共查询到20条相似文献,搜索用时 31 毫秒
1.
Raul Cordovil 《Journal of Combinatorial Theory, Series B》1983,34(2):209-223
A natural sufficient condition for a finite family of single element extensions of a matroid to be compatible is given. Characterizations of all the finite extensions N of a matroid M(E) are given for which the rank function satisfies or equivalently the closure operator satisfies . The single element extensions and the principal extensions are examples of such matroids. The notion of a sheaf of flats of M. Las Vergnas is used in the proof of a new necessary and sufficient condition for two single element extensions of a matroid to be compatible. An initial announcement of part of these results appeared in R. Cordovil (C. R. Acad. Sci. Paris. A284 (1977), 1249–1252). 相似文献
2.
On , n?1 and n≠2, we prove the existence of a sharp constant for Sobolev inequalities with higher fractional derivatives. Let s be a positive real number. For n>2s and any function satisfies where the operator (?Δ)s in Fourier spaces is defined by . To cite this article: A. Cotsiolis, N.C. Tavoularis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 801–804. 相似文献
3.
Brother Joseph Heisler 《Journal of Number Theory》1974,6(1):50-51
We shall establish for all finite fields GF(pn) the following result of Chowla: given a positive integer m greater than one and the finite field GF(p), p a prime, such that xm = ?1 is solvable in GF(p), then there exists an absolute positive constant c, , such that for each set of s nonzero elements ai of GF(p), has a non-trivial zero in GF(p) if s ≥ c ln m. 相似文献
4.
We compare several algorithms for computing the discrete Fourier transform of n numbers. The number of “operations” of the original Cooley-Tukey algorithm is approximately 2nA(n), where A(n) is the sum of the prime divisors of n. We show that the average number of operations satisfies . The average is not a good indication of the number of operations. For example, it is shown that for about half of the integers n less than x, the number of “operations” is less than n1.61. A similar analysis is given for Good's algorithm and for two algorithms that compute the discrete Fourier transform in O(n log n) operations: the chirp-z transform and the mixed-radix algorithm that computes the transform of a series of prime length p in O(p log p) operations. 相似文献
5.
In this Note we give a generalization of Hardy's theorem for the Dunkl transform on . More precisely, for all a>0, b>0 and p,q∈[1,+∞], we determine the measurable functions f such that and , where are the Lp spaces associated with the Dunkl transform. To cite this article: L. Gallardo, K. Trimèche, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 849–854. 相似文献
6.
Let T denote a random duration until some event of interest. In the Cox model , if the value of Z at event time is unobserved, Dupuy and Mesbah (Lifetime Data Analysis 8 (2002) 99–115) have proposed to estimate the parameters β and by maximizing a likelihood obtained from a joint model for survival and the longitudinal covariate data. We show that the estimators derived from this joint likelihood are asymptotically normally distributed. To cite this article: J.-F. Dupuy et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
7.
8.
In this Note we present some results on the existence of radially symmetric solutions for the nonlinear elliptic equation
(1)
Here N?3, p>1 and denotes the Pucci's extremal operators with parameters 0<λ?Λ. The goal is to describe the solution set as function of the parameter p. We find critical exponents , that satisfy: (i) If then there is no nontrivial solution of (). (ii) If then there is a unique fast decaying solution of (). (iii) If then there is a unique pseudo-slow decaying solution to (). (iv) If pp+<p then there is a unique slow decaying solution to (). Similar results are obtained for the operator . To cite this article: P.L. Felmer, A. Quaas, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 909–914. 相似文献
9.
M.M Dodson 《Journal of Number Theory》1973,5(4):287-292
Let θ(k, pn) be the least s such that the congruence (mod pn) has a nontrivial solution. It is shown that if k is sufficiently large and divisible by p but not by p ? 1, then . We also obtain the average order of θ(k), the least s such that the above congruence has a nontrivial solution for every prime p and every positive integer n. 相似文献
10.
Max Karoubi 《Comptes Rendus Mathematique》2002,335(2):121-126
In a previous Note [1], we suggested a quantum model of the unit interval [0,1], using convergent power series, parametrized by a variable q (a remarkable example is the quantum exponential, defined by Euler). In the present Note, we suggest a simpler model based on functions (with an arbitrary commutative ring k) which are constant when x?+∞ or x??∞ and their “differentials” considered as functions x?f(x+1)?f(x) (difference calculus). Thanks to this new “differential calculus over the integers”, we can associate to any simplicial set or topological space X a braided differential graded algebra which is similar in spirit to the algebra introduced in [1]. We notice that the p-homotopy type of X can be read from the braiding of . In particular, if , we recover in a purely algebraic way the integral cohomology, Steenrod operations, homotopy groups from this braiding. To cite this article: M. Karoubi, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 121–126. 相似文献
11.
J.E Nymann 《Journal of Number Theory》1975,7(4):406-412
Given a set S of positive integers let denote the number of k-tuples 〈m1, …, mk〉 for which and (m1, …, mk) = 1. Also let denote the probability that k integers, chosen at random from , are relatively prime. It is shown that if P = {p1, …, pr} is a finite set of primes and S = {m : (m, p1 … pr) = 1}, then if k ≥ 3 and where d(S) denotes the natural density of S. From this result it follows immediately that as n → ∞. This result generalizes an earlier result of the author's where and S is then the whole set of positive integers. It is also shown that if S = {p1x1 … prxr : xi = 0, 1, 2,…}, then as n → ∞. 相似文献
12.
Robert L McFarland 《Journal of Combinatorial Theory, Series A》1973,15(1):1-10
A construction is given for difference sets in certain non-cyclic groups with the parameters , , , n = q2s for every prime power q and every positive integer s. If qs is odd, the construction yields at least inequivalent difference sets in the same group. For q = 5, s = 2 a difference set is obtained with the parameters (v, k, λ, n) = (4000, 775, 150, 625), which has minus one as a multiplier. 相似文献
13.
Aimo Tietäväinen 《Journal of Number Theory》1975,7(3):353-356
Let θ(k, p) be the least s such that the congruence has a nontrivial solution. Let θ(k) = {max θ(k, p)| p > 1 + 2k}. The purpose of this note is to prove the following conjecture of S. Chowla: . 相似文献
14.
Let , let , where g2 and g3 are coefficients of the elliptic curve: Y2 = 4X3 ? g2X ? g3 over a finite field and Δ = g23 ? 27g32 and let . Then the p-adic cohomology theory will be applied to compute explicitly the zeta matrices of the elliptic curves, induced by the pth power map on the free -module . Main results are; Theorem 1.1: X2dY and YdX are basis elements for ; Theorem 1.2: YdX, X2dY, Y?1dX, Y?2dX and XY?2dX are basis elements for , where is a lifting of X, and all the necessary recursive formulas for this explicit computation are given. 相似文献
15.
A mean M(u, v) is defined to be a homogeneous symmetric function of two positive real variables satisfying min(u, v) ? M(u, v) ? max(u, v) for all u and v. Setting M(u, v) = uM(1, vu?1) = uM(1, 1 ? t), 0 ? t < 1, we determine power series expansions in t of various generalized means, including (Stolarsky's mean), (Lehmer's mean), (Leach and Sholander's mean), and (Gini's mean). The explicit power series coefficients and recurrence relations for these coefficients are found. Finally, applications are shown by proving a theorem that generalizes one due to Lehmer. 相似文献
16.
In two party elections with popular vote ratio , a theoretical model suggests replacing the so-called MacMahon cube law approximation , for the ratio of candidates elected, by the ratio of the two half sums in the binomial expansion of (p+q)2k+1 for some k. This ratio is nearly when k = 6. The success probability for the power law is shown to so closely approximate , if we choose , that for . Computationally, we avoid large binomial coefficients in computing for k>22 by expressing as the sum , whose terms decrease by the factors . Setting K = 4k+3, we compute ak for the large k using a continued fraction derived from the ratio of π to the finite Wallis product approximation. 相似文献
17.
Let M be an n-dimensional manifold supporting a quasi-Anosov diffeomorphism. If n=3 then either , in which case the diffeomorphisms is Anosov, or else its fundamental group contains a copy of . If n=4 then Π1(M) contains a copy of , provided that the diffeomorphism is not Anosov. To cite this article: J. Rodriguez Hertz et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 321–323. 相似文献
18.
Let Ms, be the number of solutions of the equation in the finite field GF(p). For a prime p ≡ 1(mod 3), , , and . Here d is uniquely determined by . 相似文献
19.
H.D Victory 《Journal of Mathematical Analysis and Applications》1982,89(2):420-441
Let K be an eventually compact linear integral operator on , with nonnegative kernel k(x, y), where the underlying measure μ is totally σ-finite on the domain set Ω when p = 1. In considering the equation λf = Kf + g for given nonnegative , P. Nelson, Jr. provided necessary and sufficient conditions, in terms of the support of g, such that a nonnegative solution was attained. Such conditions led to generalizing some of the graph-theoretic ideas associated with the normal form of a nonnegative reducible matrix. The purpose of this paper is to show that the analysis by Nelson can be enlarged to provide a more complete generalization of the normal form of a nonnegative matrix which can be used to characterize the distinguished eigenvalues of K and K1, and to describe sets of support for the eigenfunctions and generalized eigenfunctions of both K and K1 belonging to the spectral radius of K. 相似文献