共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove that if for a continuous map f on a compact metric space X, the chain recurrent set, R(f) has more than one chain component, then f does not satisfy the asymptotic average shadowing property. We also show that if a continuous map f on a compact metric space X has the asymptotic average shadowing property and if A is an attractor for f, then A is the single attractor for f and we have A=R(f). We also study diffeomorphisms with asymptotic average shadowing property and prove that if M is a compact manifold which is not finite with dimM=2, then the C1 interior of the set of all C1 diffeomorphisms with the asymptotic average shadowing property is characterized by the set of Ω-stable diffeomorphisms. 相似文献
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In 2011, the fundamental gap conjecture for Schrödinger operators was proven. This can be used to estimate the ground state energy of the time-independent Schrödinger equation with a convex potential and relative error ε. Classical deterministic algorithms solving this problem have cost exponential in the number of its degrees of freedom d. We show a quantum algorithm, that is based on a perturbation method, for estimating the ground state energy with relative error ε. The cost of the algorithm is polynomial in d and ε−1, while the number of qubits is polynomial in d and logε−1. In addition, we present an algorithm for preparing a quantum state that overlaps within 1−δ,δ∈(0,1), with the ground state eigenvector of the discretized Hamiltonian. This algorithm also approximates the ground state with relative error ε. The cost of the algorithm is polynomial in d, ε−1 and δ−1, while the number of qubits is polynomial in d, logε−1 and logδ−1. 相似文献
3.
We examine the regularity of weak solutions of quasi-geostrophic (QG) type equations with supercritical (α<1/2) dissipation α(−Δ). This study is motivated by a recent work of Caffarelli and Vasseur, in which they study the global regularity issue for the critical (α=1/2) QG equation [L. Caffarelli, A. Vasseur, Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation, arXiv: math.AP/0608447, 2006]. Their approach successively increases the regularity levels of Leray–Hopf weak solutions: from L2 to L∞, from L∞ to Hölder (Cδ, δ>0), and from Hölder to classical solutions. In the supercritical case, Leray–Hopf weak solutions can still be shown to be L∞, but it does not appear that their approach can be easily extended to establish the Hölder continuity of L∞ solutions. In order for their approach to work, we require the velocity to be in the Hölder space C1−2α. Higher regularity starting from Cδ with δ>1−2α can be established through Besov space techniques and will be presented elsewhere [P. Constantin, J. Wu, Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, in press]. 相似文献
4.
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
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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
6.
Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 相似文献
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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.
In many applications it has been observed that hybrid-Monte Carlo sequences perform better than Monte Carlo and quasi-Monte Carlo sequences, especially in difficult problems. For a mixed s-dimensional sequence m, whose elements are vectors obtained by concatenating d-dimensional vectors from a low-discrepancy sequence q with (s−d)-dimensional random vectors, probabilistic upper bounds for its star discrepancy have been provided. In a paper of G. Ökten, B. Tuffin and V. Burago [G. Ökten, B. Tuffin, V. Burago, J. Complexity 22 (2006), 435–458] it was shown that for arbitrary ε>0 the difference of the star discrepancies of the first N points of m and q is bounded by ε with probability at least 1−2exp(−ε2N/2) for N sufficiently large. The authors did not study how large N actually has to be and if and how this actually depends on the parameters s and ε. In this note we derive a lower bound for N, which significantly depends on s and ε. Furthermore, we provide a probabilistic bound for the difference of the star discrepancies of the first N points of m and q, which holds without any restrictions on N. In this sense it improves on the bound of Ökten, Tuffin and Burago and is more helpful in practice, especially for small sample sizes N. We compare this bound to other known bounds. 相似文献
10.
This paper is devoted to a problem of finding the smallest positive integer s(m,n,k) such that (m+1) generic skew-symmetric (k+1)-forms in (n+1) variables as linear combinations of the same s(m,n,k) decomposable skew-symmetric (k+1)-forms. 相似文献
11.
Dongwen Qi 《Expositiones Mathematicae》2009,27(1):87-91
A new proof is given for the statement: For an irreducible, infinite Coxeter group (W,S) and w∈W, if wSw-1=S, then w=1 (the identity element of W). 相似文献
12.
This paper treats some variational principles for solutions of inhomogeneous p -Laplacian boundary value problems on exterior regions U?RN with dimension N?3. Existence-uniqueness results when p∈(1,N) are provided in a space E1,p(U) of functions that contains W1,p(U). Functions in E1,p(U) are required to decay at infinity in a measure theoretic sense. Various properties of this space are derived, including results about equivalent norms, traces and an Lp-imbedding theorem. Also an existence result for a general variational problem of this type is obtained. 相似文献
13.
Pavle V.M. Blagojević Aleksandra Dimitrijević Blagojević Ljubiša D.R. Kočinac 《Topology and its Applications》2013
In this paper we give the complete answer to a question posed by A. Arhangel?skii and prove that the sphere Sn is diagonal resolvable if and only if Sn is an H -space if and only if n∈{0,1,3,7}. Moreover, we prove that any upper half even dimensional Q-sphere cannot be diagonal resolvable. 相似文献
14.
By a perturbation method and constructing comparison functions, we reveal how the inhomogeneous term h affects the exact asymptotic behaviour of solutions near the boundary to the problem △u=b(x)g(u)+λh(x), u>0 in Ω, u|∂Ω=∞, where Ω is a bounded domain with smooth boundary in RN, λ>0, g∈C1[0,∞) is increasing on [0,∞), g(0)=0, g′ is regularly varying at infinity with positive index ρ, the weight b, which is non-trivial and non-negative in Ω, may be vanishing on the boundary, and the inhomogeneous term h is non-negative in Ω and may be singular on the boundary. 相似文献
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For α∈R, let pR(t,x,x) denote the diagonal of the transition density of the α-Bessel process in (0,1], killed at 0 and reflected at 1. As a function of x, if either α≥3 or α=1, then for t>0, the diagonal is nondecreasing. This monotonicity property fails if 1≠α<3. 相似文献
17.
Let R be a commutative ring with identity. We will say that an R-module M satisfies the weak Nakayama property, if IM=M, where I is an ideal of R, implies that for any x∈M there exists a∈I such that (a−1)x=0. In this paper, we will study modules satisfying the weak Nakayama property. It is proved that if R is a local ring, then R is a Max ring if and only if J(R), the Jacobson radical of R, is T-nilpotent if and only if every R-module satisfies the weak Nakayama property. 相似文献
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In this note we study distance-regular graphs with a small number of vertices compared to the valency. We show that for a given α>2, there are finitely many distance-regular graphs Γ with valency k, diameter D≥3 and v vertices satisfying v≤αk unless (D=3 and Γ is imprimitive) or (D=4 and Γ is antipodal and bipartite). We also show, as a consequence of this result, that there are finitely many distance-regular graphs with valency k≥3, diameter D≥3 and c2≥εk for a given 0<ε<1 unless (D=3 and Γ is imprimitive) or (D=4 and Γ is antipodal and bipartite). 相似文献