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101.
In this paper, the authors use the analytic methods and the properties of
character sums mod p to study the computational problem of one kind of mean value
involving the classical Dedekind sums and two-term exponential sums, and give an exact
computational formula for it. 相似文献
102.
Philip A.H. Brooker 《Journal of Functional Analysis》2011,260(8):2222-2246
For α an ordinal and 1<p<∞, we determine a necessary and sufficient condition for an ?p-direct sum of operators to have Szlenk index not exceeding ωα. It follows from our results that the Szlenk index of an ?p-direct sum of operators is determined in a natural way by the behaviour of the ε-Szlenk indices of its summands. Our methods give similar results for c0-direct sums. 相似文献
103.
Dianliang Deng 《Journal of Mathematical Analysis and Applications》2011,376(1):136-153
Let X,X1,X2,… be a sequence of nondegenerate i.i.d. random variables with zero means. Set Sn=X1+?+Xn and . In the present paper we examine the precise asymptotic behavior for the general deviation probabilities of self-normalized sums, Sn/Wn. For positive functions g(x), ?(x), α(x) and κ(x), we obtain the precise asymptotics for the following deviation probabilities of self-normalized sums:
104.
Sergi Elizalde 《Journal of Combinatorial Theory, Series A》2011,118(8):2474-2497
Given a real number β>1, a permutation π of length n is realized by the β-shift if there is some x∈[0,1] such that the relative order of the sequence x,f(x),…,fn−1(x), where f(x) is the fractional part of βx, is the same as that of the entries of π. Widely studied from such diverse fields as number theory and automata theory, β-shifts are prototypical examples of one-dimensional chaotic dynamical systems. When β is an integer, permutations realized by shifts were studied in Elizalde (2009) [5]. In this paper we generalize some of the results to arbitrary β-shifts. We describe a method to compute, for any given permutation π, the smallest β such that π is realized by the β-shift. We also give a way to determine the length of the shortest forbidden (i.e., not realized) pattern of an arbitrary β-shift. 相似文献
105.
Aurel Sp?taru 《Statistics & probability letters》2011,81(10):1547-1551
Let X,X1,X2,… be i.i.d. random variables, and set Sn=X1+?+Xn. We prove that for three important distributions of X, namely normal, exponential and geometric, series of the type ∑n≥1anP(|Sn|≥xbn) or ∑n≥1anP(Sn≥xbn) behave like their first term as x→∞. 相似文献
106.
Hai-zhong Yang 《应用数学学报(英文版)》2011,27(2):277-280
This paper investigates the asymptotic behavior of tail probability of randomly weighted sums of dependent and real-valued
random variables with dominated variation, where the weights form another sequence of nonnegative random variables. The result
we obtain extends the corresponding result of Wang and Tang[7]. 相似文献
107.
We use the sampling representations associated with Sturm-Liouville difference operators to derive generalized integral-valued trigonometric sums. This extends the known results where zeros of Chebyshev polynomials of the first kind are involved to the use of the eigenvalues of difference operators, which leads to new identities. In these identities Bernoulli’s numbers play a role similar to that of Euler’s in the old ones. Our technique differs from that of Byrne-Smith (1997) and Berndt-Yeap (2002). 相似文献
108.
109.
本文利用正整数模q的正则数的定义以及解析方法研究一类与Dedekind和有关的和式的计算问题,并给出这个和式在一些特殊点上有趣的恒等式. 相似文献
110.
In this paper, by making use of Abel's theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet L-function at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered. 相似文献