共查询到20条相似文献,搜索用时 15 毫秒
1.
Jacob E. Goodman 《Discrete Mathematics》1980,32(1):27-35
We establish a duality principle for arrangements of pseudolines in the projective plane, and thereby prove the conjecture of Burr, Grünbaum, and Sloane that the solution of the “orchard problem” for pseudoline arrangements and the solution t?(p) of the dual problem are equal. 相似文献
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In 1923, Hardy and Littlewood[1] conjectured that each integer n can be written asp+m12+ m22 = n,and Linnik[2,3] proved that this conjecture is true. But if these mi with i = 1,2 are restricted to primes Pi, the corresponding result is out of reach at present. We consider the following Diophantine equation 相似文献
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文志荧 《数学年刊B辑(英文版)》1983,(1)
In this paper,we extend the following results to the case of two variables:S.Mandelbrojit'stheorems on the differentiable classes and on the trigonometric classes;H.Cartan's theorems on theclasses of composition and on the equivalence of two classes on a finite interval.All the results in thispaper can be transfered immediately to the case of more than two variables. 相似文献
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We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain
multi-brackets of differential operators. These multi-brackets generalize the higher Jacobi-Mayer brackets, important in the
study of evolutionary equations and the integrability problem. We also calculate Spencer δ-cohomology of generalized complete intersections and evaluate the formal functional dimension of the solutions space. The
results are used to establish new integration methods. 相似文献
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Andrew Schultz 《Discrete Mathematics》2006,306(2):244-253
For positive integers m and r, one can easily show there exist integers N such that for every map Δ:{1,2,…,N}→{1,2,…,r} there exist 2m integers
x1<?<xm<y1<?<ym, 相似文献
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Bernardo M. ábrego Mario Cetina Silvia Fernández-Merchant Jesús Lea?os Gelasio Salazar 《Discrete and Computational Geometry》2012,48(1):192-215
Let P be a set of points in general position in the plane. Join all pairs of points in P with straight line segments. The number of segment-crossings in such a drawing, denoted by $\operatorname {cr}(P)$ , is the rectilinear crossing number of P. A halving line of P is a line passing through two points of P that divides the rest of the points of P in (almost) half. The number of halving lines of P is denoted by h(P). Similarly, a k-edge, 0??k??n/2?1, is a line passing through two points of P and leaving exactly k points of P on one side. The number of ??k-edges of P is denoted by E ??k (P). Let $\overline {\mathrm {cr}}(n)$ , h(n), and E ??k (n) denote the minimum of $\operatorname {cr}(P)$ , the maximum of h(P), and the minimum of E ??k (P), respectively, over all sets P of n points in general position in the plane. We show that the previously best known lower bound on E ??k (n) is tight for k<?(4n?2)/9? and improve it for all k???(4n?2)/9?. This in turn improves the lower bound on $\overline {\mathrm {cr}}(n)$ from $0.37968\binom{n}{4}+\varTheta (n^{3})$ to $\frac{277}{729}\binom{n}{4}+\varTheta (n^{3})\geq 0.37997\binom{n}{4}+\varTheta (n^{3})$ . We also give the exact values of $\overline {\mathrm {cr}}(n)$ and h(n) for all n??27. Exact values were known only for n??18 and odd n??21 for the crossing number, and for n??14 and odd n??21 for halving lines. 相似文献
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Density,SpreadandCharacterofSpacesofBorel SubsetsYangXu(杨旭)(DepertmentofMathematics,SipingNormalCollege,Siping,136000)CaoYe(曹... 相似文献
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A special solution of the Kadomtsev-Petviashvili equation $$u_{tx} + u_{xxxx} + 3u_{yy} + 3(u^2 )_{xx} = 0$$ that is a “nonlinear” analog of the special function of wave catastrophe corresponding to a singularity of swallowtail type is considered. On the basis of a symmetry analysis it is shown that the solution must simultaneously satisfy nonlinear ordinary differential equations with respect to all three independent variables. After “dressing” of the corresponding Ψ function, equations with respect to a spectral parameter arise in a regular manner, and this indicates the possibility of applying the method of isomonodromic deformation. 相似文献
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《代数通讯》2013,41(9):4547-4569
Abstract A projective valuation on a set Eis a mapping w : E 4 → Λ ∪ {±∞}, where Λ is an ordered abelian group, satisfying certain axioms. A D-relation on Eis a four-place relation on E, again with certain properties. There is a projective valuation on the set of ends of a Λ-tree (and on any subset, by restriction) and we show, using a construction suggested by Tits in the case Λ = ?, that every projective valuation arises in this way. Every projective valuation wdefines a D-relation, and there is a simple geometric interpretation of the D-relation, given a Λ-tree defining w. Our main result is a converse, that any D-relation can be defined by a projective valuation, hence arises from an embedding into the set of ends of a Λ-tree. 相似文献
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ZHANG Shu-min 《数学季刊》2004,(2)
In the paper, we prove that the complement of Tm(1,4,m - 6)(m > 10) is chromatically unique if and only if m ≠5k(k ≥ 2). 相似文献
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Sandra Saliani 《Constructive Approximation》2011,33(1):15-39
Wavelet packets provide an algorithm with many applications in signal processing together with a large class of orthonormal
bases of L
2(ℝ), each one corresponding to a different splitting of L
2(ℝ) into a direct sum of its closed subspaces. The definition of wavelet packets is due to the work of Coifman, Meyer, and
Wickerhauser, as a generalization of the Walsh system. A question has been posed since then: one asks if a (general) wavelet
packet system can be an orthonormal basis for L
2(ℝ) whenever a certain set linked to the system, called the “exceptional set” has zero Lebesgue measure. This answer to this
question affects the quality of wavelet packet approximation. In this paper we show that the answer to this question is negative
by providing an explicit example. In the proof we make use of the “local trace function” by Dutkay and the generalized shift-invariant
system machinery developed by Ron and Shen. 相似文献
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Thawhat CHANGPHAS Klaus DENECKE 《数学学报(英文版)》2007,23(4):659-670
Hypersubstitutions are mappings which map operation symbols to terms of the corresponding arities. They were introduced as a way of making precise the concept of a hyperidentity and generalizations to M-hyperidentities. A variety in which every identity is satisfied as a hyperidentity is called solid. If every identity is an M-hyperidentity for a subset M of the set of all hypersubstitutions, the variety is called M-solid. There is a Galois connection between monoids of hypersubstitutions and sublattices of the lattice of all varieties of algebras of a given type. Therefore, it is interesting and useful to know how semigroup or monoid properties of monoids of hypersubstitutions transfer under this Galois connection to properties of the corresponding lattices of M-solid varieties. In this paper, we study the order of each hypersubstitution of type (2, 2), i.e., the order of the cyclic subsemigroup generated by that hypersubstitution of the monoid of all hypersubstitutions of type (2, 2). The main result is that the order is 1, 2, 3, 4 or infinite. 相似文献
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Let {? n (dμ)} be a system of orthonormal polynomials on the unit circle with respect to a measuredμ. Szegö's theory is concerned with the asymptotic behavior of? n (dμ) when logμ'∈L 1. In what follows we will discuss the asymptotic behavior of the ratio φn(dμ 1)/φn(dμ 2) off the unit circle in casedμ 1 anddμ 2 are close in a sense (e.g.,dμ 2=g dμ 1 whereg≥0 is such thatQ(e it )g(t) andQ(e it )/g(t) are bounded for a suitable polynomialQ) and μ 1 ′ >0 almost everywhere or (a somewhat weaker requirement) lim n→∞Φ n (dμ 1,0)=0, for the monic polynomials Φ n . The consequences for orthogonal polynomials on the real line are also discussed. 相似文献
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P. Gaillard 《Theoretical and Mathematical Physics》2018,196(2):1174-1199
We construct solutions of the Kadomtsev–Petviashvili-I equation in terms of Fredholm determinants. We deduce solutions written as a quotient of Wronskians of order 2N. These solutions, called solutions of order N, depend on 2N?1 parameters. They can also be written as a quotient of two polynomials of degree 2N(N +1) in x, y, and t depending on 2N?2 parameters. The maximum of the modulus of these solutions at order N is equal to 2(2N + 1)2. We explicitly construct the expressions up to the order six and study the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters. 相似文献