix ann ∈ ℕ. For ε>0, theC
1-map
is called an ε-perturbation ofT if
is a piecewise monotonic map with at mostn intervals of monotonicity and
is ε-close toT in theC
1-topology. The influence of small perturbations ofT on the dynamical system (R(T),T) is investigated. Under a certain condition on the continuous functionf:X → ℝ, the topological pressure is lower semi-continuous. Furthermore, the topological pressure is upper semi-continuous for
every continuous functionf:X → ℝ. If (R(T),T) has positive topological entropy and a unique measure μ of maximal entropy, then every sufficiently small perturbation
ofT has a unique measure
of maximal entropy, and the map
is continuous atT in the weak star-topology. 相似文献
18.
We prove that for every n ∈ ? there exists a metric space (X, d X), an n-point subset S ? X, a Banach space (Z, \({\left\| \right\|_Z}\)) and a 1-Lipschitz function f: S → Z such that the Lipschitz constant of every function F: X → Z that extends f is at least a constant multiple of \(\sqrt {\log n} \). This improves a bound of Johnson and Lindenstrauss [JL84]. We also obtain the following quantitative counterpart to a classical extension theorem of Minty [Min70]. For every α ∈ (1/2, 1] and n ∈ ? there exists a metric space (X, d X), an n-point subset S ? X and a function f: S → ?2 that is α-Hölder with constant 1, yet the α-Hölder constant of any F: X → ?2 that extends f satisfies \({\left\| F \right\|_{Lip\left( \alpha \right)}} > {\left( {\log n} \right)^{\frac{{2\alpha - 1}}{{4\alpha }}}} + {\left( {\frac{{\log n}}{{\log \log n}}} \right)^{{\alpha ^2} - \frac{1}{2}}}\). We formulate a conjecture whose positive solution would strengthen Ball’s nonlinear Maurey extension theorem [Bal92], serving as a far-reaching nonlinear version of a theorem of König, Retherford and Tomczak-Jaegermann [KRTJ80]. We explain how this conjecture would imply as special cases answers to longstanding open questions of Johnson and Lindenstrauss [JL84] and Kalton [Kal04]. 相似文献
19.
In classical topology it is proved, nonconstructively, that for a topological space X, every bounded Riesz map ϕ in C(X) is of the form
for a point x ∈ X. In this paper our main objective is to give the pointfree version of this result. In fact, we constructively represent each
real Riesz map on a compact frame M by prime elements.
Received March 23, 2004; accepted in final form May 14, 2005. 相似文献
20.
An (n,k)-affine source over a finite field is a random variable X = (X
1,..., X
n
) ∈ , which is uniformly distributed over an (unknown) k-dimensional affine subspace of . We show how to (deterministically) extract practically all the randomness from affine sources, for any field of size larger
than n
c
(where c is a large enough constant). Our main results are as follows:
Research supported by Israel Science Foundation (ISF) grant. 相似文献
1. | (For arbitrary k): For any n,k and any of size larger than n 20, we give an explicit construction for a function D : → , such that for any (n,k)-affine source X over , the distribution of D(X) is ∊-close to uniform, where ∊ is polynomially small in ||. |
2. | (For k=1): For any n and any of size larger than n c , we give an explicit construction for a function D: , such that for any (n, 1)-affine source X over , the distribution of D(X) is ∊-close to uniform, where ∊ is polynomially small in ||. Here, δ>0 is an arbitrary small constant, and c is a constant depending on δ. |