共查询到20条相似文献,搜索用时 46 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 this paper, we study degenerate CR embeddings f of a strictly pseudoconvex hypersurface M⊂Cn+1 into a sphere S in a higher dimensional complex space CN+1. The degeneracy of the mapping f will be characterized in terms of the ranks of the CR second fundamental form and its covariant derivatives. In 2004, the author, together with X. Huang and D. Zaitsev, established a rigidity result for CR embeddings f into spheres in low codimensions. A key step in the proof of this result was to show that degenerate mappings are necessarily contained in a complex plane section of the target sphere (partial rigidity). In the 2004 paper, it was shown that if the total rank d of the second fundamental form and all of its covariant derivatives is <n (here, n is the CR dimension of M), then f(M) is contained in a complex plane of dimension n+d+1. The converse of this statement is also true, as is easy to see. When the total rank d exceeds n, it is no longer true, in general, that f(M) is contained in a complex plane of dimension n+d+1, as can be seen by examples. In this paper, we carry out a systematic study of degenerate CR mappings into spheres. We show that when the ranks of the second fundamental form and its covariant derivatives exceed the CR dimension n, then partial rigidity may still persist, but there is a “defect” k that arises from the ranks exceeding n such that f(M) is only contained in a complex plane of dimension n+d+k+1. Moreover, this defect occurs in general, as is illustrated by examples. 相似文献
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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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This paper is devoted to construct a family of fifth degree cubature formulae for n-cube with symmetric measure and n-dimensional spherically symmetrical region. The formula forn-cube contains at most n2+5n+3 points and for n-dimensional spherically symmetrical region contains only n2+3n+3 points. Moreover, the numbers can be reduced to n2+3n+1 and n2+n+1 if n=7 respectively, the latter of which is minimal. 相似文献
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We prove that if G is a finite simple group which is the unit group of a ring, then G is isomorphic to: (a) a cyclic group of order 2; or (b) a cyclic group of prime order 2k−1 for some k; or (c) a projective special linear group PSLn(F2) for some n≥3. Moreover, these groups do all occur as unit groups. We deduce this classification from a more general result, which holds for groups G with no non-trivial normal 2-subgroup. 相似文献
7.
The oscillation of solutions of f″+Af=0 is discussed by focusing on four separate situations. In the complex case A is assumed to be either analytic in the unit disc D or entire, while in the real case A is continuous either on (−1,1) or on (0,∞). In all situations A is expected to grow beyond bounds that ensure finite oscillation for all (non-trivial) solutions, and the separation between distinct zeros of solutions is considered. 相似文献
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Jean-Stéphane Dhersin Fabian Freund Arno Siri-Jégousse Linglong Yuan 《Stochastic Processes and their Applications》2013
In this paper, we consider Beta(2−α,α) (with 1<α<2) and related Λ-coalescents. If T(n) denotes the length of a randomly chosen external branch of the n-coalescent, we prove the convergence of nα−1T(n) when n tends to ∞, and give the limit. To this aim, we give asymptotics for the number σ(n) of collisions which occur in the n-coalescent until the end of the chosen external branch, and for the block counting process associated with the n-coalescent. 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
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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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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
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We show that if T:X→X is a continuous linear operator on an F-space X≠{0}, then the set of frequently hypercyclic vectors of T is of first category in X, and this answers a question of A. Bonilla and K.-G. Grosse-Erdmann. We also show that if T:X→X is a bounded linear operator on a Banach space X≠{0} and if T is frequently hypercyclic (or, more generally, syndetically transitive), then the T∗-orbit of every non-zero element of X∗ is bounded away from 0, and in particular T∗ is not hypercyclic. 相似文献
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Let us fix a function f(n)=o(nlnn) and real numbers 0≤α<β≤1. We present a polynomial time algorithm which, given a directed graph G with n vertices, decides either that one can add at most βn new edges to G so that G acquires a Hamiltonian circuit or that one cannot add αn or fewer new edges to G so that G acquires at least e−f(n)n! Hamiltonian circuits, or both. 相似文献
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Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are Lipschitz ?-strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
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Consider a face-to-face parallelohedral tiling of Rd and a (d−k)-dimensional face F of the tiling. We prove that the valence of F (i.e. the number of tiles containing F as a face) is not greater than 2k. If the tiling is affinely equivalent to a Voronoi tiling for some lattice (the so called Voronoi case), this gives a well-known upper bound for the number of vertices of a Delaunay k-cell. Yet we emphasize that such an affine equivalence is not assumed in the proof. 相似文献
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A fast and accurate algorithm to compute interactions between N point vortices and between N vortex blobs on a sphere is proposed. It is an extension of the fast tree-code algorithm developed by Draghicescu for the vortex method in the plane. When we choose numerical parameters in the fast algorithm suitably, the computational cost of O(N2) is reduced to O(N(logN)4) and the approximation error decreases like O(1/N) when N→∞, as demonstrated in the present article. We also apply the fast method to long-time evolution of two vortex sheets on the sphere to see the efficiency. A key point is to describe the equation of motion for the N points in the three-dimensional Cartesian coordinates. 相似文献
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For a Gaussian process X and smooth function f, we consider a Stratonovich integral of f(X), defined as the weak limit, if it exists, of a sequence of Riemann sums. We give covariance conditions on X such that the sequence converges in law. This gives a change-of-variable formula in law with a correction term which is an Itô integral of f? with respect to a Gaussian martingale independent of X. The proof uses Malliavin calculus and a central limit theorem from Nourdin and Nualart (2010) [8]. This formula was known for fBm with H=1/6 Nourdin et al. (2010) [9]. We extend this to a larger class of Gaussian processes. 相似文献