共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we show that the complete symmetric directed graph with n vertices admits an almost resolvable decomposition into TT3 (the transitive tournament on 3 vertices) or C3 (the directed cycle of length 3) if and only if n ≡ 1(mod 3). 相似文献
2.
Douglas Hensley 《Journal of Number Theory》1984,18(2):206-212
For a > 0 let , the sum taken over all n, 1 ≤ n ≤ x such that if p is prime and p|n then a < p ≤ y. It is shown for u < about () that , where pa(u) solves a delay differential equation much like that for the Dickman function p(u), and the asymptotic behavior of pa(u) is worked out. 相似文献
3.
Timothy W Tillson 《Journal of Combinatorial Theory, Series B》1980,29(1):68-74
It is shown that , 2m ≥ 8, can be decomposed into Hamiltonian circuits. A direct construction utilizing difference methods is given for 2m ≡ 0 (mod 4). The case 2m ≡ 2 (mod 4) is handled inductively by means of a construction which shows that admits such a decomposition if does. 相似文献
4.
Z.A Karian 《Journal of Number Theory》1976,8(2):233-244
Let k be a positive square free integer, the ring of algebraic integers in and S the unit sphere in Cn, complex n-space. If A1,…, An are n linearly independent points of Cn then L = {u1Au + … + unAn} with is called a k-lattice. The determinant of L is denoted by d(L). If L is a covering lattice for S, then is the covering density. L is called locally (absolutely) extreme if θ(S, L) is a local (absolute) minimum. In this paper we determine unique classes of extreme lattices for k = 1 and k = 3. 相似文献
5.
Let be a Dirichlet form in , where Ω is an open subset of n, n ? 2, and m a Radon measure on Ω; for each integer k with 1 ? k < n, let k be a Dirichlet form on some k-dimensional submanifold of Ω. The paper is devoted to the study of the closability of the forms E with domain and defined by: ki where 1 ? kp < ? < n, and where , gki denote restrictions of ?, g in to . Conditions are given for E to be closable if, for each i = 1,…, p, one has ki = n ? i. Other conditions are given for E to be nonclosable if, for some i, ki < n ? i. 相似文献
6.
For matrices , the C-numerical radius of A is the nonnegative quantity . This generalizes the classical numerical radius r(A). It is known that rc constitutes a norm on if and only if C is nonscalar and trC≠0. For all such C we obtain multiplicativity factors for rc, i.e., constant μ>0 for which μrc is submultiplicative on . 相似文献
7.
D Sotteau 《Journal of Combinatorial Theory, Series B》1981,30(1):75-81
In this paper we give necessary and sufficient conditions in order that Km,n () admits a decomposition into 2k-cycles (2k-circuits). This answers conjectures of J. C. Bermond (Thesis, Paris XI (Orsay), 1975) and J. C. Bermond and V. Faber (J. Combinatorial Theory Ser. B21 (1976), 146–155). 相似文献
8.
This paper is a study of the distribution of eigenvalues of various classes of operators. In Section 1 we prove that the eigenvalues (λn(T)) of a p-absolutely summing operator, p ? 2, satisfy This solves a problem of A. Pietsch. We give applications of this to integral operators in Lp-spaces, weakly singular operators, and matrix inequalities.In Section 2 we introduce the quasinormed ideal Π2(n), P = (p1, …, pn) and show that for T ∈ Π2(n), 2 = (2, …, 2) ∈ Nn, the eigenvalues of T satisfy More generally, we show that for T ∈ Πp(n), P = (p1, …, pn), pi ? 2, the eigenvalues are absolutely p-summable, We also consider the distribution of eigenvalues of p-nuclear operators on Lr-spaces.In Section 3 we prove the Banach space analog of the classical Weyl inequality, namely , 0 < p < ∞, where αn denotes the Kolmogoroff, Gelfand of approximation numbers of the operator T. This solves a problem of Markus-Macaev.Finally we prove that Hilbert space is (isomorphically) the only Banach space X with the property that nuclear operators on X have absolutely summable eigenvalues. Using this result we show that if the nuclear operators on X are of type l1 then X must be a Hilbert space. 相似文献
9.
Let Fn be the ring of n × n matrices over the finite field F; let o(Fn) be the number of elements in Fn, and s(Fn) be the number of singular matrices in Fn. We prove that if n ? 2, and if n = 2 and o(F) ? 3, then . 相似文献
10.
S. Krass 《Journal of Number Theory》1985,20(2):172-176
The explicit lower bound due to Furtwangler of Cn, the n-dimensional Diophantine approximation constant is , where Δn+1 is the minimum absolute discriminant of a real number field of degree n+1; , n = 1, 2, 3, …, is obtained, where [x] is the integer part of the real number x. The number 1 in the Furtwangler inequality is (explicitly) improved for all n ≥ 4. 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.
An n-tournament is a complete labelled digraph on n vertices without loops or multiple arcs. A tournament's score sequence is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The number Sn of distinct score sequences arising from all possible n-tournaments, as well as certain generalizations are investigated. A lower bound of the form (C1 a constant) and an upper bound of the form are proved. A q-extension of the Catalan numbers is defined. It is conjectured that all coefficients in the polynomial Cn(q) are at most . It is shown that if this conjecture is true, then 相似文献
13.
Raymond C Roan 《Journal of Functional Analysis》1980,39(1):67-74
Let α ? 0 and let . Then D(α) is a subalgebra of l1. We discuss the weak-1 generators of D(α). We use some of our techniques to prove that if ? is a weak-1 generator of H∞ and ∥ ? ∥∞ ? 1, then the composition operator C? on the Dirichlet space has dense range. 相似文献
14.
H.B Kushner 《Journal of multivariate analysis》1985,17(1):84-98
The coefficients aτ?, sometimes called “generalized binomial coefficients” in the expansion , are computed explicitly when t = r + 1, where ? is a partition of r and τ a partition of t. A recursion formula permits the calculation of the general aτ?. Several properties of aτ? are proved. A connection between the aτ? and other coefficients is established. The main tools used are Bingham's identity, results from the theory of invariant differential operators, and a lemma concerning zonal polynomials. 相似文献
15.
Affine and combinatorial properties of the polytope of all n × n nonnegative doubly stochastic matrices are investigated. One consequence of this investigation is that if is a face of of dimension d > 2, then has at most 3(d?1) facets. The special faces of which were characterized in Part I of our study of in terms of the corresponding (0, 1)- matrices are classified with respect to affine equivalence. 相似文献
16.
Properties of the graph of the polytope of all n × n nonnegative doubly stochastic matrices are studied. If is a face of which is not a k-dimensional rectangular parallelotope for k ≥ 2, then G() is Hamilton connected. Prime factor decompositions of the graphs of faces of relative to Cartesian product are investigated. In particular, if is a face of , then the number of prime graphs in any prime factor decomposition of G() equals the number of connected components of the neighborhood of any vertex of G(). Distance properties of the graphs of faces of are obtained. Faces of for which G() is a clique of are investigated. 相似文献
17.
Robert A. Morris 《Journal of Pure and Applied Algebra》1980,18(1):91-96
The absolute Kähler module of the truncated generalized Witt vectors of a field k of positive characteristic is zero if and only if k is perfect. This recovers known information on with which the structure of K2(k((t))) can be studied. 相似文献
18.
Gideon Nettler 《Journal of Number Theory》1981,13(4):456-462
In a previous paper it was proven that given the continued fractions where the a's and b's are positive integers, then A, B, A ± B, and AB are irrational numbers if for all n sufficiently large, and transcendental numbers if for all n sufficiently large. Using a more direct approach it is proven in this paper that A, B, A ± B, and AB are transcendental numbers if an > bn > an?1(n?1)2 for all n sufficiently large. 相似文献
19.
W Fernandez de la Vega 《Journal of Combinatorial Theory, Series B》1983,35(3):328-332
For any tournament T on n vertices, let h(T) denote the maximum number of edges in the intersection of T with a transitive tournament on the same vertex set. Sharpening a previous result of Spencer, it is proved that, if Tn denotes the random tournament on n vertices, then, as n → ∞. 相似文献
20.
Let Ω = {1, 0} and for each integer n ≥ 1 let (n-tuple) and for all k = 0,1,…,n. Let {Ym}m≥1 be a sequence of i.i.d. random variables such that . For each A in , let TA be the first occurrence time of A with respect to the stochastic process {Ym}m≥1. R. Chen and A.Zame (1979, J. Multivariate Anal. 9, 150–157) prove that if n ≥ 3, then for each element A in , there is an element B in such that the probability that TB is less than TA is greater than . This result is sharpened as follows: (I) for n ≥ 4 and 1 ≤ k ≤ n ? 1, each element A in , there is an element B also in such that the probability that TB is less than TA is greater than ; (II) for n ≥ 4 and 1 ≤ k ≤ n ? 1, each element A = (a1, a2,…,an) in , there is an element C also in such that the probability that TA is less than TC is greater than if n ≠ 2m or n = 2m but ai = ai + 1 for some 1 ≤ i ≤ n?1. These new results provide us with a better and deeper understanding of the fair coin tossing process. 相似文献