共查询到20条相似文献,搜索用时 31 毫秒
1.
Let be the n-dimensional ice cream cone, and let Γ(Kn) be the cone of all matrices in nn mapping Kn into itself. We determine the structure of Γ(Kn), and in particular characterize the extreme matrices in Γ(Kn). 相似文献
2.
Helmut Strasser 《Journal of multivariate analysis》1975,5(2):206-226
Let (X, ) be a measurable space, Θ ? an open interval and PΩ ∥ , Ω ? Θ, a family of probability measures fulfilling certain regularity conditions. Let be the maximum likelihood estimate for the sample size n. Let λ be a prior distribution on Θ and let be the posterior distribution for the sample size n given . denotes a loss function fulfilling certain regularity conditions and Tn denotes the Bayes estimate relative to λ and L for the sample size n. It is proved that for every compact K ? Θ there exists cK ≥ 0 such that This theorem improves results of Bickel and Yahav [3], and Ibragimov and Has'minskii [4], as far as the speed of convergence is concerned. 相似文献
3.
Let H and K be symmetric linear operators on a C1-algebra with domains D(H) and D(K). H is defined to be strongly K-local if implies for A?D(H) ∩ D(K) and ω in the state space of , and H is completely strongly K-local if implies for A ∈ D(H) ∩ D(K) and Ω in the state of , and H is cpmpletely strongly K-local if is -local on U?Mn for all n ? 1, where n is the identity on the n × n matrices Mn. If is abelian then strong locality and complete strong locality are equivalent. The main result states that if τ is a strongly continuous one-parameter group of 1-automorphisms of with generator δ0 and δ is a derivation which commutes with τ and is completely strongly δ0-local then δ generates a group α of 1-automorphisms of . Various characterizations of α are given and the particular case of periodic τ is discussed. 相似文献
4.
Ioan Tomescu 《Journal of Combinatorial Theory, Series B》1980,28(2):127-141
In this paper some recursion formulas and asymptotic properties are derived for the numbers, denoted by N(p, q), of irreducible coverings by edges of the vertices of complete bipartite (labeled) graphs Kp,q. The problem of determining numbers N(p, q) has been raised by I. Tomescu (dans “Logique, Automatique, Informatique,” pp. 269–423, Ed. Acad. R.S.R., Bucharest, 1971). A result concerning the asymptotic behavior of the number of irreducible coverings by cliques of q-partite complete graphs is obtained and it is proved that , , and , where I(n) and M(n) are the maximal numbers of irreducible coverings, respectively, coverings by cliques of the vertices of an n-vertex graph, and C(n) is the maximal number of minimal colorings of an n-vertex graph. It is also shown that maximal number of irreducible coverings by n ? 2 cliques of the vertices of an n-vertex graph (n ≥ 4) is equal to 2n?2 ? 2 and this number of coverings is attained only for K2,n?2 and the value of is obtained, where I(n, n ? k) denotes the maximal number of irreducible coverings of an n-vertex graph by n ? k cliques. 相似文献
5.
J Bustoz 《Journal of Mathematical Analysis and Applications》1981,79(1):71-79
It is known that the classical orthogonal polynomials satisfy inequalities of the form Un2(x) ? Un + 1(x) Un ? 1(x) > 0 when x lies in the spectral interval. These are called Turan inequalities. In this paper we will prove a generalized Turan inequality for ultraspherical and Laguerre polynomials. Specifically if Pnλ(x) and Lnα(x) are the ultraspherical and Laguerre polynomials and . We also prove the inequality is a positive constant depending on α and β. 相似文献
6.
Alladi Sitaram 《Journal of Functional Analysis》1978,27(2):179-184
Let G be a semisimple noncompact Lie group with finite center and let K be a maximal compact subgroup. Then W. H. Barker has shown that if T is a positive definite distribution on G, then T extends to Harish-Chandra's Schwartz space 1(G). We show that the corresponding property is no longer true for the space of double cosets . If G is of real-rank 1, we construct liner functionals for each p, 0 < p ? 2, such that but Tp does not extend to a continuous functional on . In particular, if p ? 1, Tv does not extend to a continuous functional on . We use this to answer a question (in the negative) raised by Barker whether for a K-bi-invariant distribution T on G to be positive definite it is enough to verify that . The main tool used is a theorem of Trombi-Varadarajan. 相似文献
7.
Attila Pethö 《Journal of Number Theory》1980,12(3):334-338
In this paper I prove the following Theorem: Let α be a quadratic irrational number and let ? > 0, . Then there exists an effectively computable, positive constant c depending on α and ? such that has no solutions in natural numbers q. 相似文献
8.
George B Purdy 《Journal of Combinatorial Theory, Series A》1974,17(1):131-133
There are at most 2n spheres tangent to all n + 1 faces of an n-simplex. It has been shown that the minimum number of such spheres is if n is odd and if n is even. The object of this note is to show that this result is a consequence of a theorem in graph theory. 相似文献
9.
A Hedayat 《Journal of Combinatorial Theory, Series A》1978,24(2):202-210
A generalization of the theory of sum composition of Latin square designs is given. Via this generalized theory it is shown that a self orthogonal Latin square design of order with a subself orthogonal Latin square design of order can be constructed for any prime p > 2 and any positive integer α as long as p ≠ 3, 5, 7 and 13 if α = 1. Additional results concerning sets of orthogonal Latin square designs are also provided. 相似文献
10.
The number of crossing-free Hamiltonian circuits in planar drawings of Kn is studied. In particular, it is shown that for planar drawings of Kn, (1) there are drawings having as many as such circuits and (2) no drawing contains more than 相似文献
11.
S.L.G. Choi 《Journal of Number Theory》1974,6(2):105-111
We define h(n) to be the largest function of n such that from any set of n nonzero integers, one can always extract a subset of h(n) integers with the property that any two sums formed from its elements are equal only if they have equal number of summands. A result of Erdös implies that , and it is the aim of the present paper to obtain the refinement . 相似文献
12.
Volker Strehl 《Discrete Mathematics》1977,18(1):99-101
A simple proof is given for the fact that the number of nonsingular similarity relations on {1, 2,… n}, for which the transitive closure of k blocks, equals 1 ? k ? n > ?2. In particular, this implies a recent result of Shapiro about Catalan numbers and Fine's sequence. 相似文献
13.
The initial and boundary value problem for the degenerate parabolic equation vt = Δ(?(v)) + F(v) in the cylinder bounded, for a certain class of point functions ? satisfying ?′(v) ? 0 (e.g., ) is considered. In the case that F(v) sign , the equation has a global time solution. The same is true for α = 1 provided the measure of Ω is sufficiently small. In the case that is nondecreasing a condition is given on the initial state v(x, 0) which implies that the solution must blow up in finite time. The existence of such initial states is discussed. 相似文献
14.
15.
Daniel J. Madden 《Journal of Number Theory》1978,10(3):303-323
If k is a perfect field of characteristic p ≠ 0 and k(x) is the rational function field over k, it is possible to construct cyclic extensions Kn over k(x) such that [K : k(x)] = pn using the concept of Witt vectors. This is accomplished in the following way; if [β1, β2,…, βn] is a Witt vector over k(x) = K0, then the Witt equation generates a tower of extensions through where . In this paper, it is shown that there exists an alternate method of generating this tower which lends itself better for further constructions in Kn. This alternate generation has the form Ki = Ki?1(yi); yip ? yi = Bi, where, as a divisor in Ki?1, Bi has the form . In this form q is prime to Πpjλj and each λj is positive and prime to p. As an application of this, the alternate generation is used to construct a lower-triangular form of the Hasse-Witt matrix of such a field Kn over an algebraically closed field of constants. 相似文献
16.
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
17.
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
18.
Let Ω be a simply connected domain in the complex plane, and , the space of functions which are defined and analytic on , if K is the operator on elements defined in terms of the kernels ki(t, s, a1, …, an) in by is the identity operator on , then the operator I ? K may be factored in the form (I ? K)(M ? W) = (I ? ΠK)(M ? ΠW). Here, W is an operator on defined in terms of a kernel w(t, s, a1, …, an) in by Wu = ∝antw(t, s, a1, …, an) u(s, a1, …, an) ds. ΠW is the operator; ΠWu = ∝an ? 1w(t, s, a1, …, an) u(s, a1, …, an) ds. ΠK is the operator; ΠKu = ∑i = 1n ? 1 ∝aitki(t, s, a1, …, an) ds + ∝an ? 1tkn(t, s, a1, …, an) u(s, a1, …, an) ds. The operator M is of the form m(t, a1, …, an)I, where and maps elements of into itself by multiplication. The function m is uniquely derived from K in the following manner. The operator K defines an operator on functions u in , by . A determinant of the operator is defined as an element of . This is mapped into by setting an + 1 = t to give m(t, a1, …, an). The operator I ? ΠK may be factored in similar fashion, giving rise to a chain factorization of I ? K. In some cases all the matrix kernels ki defining K are separable in the sense that ki(t, s, a1, …, an) = Pi(t, a1, …, an) Qi(s, a1, …, an), where Pi is a 1 × pi matrix and Qi is a pi × 1 matrix, each with elements in , explicit formulas are given for the kernels of the factors W. The various results are stated in a form allowing immediate extension to the vector-matrix case. 相似文献
19.
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
20.
Edward A Bender Herbert S Wilf 《Journal of Algorithms in Cognition, Informatics and Logic》1985,6(2):275-282
The graph coloring problem is: Given a positive integer K and a graph G. Can the vertices of G be properly colored in K colors? The problem is NP-complete. The average behavior of the simplest backtrack algorithm for this problem is studied. Average run time over all graphs is known to be bounded. Average run time over all graphs with n vertices and q edges behaves like . It is shown that similar results hold for all higher moments of the run time distribution. For all graphs and for graphs where lim exists, the run time has a limiting disibution as n → ∞. 相似文献