共查询到20条相似文献,搜索用时 46 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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Let E be a real Banach space, C be a nonempty closed convex subset of E and T:C→C be a continuous generalized Φ-pseudocontractive mapping. It is proved that T has a unique fixed point in C. 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
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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
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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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Let T be a tree with s ends and f,g be continuous maps from T to T with f°g=g°f. In this note we show that if there exists a positive integer m≥2 such that gcd(m,l)=1 for any 2≤l≤s and f,g share a periodic point which is a km-periodic point of f for some positive integer k, then the topological entropy of f°g is positive. 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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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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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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This paper considers the short- and long-memory linear processes with GARCH (1,1) noises. The functional limit distributions of the partial sum and the sample autocovariances are derived when the tail index α is in (0,2), equal to 2, and in (2,∞), respectively. The partial sum weakly converges to a functional of α-stable process when α<2 and converges to a functional of Brownian motion when α≥2. When the process is of short-memory and α<4, the autocovariances converge to functionals of α/2-stable processes; and if α≥4, they converge to functionals of Brownian motions. In contrast, when the process is of long-memory, depending on α and β (the parameter that characterizes the long-memory), the autocovariances converge to either (i) functionals of α/2-stable processes; (ii) Rosenblatt processes (indexed by β, 1/2<β<3/4); or (iii) functionals of Brownian motions. The rates of convergence in these limits depend on both the tail index α and whether or not the linear process is short- or long-memory. Our weak convergence is established on the space of càdlàg functions on [0,1] with either (i) the J1 or the M1 topology (Skorokhod, 1956); or (ii) the weaker form S topology (Jakubowski, 1997). Some statistical applications are also discussed. 相似文献
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Two modifications of Newton’s method to accelerate the convergence of the nth root computation of a strictly positive real number are revisited. Both modifications lead to methods with prefixed order of convergence p∈N,p≥2. We consider affine combinations of the two modified pth-order methods which lead to a family of methods of order p with arbitrarily small asymptotic constants. Moreover the methods are of order p+1 for some specific values of a parameter. Then we consider affine combinations of the three methods of order p+1 to get methods of order p+1 again with arbitrarily small asymptotic constants. The methods can be of order p+2 with arbitrarily small asymptotic constants, and also of order p+3 for some specific values of the parameters of the affine combination. It is shown that infinitely many pth-order methods exist for the nth root computation of a strictly positive real number for any p≥3. 相似文献
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We derive a Molchan–Golosov-type integral transform which changes fractional Brownian motion of arbitrary Hurst index K into fractional Brownian motion of index H. Integration is carried out over [0,t], t>0. The formula is derived in the time domain. Based on this transform, we construct a prelimit which converges in L2(P)-sense to an analogous, already known Mandelbrot–Van Ness-type integral transform, where integration is over (−∞,t], t>0. 相似文献
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We study a family of differential operators Lα in two variables, depending on the coupling parameter α?0 that appears only in the boundary conditions. Our main concern is the spectral properties of Lα, which turn out to be quite different for α<1 and for α>1. In particular, Lα has a unique self-adjoint realization for α<1 and many such realizations for α>1. In the more difficult case α>1 an analysis of non-elliptic pseudodifferential operators in dimension one is involved. 相似文献
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