共查询到20条相似文献,搜索用时 31 毫秒
1.
Noga Alon 《Journal of Combinatorial Theory, Series A》1985,40(1):82-89
Let X1, …, Xn be n disjoint sets. For 1 ? i ? n and 1 ? j ? h let Aij and Bij be subsets of Xi that satisfy |Aij| ? ri and |Bij| ? si for 1 ? i ? n, 1 ? j ? h, for 1 ? j ? h, for 1 ? j < l ? h. We prove that . This result is best possible and has some interesting consequences. Its proof uses multilinear techniques (exterior algebra). 相似文献
2.
The sequence Hk, k? 1, of n×n nonnegative matrices is said to be asymptotically homogeneous (with respect to D) if, for some probability vector D, as k→∞. Under a prior compactness assumption on the set {Hk}, asymptotic homogeneity is shown to be necessary and sufficient for strong ergodicity, as r→∞, of Tp,r=Hp+1Hp+2?Hp+r in a unified expository account for the two cases: (i) each Tp,r is primitive; (ii) each Tp,r is stochastic and regular. The first of these generalizes a known result [2]; and further generalizations are made. 相似文献
3.
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
4.
C.G Khatri 《Journal of multivariate analysis》1978,8(3):453-467
Optimization problems are connected with maximization of three functions, namely, geometric mean, arithmetic mean and harmonic mean of the eigenvalues of (X′ΣX)?1ΣY(Y′ΣY)?1Y′ΣX, where Σ is positive definite, X and Y are p × r and p × s matrices of ranks r and s (≥r), respectively, and X′Y = 0. Some interpretations of these functions are given. It is shown that the maximum values of these functions are obtained at the same point given by X = (h1 + ?1hp, …, hr + ?rhp?r+1) and , where h1, …, hp are the eigenvectors of Σ corresponding to the eigenvalues λ1 ≥ λ2 ≥ … ≥ λp > 0, ?j = +1 or ?1 for j = 1,2,…, r and , are linear functions of hr+1,…, hp?r. These results are extended to intermediate stationary values. They are utilized in obtaining the inequalities for canonical correlations θ1,…,θr and they are given by expressions (3.8)–(3.10). Further, some new union-intersection test procedures for testing the sphericity hypothesis are given through test statistics (3.11)–(3.13). 相似文献
5.
In this paper, we establish the following results: Let A be a square matrix of rank r. Then (a) is idempotent of rank r, and trrA (defined as the sum of the principal minors of order r in A) is one iff A is Hermitian idempotent. (b) As=At for some positive integers s≠t, and trA=rankA iff A is idempotent. (c) for some integers s≠t iff is idempotent, while for some integers s≠0 iff . (d) for some integers s≠t and rankA=trA iff A is Hermitian idempotent, while for some integer s iff A is Hermitian. Here indicates the conjugate transpose of A, and P-α is defined iff (P+)α=(Pα)+ for all positive integers α and P+ is the Moore-Penrose inverse of P. 相似文献
6.
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
7.
In this Note we consider nonnegative solutions for the nonlinear equation in , where is the so called Pucci operator and the ei are the eigenvalues of M et Λ?λ>0. We prove that if u satisfies the decreasing estimate for some β satisfying (β?1)(p?1)>2+α then u is radial. In a second time we prove that if and u is a nonnegative radial solution of (1), u(x)=g(r), such that g″ changes sign at most once, then u is zero. To cite this article: I. Birindelli, F. Demengel, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
8.
Given a polynomial , we calculate a subspace Gp of the linear space 〈X〉 generated by the indeterminates which is minimal with respect to the property (the algebra generated by Gp, and prove its uniqueness. Furthermore, we use this result to characterize the pairs (P,Q) of polynomials P(X1,…,Xn) and Q(X1,…,Xn) for which there exists an isomorphism T:〈X〉 →〈X〉 that “separates P from Q,” i.e., such that for some k(1<k<n) we can write P and Q as and respectively, where . 相似文献
9.
L Carlitz 《Journal of Combinatorial Theory, Series A》1978,24(3):261-277
Let Φ denote the set of arithmetic functions such that , where n = p1e1p2e2…prer and f(e1, e2,…,er) depends on the ej but is independent of the primes pj. The general Möbius inversion theorem then becomes the equivalence of (1.11) and (1.12) below. This in turn leads to relations between exponential generating functions as well as several applications. 相似文献
10.
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
11.
In this Note, we study the family of polynomials: P(X)=X3?nX2?n, with n=3sp1…pt, where s=0 or 1 and where the pi, for 1?i?t, are distinct prime numbers and all different from 3, and (4n2+27)/9s is squarefree. For this family, we determine the arithmetic invariants of the number field where α is the only real root of the polynomial P(X), and we find the following results: is the ring of integers of K, dK=?n2(4n2+27) is the discriminant of K; ε=α2+1 is the fundamental unit of OK and RK=Log(α2+1) is the regulator of K. To cite this article: O. Lahlou, M. El Hassani Charkani, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
12.
Kenneth Kramer 《Journal of Number Theory》1985,21(2):204-213
Explicit formulas are given for the quadratic and quartic characters of units of certain quadratic fields in terms of representations by positive definite binary quadratic forms, as conjectured by Leonard and Williams (Pacific J. Math.71 (1977), Rocky Mountain J. Math.9 (1979)), and by Lehmer (J. Reine Angew. Math.268/69 (1974)). For example, if p and a are primes such that p≡1 (mod 8), q≡5 (mod 8) and the Legendre symbol , and if ε is the fundamental unit of (√q), then , where p=a2+16b2 and pk=c2+16qd2 with k odd. 相似文献
13.
R.J. Williams 《Advances in Applied Mathematics》1985,6(1):1-3
Let {Xt, t ≥ 0} be Brownian motion in d (d ≥ 1). Let D be a bounded domain in d with C2 boundary, ?D, and let q be a continuous (if d = 1), Hölder continuous (if d ≥ 2) function in D?. If the Feynman-Kac “gauge” Ex{exp(∝0τDq(Xt)dt)1A(XτD)}, where τD is the first exit time from D, is finite for some non-empty open set A on ?D and some x?D, then for any ), is the unique solution in of the Schrödinger boundary value problem . 相似文献
14.
Daniel Caro 《Comptes Rendus Mathematique》2004,338(2):145-150
Let be a mixed characteristic complete discrete valuation ring, a smooth formal scheme over , P its special fiber, X a smooth subscheme of P, T a divisor in P such that TX=T∩X is a divisor in X and the weak completion of the sheaf of differential operators on . We prove that the unit-root F-isocrystals on X?TX overconvergent along TX are coherent over . To cite this article: D. Caro, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
15.
Let An(ω) be the nxn matrix An(ω)=(aij with aij=ωij, 0?i,j?n?1, ωn=1. For n=rs we show =(Ar?Is)Tsr(Ir?As). When r and s are relatively prime this identity implies a wide class of identities of the form PAn(ω)QT=Ar(ωαs)?As(ωβr). The matrices Psr, Prs, P, and Q are permutation matrices corresponding to the “data shuffling” required in a computer implementation of the FFT, and Tsr is a diagonal matrix whose nonzeros are called “twiddle factors.” We establish these identities and discuss their algorithmic significance. 相似文献
16.
Jean Bourgain 《Comptes Rendus Mathematique》2004,338(11):825-830
Given (p prime) of multiplicative order t>pδ, we obtain nontrivial bounds on exponential sums as well as the corresponding incomplete sums. These estimates are of relevance to several issues, such as the Diffie–Hellman distributions in cryptography, prime divisors of ‘sparse integers’, the distribution of Mersenne numbers Mq=2q?1 (q prime). The method is closely related to that of Bourgain and Konyagin (C. R. Acad. Sci. Paris, Ser. I 337 (2) (2003) 75–80). To cite this article: J. Bourgain, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
17.
William E Strawderman 《Journal of multivariate analysis》1974,4(3):255-264
Families of minimax estimators are found for the location parameters of a p-variate distribution of the form , where G(·) is a known c.d.f. on (0, ∞), p ≥ 3 and the loss is sum of squared errors. The estimators are of the form where 0 ≤ a ≤ 2, r(X′X) is nondecreasing, and is nonincreasing. Generalized Bayes minimax estimators are found for certain G(·)'s. 相似文献
18.
Roy Saunders Richard J. Kryscio Gerald M. Funk 《Stochastic Processes and their Applications》1981,12(1):97-106
Let X1n,…,X>nn denote the locations of n points in a bounded, γ-dimensional, Euclidean region Dn which has positive γ-dimensional Lebesgue measure μ(Dn). Let {Yn(r): r > 0} be the interpoint distance process for these points where Yn(r) is the number of pairs of points(Xin, Xin) which with i < j have Euclidean distance 6Xin ? X>in6 < r. In this article we study the limiting distribution of Yn(r) when n → ∞ and μ(Dn) → ∞, and the joint density of X1n,…,Xnnis of the form where r0 is a positive constant and Cn is a normalizing constant. These joint densities modify the Strauss [11] clustering model densities by introducing a hard-core component (no two points can have 6Xin ? Xin6 < r0) found in the Matérn [4] models. In our main result we show that the interpoint distance process converges to a non-homogeneous Poisson process for r values in a bounded interval 0 < r0 < r < r00 provided sparseness conditions discussed by Saunders and Funk [9] hold. The sparseness conditions which require converges to a positive constant and the boundary of Dn is negligible are essentially equivalent to requiring that although the number of points n is large the region is large enough so that the points are sparse in this region. That is, it is rare for a point to have another point close to it. These results extend results for v ? 0 given by Saunders and Funk [9] where it is shown that without the hard core component such results do not hold for v > 0. Statistical applications are discussed. 相似文献
19.
Joseph H. Silverman 《Journal of Number Theory》1984,19(3):437-442
Let K be a number field of degree d with regulator RK and absolute discriminant DK. Let r(K) be the rank of the unit group in K, and let p(K) be the maximum of r(k) as k ranges over proper subfields of K. We prove for constants cd, γd > 0 depending only on d. 相似文献
20.
Let be a connected and simply-connected open subset of such that the geodesic distance in is equivalent to the Euclidean distance. Let there be given a Riemannian metric (gij) of class and of vanishing curvature in , such that the functions gij and their partial derivatives of order have continuous extensions to . Then there exists a connected open subset of containing and a Riemannian metric of class and of vanishing curvature in that extends the metric (gij). To cite this article: P.G. Ciarlet, C. Mardare, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献