共查询到20条相似文献,搜索用时 125 毫秒
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J. Mc Laughlin 《Journal of Number Theory》2007,127(2):184-219
Let f(x)∈Z[x]. Set f0(x)=x and, for n?1, define fn(x)=f(fn−1(x)). We describe several infinite families of polynomials for which the infinite product
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Jun Tarui 《Discrete Mathematics》2008,308(8):1350-1354
A family P={π1,…,πq} of permutations of [n]={1,…,n} is completely k-scrambling [Spencer, Acta Math Hungar 72; Füredi, Random Struct Algor 96] if for any distinct k points x1,…,xk∈[n], permutations πi's in P produce all k! possible orders on πi(x1),…,πi(xk). Let N*(n,k) be the minimum size of such a family. This paper focuses on the case k=3. By a simple explicit construction, we show the following upper bound, which we express together with the lower bound due to Füredi for comparison.
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This paper concerns polynomials in g noncommutative variables x=(x1,…,xg), inverses of such polynomials, and more generally noncommutative “rational expressions” with real coefficients which are formally symmetric and “analytic near 0.” The focus is on rational expressions r=r(x) which are “matrix convex” near 0; i.e., those rational expressions r for which there is an ?>0 such that if X=(X1,…,Xg) is a g-tuple of n×n symmetric matrices satisfying
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J.A. De Loera R. Hemmecke S. Onn U.G. Rothblum R. Weismantel 《Journal of Pure and Applied Algebra》2009,213(8):1569-1577
We present a new algebraic algorithmic scheme to solve convex integer maximization problems of the following form, where c is a convex function on Rd and w1x,…,wdx are linear forms on Rn,
max{c(w1x,…,wdx):Ax=b,x∈Nn}. 相似文献
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For finite subsets A1,…,An of a field, their sumset is given by . In this paper, we study various restricted sumsets of A1,…,An with restrictions of the following forms:
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Let P be a semigroup presentation of the form
〈a1,…,an∣w1=a1,…,wn=an〉. 相似文献
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Hao Pan 《Discrete Mathematics》2006,306(16):1921-1940
By a very simple argument, we prove that if l,m,n∈{0,1,2,…} then
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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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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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Suk-Geun Hwang 《Linear algebra and its applications》2011,434(2):475-479
A family F of square matrices of the same order is called a quasi-commuting family if (AB-BA)C=C(AB-BA) for all A,B,C∈F where A,B,C need not be distinct. Let fk(x1,x2,…,xp),(k=1,2,…,r), be polynomials in the indeterminates x1,x2,…,xp with coefficients in the complex field C, and let M1,M2,…,Mr be n×n matrices over C which are not necessarily distinct. Let and let δF(x1,x2,…,xp)=detF(x1,x2,…,xp). In this paper, we prove that, for n×n matrices A1,A2,…,Ap over C, if {A1,A2,…,Ap,M1,M2,…,Mr} is a quasi-commuting family, then F(A1,A2,…,Ap)=O implies that δF(A1,A2,…,Ap)=O. 相似文献
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Bing Li 《Journal of Mathematical Analysis and Applications》2008,339(2):1322-1331
For any real number β>1, let ε(1,β)=(ε1(1),ε2(1),…,εn(1),…) be the infinite β-expansion of 1. Define . Let x∈[0,1) be an irrational number. We denote by kn(x) the exact number of partial quotients in the continued fraction expansion of x given by the first n digits in the β-expansion of x. If is bounded, we obtain that for all x∈[0,1)?Q,
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Matthew Boylan 《Journal of Number Theory》2003,98(2):377-389
Let F(z)=∑n=1∞a(n)qn denote the unique weight 16 normalized cuspidal eigenform on . In the early 1970s, Serre and Swinnerton-Dyer conjectured that
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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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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
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Hao Pan 《Journal of Number Theory》2006,117(1):216-221
Let k,m,n?2 be integers. Let A be a subset of {0,1,…,n} with 0∈A and the greatest common divisor of all elements of A is 1. Suppose that
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Dongho Byeon 《Journal of Number Theory》2011,131(8):1513-1529
Let m be a positive integer and fm(x) be a polynomial of the form fm(x)=x2+x−m. We call a polynomial fm(x) a Rabinowitsch polynomial if for and consecutive integers x=x0,x0+1,…,x0+s−1, |fm(x)| is either 1 or prime. In this paper, we show that there are exactly 14 Rabinowitsch polynomials fm(x). 相似文献
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We prove for the Sierpinski Gasket (SG) an analogue of the fractal interpolation theorem of Barnsley. Let V0={p1,p2,p3} be the set of vertices of SG and the three contractions of the plane, of which the SG is the attractor. Fix a number n and consider the iterations uw=uw1uw2?uwn for any sequence w=(w1,w2,…,wn)∈n{1,2,3}. The union of the images of V0 under these iterations is the set of nth stage vertices Vn of SG. Let F:Vn→R be any function. Given any numbers αw(w∈n{1,2,3}) with 0<|αw|<1, there exists a unique continuous extension of F, such that
f(uw(x))=αwf(x)+hw(x) 相似文献
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Let ?0,n be the real Clifford algebra generated by e1, e2,…, en satisfying eiej+ejei=−2δij, i, j=1,2,…, n. e0 is the unit element. Let Ω be an open set. A function f is called left generalized analytic in Ω if f satisfies the equation
where
qi <0, i=0,1,…, n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in ?n+1+ will be investigated. 相似文献
equation(0.1)
Lf=0,
L=q0e0∂x0+ q1e1∂x1+…+qnen∂xn,