共查询到20条相似文献,搜索用时 31 毫秒
1.
Florian Luca 《Discrete Mathematics》2007,307(13):1672-1678
In this note, we supply the details of the proof of the fact that if a1,…,an+Ω(n) are integers, then there exists a subset M⊂{1,…,n+Ω(n)} of cardinality n such that the equation
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For positive integers α1,α2,…,αr with αr?2, the multiple zeta value or r-fold Euler sum is defined as
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Igor E. Shparlinski 《Indagationes Mathematicae》2004,15(2):283-289
For a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of positive integers n ≤ such that l2|n for any prime divisor l|n. We estimate exponential sums of the form
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Fang Jia 《Differential Geometry and its Applications》2007,25(5):433-451
Let be a locally strongly convex hypersurface, given by the graph of a convex function xn+1=f(x1,…,xn) defined in a convex domain Ω⊂Rn. M is called a α-extremal hypersurface, if f is a solution of
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Benoit Loridant 《Topology and its Applications》2008,155(7):667-695
Let be a root of the polynomial p(x)=x2+4x+5. It is well known that the pair (p(x),{0,1,2,3,4}) forms a canonical number system, i.e., that each x∈Z[α] admits a finite representation of the shape x=a0+a1α+?+a?α? with ai∈{0,1,2,3,4}. The set T of points with integer part 0 in this number system
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Answering a question of Liardet, we prove that if 1,α1,α2,…,αt are real numbers linearly independent over the rationals, then there is an infinite subset A of the positive integers such that for real β, we have (|||| denotes the distance to the nearest integer)
9.
Yong-Gao Chen 《Journal of Number Theory》2003,100(2):326-331
Let p1,p2,… be the sequence of all primes in ascending order. The following result is proved: for any given positive integer k and any given , there exist infinitely many positive integers n with
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Yong Luo 《Journal of Differential Equations》2012,253(12):3266-3285
11.
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:
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In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))n?0 and (U(n))n?0, which are ultimately periodic modulo m, e.g.
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R.C. Vaughan 《Journal of Number Theory》2003,100(1):169-183
Let r(n) denote the number of integral ideals of norm n in a cubic extension K of the rationals, and define and Δ(x)=S(x)−αx where α is the residue of the Dedekind zeta function ζ(s,K) at 1. It is shown that the abscissa of convergence of
15.
Let a, b, c, d be given nonnegative integers with a,d?1. Using Chebyshev?s inequalities for the function π(x) and some results concerning arithmetic progressions of prime numbers, we study the Diophantine equation
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Pieter C. Allaart 《Journal of Mathematical Analysis and Applications》2011,381(2):689-694
Let ?(x)=2inf{|x−n|:n∈Z}, and define for α>0 the function
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V. Nitica 《Linear algebra and its applications》2010,432(1):402-1597
In this article, continuing [12,13], further contributions to the theory of max-min convex geometry are given. The max-min semiring is the set endowed with the operations ⊕=max,⊗=min in . A max-min hyperplane (briefly, a hyperplane) is the set of all points satisfying an equation of the form
a1⊗x1⊕…⊕an⊗xn⊕an+1=b1⊗x1⊕…⊕bn⊗xn⊕bn+1, 相似文献
19.
This paper gives upper and lower bounds of the Christoffel-type functions , for the m-orthogonal polynomials for a Freud weight W=e-Q, which are given as follows. Let an=an(Q) be the nth Mhaskar–Rahmanov–Saff number, φn(x)=max{n-2/3,1-|x|/an}, and d>0. Assume that QC(R) is even, , and for some A,B>1Then for xRand for |x|an(1+dn-2/3) 相似文献