共查询到20条相似文献,搜索用时 31 毫秒
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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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The aim of this work is to contribute to the classification of projective varieties according to their representation type, providing examples of n -dimensional varieties of wild representation type, for arbitrary n?2. More precisely, we prove that all Fano blow-ups of Pn at a finite number of points are of wild representation type exhibiting families of dimension of order r2 of simple (hence, indecomposable) ACM rank r vector bundles for any r?n. In the two dimensional case, the vector bundles that we construct are moreover Ulrich bundles and μ-stable with respect to certain ample divisor. 相似文献
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The Severi variety parameterizes plane curves of degree d with δ nodes. Its degree is called the Severi degree. For large enough d, the Severi degrees coincide with the Gromov–Witten invariants of CP2. Fomin and Mikhalkin (2010) [10] proved the 1995 conjecture that for fixed δ, Severi degrees are eventually polynomial in d. 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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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 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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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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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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We construct new examples of exceptional collections of line bundles on the variety of Borel subgroups of a split semisimple linear algebraic group G of rank 2 over a field. We exhibit exceptional collections of the expected length for types A2 and B2=C2 and prove that no such collection exists for type G2. This settles the question of the existence of full exceptional collections of line bundles on projective homogeneous G-varieties for split linear algebraic groups G of rank at most 2. 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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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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A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence x over a finite alphabet is ultimately periodic if and only if, for some n, the number of different factors of length n appearing in x is less than n+1. Attempts to extend this fundamental result, for example, to higher dimensions, have been considered during the last fifteen years. Let d≥2. A legitimate extension to a multidimensional setting of the notion of periodicity is to consider sets of Zd definable by a first order formula in the Presburger arithmetic 〈Z;<,+〉. With this latter notion and using a powerful criterion due to Muchnik, we exhibit a complete extension of the Morse–Hedlund theorem to an arbitrary dimension d and characterize sets of Zd definable in 〈Z;<,+〉 in terms of some functions counting recurrent blocks, that is, blocks occurring infinitely often. 相似文献
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We consider G=Γ×S1 with Γ being a finite group, for which the complete Euler ring structure in U(G) is described. The multiplication tables for Γ=D6, S4 and A5 are provided in the Appendix. The equivariant degree for G-orthogonal maps is constructed using the primary equivariant degree with one free parameter. We show that the G-orthogonal degree extends the degree for G-gradient maps (in the case of G=Γ×S1) introduced by G?ba in [K. G?ba, W. Krawcewicz, J. Wu, An equivariant degree with applications to symmetric bifurcation problems I: Construction of the degree, Bull. London. Math. Soc. 69 (1994) 377–398]. The computational results obtained are applied to a Γ-symmetric autonomous Newtonian system for which we study the existence of 2π-periodic solutions. For some concrete cases, we present the symmetric classification of the solution set for the systems considered. 相似文献
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Let C be an irreducible plane curve. A point P in the projective plane is said to be Galois with respect to C if the function field extension induced by the projection from P is Galois. We denote by δ′(C) the number of Galois points contained in P2?C. In this article we will present two results with respect to determination of δ′(C) in characteristic two. First we determine δ′(C) for smooth plane curves of degree a power of two. In particular, we give a new characterization of the Klein quartic in terms of δ′(C). Second we determine δ′(C) for a generalization of the Klein quartic, which is related to an example of Artin–Schreier curves whose automorphism group exceeds the Hurwitz bound. This curve has many Galois points. 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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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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Michel Mandjes Petteri Mannersalo Ilkka Norros Miranda van Uitert 《Stochastic Processes and their Applications》2006
Consider events of the form {Zs≥ζ(s),s∈S}, where Z is a continuous Gaussian process with stationary increments, ζ is a function that belongs to the reproducing kernel Hilbert space R of process Z, and S⊂R is compact. The main problem considered in this paper is identifying the function β∗∈R satisfying β∗(s)≥ζ(s) on S and having minimal R-norm. The smoothness (mean square differentiability) of Z turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when ζ(s)=s for s∈[0,1] and Z is either a fractional Brownian motion or an integrated Ornstein–Uhlenbeck process. 相似文献