共查询到20条相似文献,搜索用时 421 毫秒
1.
Let I=[0,1] and let P be a partition of I into a finite number of intervals. Let τ1, τ2; I→I be two piecewise expanding maps on P . Let G⊂I×I be the region between the boundaries of the graphs of τ1 and τ2. Any map τ:I→I that takes values in G is called a selection of the multivalued map defined by G . There are many results devoted to the study of the existence of selections with specified topological properties. However, there are no results concerning the existence of selection with measure-theoretic properties. In this paper we prove the existence of selections which have absolutely continuous invariant measures (acim). By our assumptions we know that τ1 and τ2 possess acims preserving the distribution functions F(1) and F(2). The main result shows that for any convex combination F of F(1) and F(2) we can find a map η with values between the graphs of τ1 and τ2 (that is, a selection) such that F is the η-invariant distribution function. Examples are presented. We also study the relationship of the dynamics of our multivalued maps to random maps. 相似文献
2.
Let S(Gσ) be the skew adjacency matrix of the oriented graph Gσ of order n and λ1,λ2,…,λn be all eigenvalues of S(Gσ). The skew spectral radius ρs(Gσ) of Gσ is defined as max{|λ1|,|λ2|,…,|λn|}. In this paper, we investigate oriented graphs whose skew spectral radii do not exceed 2. 相似文献
3.
Sergey A. Antonyan Natalia Jonard-Pérez Saúl Juárez-Ordóñez 《Journal of Mathematical Analysis and Applications》2014
A compact convex subset K of a topological linear space is called a Keller compactum if it is affinely homeomorphic to an infinite-dimensional compact convex subset of the Hilbert space ?2. Let G be a compact topological group acting affinely on a Keller compactum K and let 2K denote the hyperspace of all non-empty compact subsets of K endowed with the Hausdorff metric topology and the induced action of G . Further, let cc(K) denote the subspace of 2K consisting of all compact convex subsets of K. In a particular case, the main result of the paper asserts that if K is centrally symmetric, then the orbit spaces 2K/G and cc(K)/G are homeomorphic to the Hilbert cube. 相似文献
4.
5.
Consider in a real Hilbert space H the Cauchy problem (P0): u′(t)+Au(t)+Bu(t)=f(t), 0≤t≤T; u(0)=u0, where −A is the infinitesimal generator of a C0-semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem (P0) the following regularization (Pε): −εu″(t)+u′(t)+Au(t)+Bu(t)=f(t), 0≤t≤T; u(0)=u0, u′(T)=uT, where ε>0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem (Pε). Then we establish asymptotic expansions of order zero, and of order one, for the solution of (Pε). Problem (Pε) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C([0,T];H). However, the boundary layer of order one is not visible through the norm of L2(0,T;H). 相似文献
6.
Let K be a hypergroup with a Haar measure. The purpose of the present paper is to initiate a systematic approach to the study of the class of invariant complemented subspaces of L∞(K) and C0(K), the class of left translation invariant w?-subalgebras of L∞(K) and finally the class of non-zero left translation invariant C?-subalgebras of C0(K) in the hypergroup context with the goal of finding some relations between these function spaces. Among other results, we construct two correspondences: one, between closed Weil subhypergroups and certain left translation invariant w?-subalgebras of L∞(K), and another, between compact subhypergroups and a specific subclass of the class of left translation invariant C?-subalgebras of C0(K). By the help of these two characterizations, we extract some results about invariant complemented subspaces of L∞(K) and C0(K). 相似文献
7.
8.
In this paper, we consider the problem (Pε) : Δ2u=un+4/n-4+εu,u>0 in Ω,u=Δu=0 on ∂Ω, where Ω is a bounded and smooth domain in Rn,n>8 and ε>0. We analyze the asymptotic behavior of solutions of (Pε) which are minimizing for the Sobolev inequality as ε→0 and we prove existence of solutions to (Pε) which blow up and concentrate around a critical point of the Robin's function. Finally, we show that for ε small, (Pε) has at least as many solutions as the Ljusternik–Schnirelman category of Ω. 相似文献
9.
We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical (α<1/2) dissipation α(−Δ): If a Leray–Hopf weak solution is Hölder continuous θ∈Cδ(R2) with δ>1−2α on the time interval [t0,t], then it is actually a classical solution on (t0,t]. 相似文献
10.
Jean-Pierre Kahane 《Comptes Rendus Mathematique》2014,352(5):383-385
For almost all x>1, (xn)(n=1,2,…) is equidistributed modulo 1, a classical result. What can be said on the exceptional set? It has Hausdorff dimension one. Much more: given an (bn) in [0,1[ and ε>0, the x -set such that |xn−bn|<ε modulo 1 for n large enough has dimension 1. However, its intersection with an interval [1,X] has a dimension <1, depending on ε and X. Some results are given and a question is proposed. 相似文献
11.
Let G be a simple connected graph of order n with degree sequence d1,d2,…,dn in non-increasing order. The signless Laplacian spectral radius ρ(Q(G)) of G is the largest eigenvalue of its signless Laplacian matrix Q(G). In this paper, we give a sharp upper bound on the signless Laplacian spectral radius ρ(Q(G)) in terms of di, which improves and generalizes some known results. 相似文献
12.
We study the problem (−Δ)su=λeu in a bounded domain Ω⊂Rn, where λ is a positive parameter. More precisely, we study the regularity of the extremal solution to this problem. Our main result yields the boundedness of the extremal solution in dimensions n≤7 for all s∈(0,1) whenever Ω is, for every i=1,...,n, convex in the xi-direction and symmetric with respect to {xi=0}. The same holds if n=8 and s?0.28206..., or if n=9 and s?0.63237.... These results are new even in the unit ball Ω=B1. 相似文献
13.
14.
15.
16.
Fritz Grunewald Andrei Jaikin-Zapirain Aline G.S. Pinto Pavel A. Zalesskii 《Journal of Pure and Applied Algebra》2014
The principal goal of the paper is to show that the existence of a finitely generated normal subgroup of infinite index in a profinite group G of non-negative deficiency gives rather strong consequences for the structure of G. To make this precise we introduce the notion of p-deficiency (p a prime) for a profinite group G. We prove that if the p-deficiency of G is positive and N is a finitely generated normal subgroup such that the p -Sylow subgroup of G/N is infinite and p divides the order of N then we have cdp(G)=2, cdp(N)=1 and vcdp(G/N)=1 for the cohomological p-dimensions; moreover either the p -Sylow subgroup of G/N is virtually cyclic or the p-Sylow subgroup of N is cyclic. If G is a profinite Poincaré duality group of dimension 3 at a prime p (PD3-group at p) we show that for N and p as above either N is PD1 at p and G/N is virtually PD2 at p or N is PD2 at p and G/N is virtually PD1 at p. 相似文献
17.
We show that for each p∈(0,1] there exists a separable p -Banach space Gp of almost universal disposition, that is, having the following extension property: for each ε>0 and each isometric embedding g:X→Y, where Y is a finite-dimensional p-Banach space and X is a subspace of Gp, there is an ε -isometry f:Y→Gp such that x=f(g(x)) for all x∈X. 相似文献
18.
20.
In this paper we investigate the one-dimensional Schrodinger operator L(q) with complex-valued periodic potential q when q∈L1[0,1] and qn=0 for n=0,−1,−2,..., where qn are the Fourier coefficients of q with respect to the system {ei2πnx}. We prove that the Bloch eigenvalues are (2πn+t)2 for n∈Z, t∈C and find explicit formulas for the Bloch functions. Then we consider the inverse problem for this operator. 相似文献