共查询到20条相似文献,搜索用时 26 毫秒
1.
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
2.
It is shown that if satisfies , where σk(A) denotes the sum of all kth order subpermanent of A, then Per[λJn+(1?λ)A] is strictly decreasing in the interval 0<λ<1. 相似文献
3.
Anne Marie Torpe 《Journal of Functional Analysis》1985,61(1):15-71
The K-theory of the C1-algebra associated to C∞-foliations (V, F) of a manifold V in the simplest non-trivial case, i.e., dim V = 2, is studied. Since the case of the Kronecker foliation was settled by Pimsner and Voiculescu (J. Operator Theory4 (1980), 93–118), the remaining problem deals with foliations by Reeb components. The K-theory of for the Reeb foliation of S3 is also computed. In these cases the C1-algebra is obtained from simpler C1-algebras by means of pullback diagrams and short exact sequences. The K-groups are computed using the associated Mayer-Vietoris and six-term exact sequences. The results characterize the C1-algebra of the Reeb foliation of 2 uniquely as an extension of C(S1) by C(S1). For the foliations of 2 it is found that the K-groups count the number of Reeb components separated by stable compact leaves. A C∞-foliation of 2 such that K1(C1(2, F)) has infinite rank is also constructed. Finally it is proved, by explicit calculation using (M. Penington, “K-Theory and C1-Algebras of Lie Groups and Foliations,” D. Phil. thesis, Oxford, 1983), that the natural map is an isomorphism for foliations by Reeb components of 2 and S3. In particular this proves the Baum-Connes conjecture (P. Baum and A. Connes, Geometric K-theory for Lie groups, preprint, 1982; A. Connes, Proc. Symp. Pure Math.38 (1982), 521–628) when V = 2. 相似文献
4.
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
5.
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
6.
L.B Richmond 《Journal of Number Theory》1976,8(4):390-396
Asymptotic results are obtained for pA(k)(n), the kth difference of the function pA(n) which is the number of partitions of n into integers from A. Under certain restrictions on A it is shown that thereby verifying for these A a conjecture of Bateman and Erdös. 相似文献
7.
D Zwick 《Journal of Mathematical Analysis and Applications》1984,104(2):435-436
For a(1) ? a(2) ? ··· ? a(n) ? 0, b(1) ? b(2) ? ··· ? b(n) ? 0, the ordered values of ai, bi, i = 1, 2,…, n, m fixed, m ? n, and p ? 1 it is shown that where is the integer such that and . The inequality is shown to be sharp. When p < 1 and a(i)'s are in increasing order then the inequality is reversed. 相似文献
8.
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
9.
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
10.
Simon Wassermann 《Journal of Functional Analysis》1976,23(3):239-254
If A and B are C1-algebras there is, in general, a multiplicity of C1-norms on their algebraic tensor product A ⊙ B, including maximal and minimal norms ν and α, respectively. A is said to be nuclear if α and ν coincide, for arbitrary B. The earliest example, due to Takesaki [11], of a nonnuclear C1-algebra was , the C1-algebra generated by the left regular representation of the free group on two generators F2. It is shown here that W1-algebras, with the exception of certain finite type I's, are nonnuclear.If is the group C1-algebra of F2, there is a canonical homomorphism λl of onto . The principal result of this paper is that there is a norm ζ on , distinct from α, relative to which the homomorphism is bounded ( being endowed with the norm α). Thus quotients do not, in general, respect the norm α; a consequence of this is that the set of ideals of the α-tensor product of C1-algebras A and B may properly contain the set of product ideals {}.Let A and B be C1-algebras. If A or B is a W1-algebra there are on A ⊙ B certain C1-norms, defined recently by Effros and Lance [3], the definitions of which take account of normality. In the final section of the paper it is shown by example that these norms, with α and ν, can be mutually distinct. 相似文献
11.
We study the weight distribution of irreducible cyclic (n, k) codeswith block lengths n = n1((q1 ? 1)/N), where N|q ? 1, gcd(n1,N) = 1, and gcd(l,N) = 1. We present the weight enumerator polynomial, A(z), when k = n1l, k = (n1 ? 1)l, and k = 2l. We also show how to find A(z) in general by studying the generator matrix of an (n1, m) linear code, over GF(qd) where d = gcd (ordn1(q), l). Specifically we study A(z) when is a maximum distance separable code, a maximal shiftregister code, and a semiprimitive code. We tabulate some numbers Aμ which completely determine the weight distributionof any irreducible cyclic (n1(21 ? 1), k) code over GF(2) for all n1 ? 17. 相似文献
12.
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
13.
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
14.
Ludwig Arnold 《Linear algebra and its applications》1976,13(3):185-199
It is proved that Wigner's semicircle law for the distribution of eigenvalues of random matrices, which is important in the statistical theory of energy levels of heavy nuclei, possesses the following completely deterministic version. Let An=(aij), 1?i, ?n, be the nth section of an infinite Hermitian matrix, {λ(n)}1?k?n its eigenvalues, and {uk(n)}1?k?n the corresponding (orthonormalized column) eigenvectors. Let , put (bookeeping function for the length of the projections of the new row v1n of An onto the eigenvectors of the preceding matrix An?1), and let finally (empirical distribution function of the eigenvalues of . Suppose (i) , (ii) limnXn(t)=Ct(0<C<∞,0?t?1). Then ,where W is absolutely continuous with (semicircle) density 相似文献
15.
Robert Donaghey 《Journal of Combinatorial Theory, Series A》1976,21(2):155-163
This paper treats the class of sequences {an} that satisfy the recurrence relation between the odd and even terms of {an} that involves the coefficients of tan(t), namely A combinatorial setting is then provided to elucidate the appearance of the tangent coefficients in this equation. 相似文献
16.
Necessary and sufficient conditions for a solution {zk} of the difference equation , with singular, to be a convergent sequence of vectors are given under a variety of assumptions. Theoretical results on iterative schemes for solving Ax = b by singular splittings, , are given first. In particular, the case when and is positive semi-definite is considered. Then applications to discrete control problems and backwards population projection are discussed. 相似文献
17.
I.J Zucker 《Journal of Number Theory》1985,20(1):92-102
Series of the form may be expressed as log sin integrals and are shown to be summable exactly in terms of Dirichlets L-series for values of n up to and including 5. Other related series are also discussed and several exact results are given. 相似文献
18.
Stanisław Lewanowicz 《Journal of Computational and Applied Mathematics》1979,5(3):193-206
In this paper we are constructing a recurrence relation of the form for integrals (called modified moments) in which Ck(λ) is the k-th Gegenbauer polynomial of order , and f is a function satisfying the differential equation of order n, where p0, p1, …, pn ? 0 are polynomials, and mk〈λ〉[p] is known for every k. We give three methods of construction of such a recurrence relation. The first of them (called Method I) is optimum in a certain sense. 相似文献
19.
20.
For 1 ? p ? ∞, let , be the lp norm of an m × n complex A = (αij) ?Cm × n. The main purpose of this paper is to find, for any p, q ? 1, the best (smallest) possible constants τ(m, k, n, p, q) and σ(m, k, n, p, q) for which inequalities of the form hold for all A?Cm × k, B?Ck × n. This leads to upper bounds for inner products on Ck and for ordinary lp operator norms on Cm × n. 相似文献