If is a B-convex normed Riesz space, then the topological completion of is a closed subspace of 7, the second Banach dual of . If or , then is a B-convex σ-Dedekind complete normed Riesz space which is the Banach dual of a normed Riesz space. In such a , if u1 ? u2 ? … ? 0 and infn{un} = 0, then limn∥un∥ = 0. This is the key step in verifying that Ogasawara's criteria that a normed Riesz space be reflexive are satisfied by 7. Thus the topological completion of as a closed subspace of 7 is also reflexive. 相似文献
Let M be a finite set consisting of ki elements of type i, i = 1, 2,…, n and let S denote the set of subsets of M or, equivalently, the set of all vectors x = (x1, x2,…,xn) with integral coefficients xi satisfying 0 ? xi ? ki, i = 1, 2,…, n. An antichain is a subset of S in which there is no pair of distinct vectors x and y such that x is contained in y (that is, there is no pair of distinct vectors x and y such that the inequalities xi ? yi, i = 1, 2,…, n all hold). Let denote the number of vectors in S which are contained in at least one vector in and let , the number of basic elements in . For given m we give procedures for calculating min and min , where the minima are taken over all m-element antichains in S. 相似文献
For an arbitrary set X, if denotes the collection of finite subsets of X, then is called the finite subset algebra of X (which we also denote by . Because of the many natural occurrences of finite subset algebras, the intent of this paper is to initiate an investigation of the semigroup, End , of endomorphisms of .Several representations of End are obtained and these representations are in turn used to obtain information about the structure of End . In particular, the Green relations are characterized; for finite X, the maximal subgroups of End are found and the number of idempotents is given. As a side result, an abstract characterization of a certain semigroup of (0,1)-matrices is obtained. 相似文献
Poincaré observed that for a differential equation depending on a parameter α, each periodic orbit generally lies in a connected family of orbits in (x, α)-space. In order to investigate certain large connected sets (denoted Q) of orbits containing a given orbit, we introduce two indices: an orbit index φ and a “center” index defined at certain stationary points. We show that genetically there are two types of Hopf bifurcation, those we call “sources” () and “sinks” (). Generically if the set Q is bounded in (x, α)-space, and if there is an upper bound for periods of the orbits in Q, then Q must have as many source Hopf bifurcations as sink Hopf bifurcations and each source is connected to a sink by an oriented one-parameter “snake” of orbits. A “snake” is a maximal path of orbits that contains no orbits whose orbit index is 0. See Fig. 1.1. 相似文献
Let {Xi, i?0} be a sequence of independent identically distributed random variables with finite absolute third moment. Then Darling and Erdös have shown that for -∞<t<∞ where and . The result is extended to dependent sequences but assuming that {Xi} is a standard stationary Gaussian sequence with covariance function {ri}. When {Xi} is moderately dependent (e.g. when we get where Ha is a constant. In the strongly dependent case (e.g. when we get for-∞<t<∞. 相似文献
Let Ω ? N be an open set with and some l > 0 satisfying an additional regularity condition. We give asymptotic estimates for the approximation numbers αn of Sobolev imbeddings over these quasibounded domains Ω. Here denotes the Sobolev space obtained by completing under the usual Sobolev norm. We prove , where . There are quasibounded domains of this type where γ is the exact order of decay, in the case p ? q under the additional assumption that either 1 ? p ? q ? 2 or 2 ? p ? q ? ∞. This generalizes the known results for bounded domains which correspond to l = ∞. Similar results are indicated for the Kolmogorov and Gelfand numbers of Ip,qm. As an application we give the rate of growth of the eigenvalues of certain elliptic differential operators with Dirichlet boundary conditions in , where Ω is a quasibounded domain of the above type. 相似文献
We prove that an automorphism of order 5 of the Del Pezzo surface S of degree 5 is conjugate through a birational map to a linear automorphism of . This completes the classification of conjugacy classes of elements of prime order in the Cremona group. To cite this article: A. Beauville, J. Blanc, C. R. Acad. Sci. Paris, Ser. I 339 (2004).相似文献
Let X be an observation from a p-variate (p ≥ 3) normal random vector with unknown mean vector θ and known covariance matrix . The problem of improving upon the usual estimator of θ, δ0(X) = X, is considered. An approach is developed which can lead to improved estimators, δ, for loss functions which are polynomials in the coordinates of (δ ? θ). As an example of this approach, the loss L(δ, θ) = |δ ? θ|4 is considered, and estimators are developed which are significantly better than δ0. When is the identity matrix, these estimators are of the form . 相似文献
In this paper, we show that the initial boundary value problem for the (singular) nonlinear EPD (Euler-Poisson-Darboux) equation does not possess global solutions for arbitrary choices of ) when 0 < k ? 1 for a wide class of nonlinearities , which includes all the even powers of u and the functions u2n + 1, n = 1, 2,…. The solutions are assumed to vanish on the “walls” of the spacetime cylinder and satisfy . The result is independent of the space dimension. 相似文献
We present in this paper some results concerning the following nonlinear system of P.D.E. where .The above system is a mathematical model which describes coupled flexural and torsional oscillations of an open cross-section beam. In Part I we consider the abstract initial value problem associated with the above system, prove the existence and uniqueness of solutions in a weak sense and mention two applications. In Part II we obtain regular solutions when adequate conditions on the data are assumed. 相似文献
Let be a σ-finite nonatomic measure space. We think of the customary analysis based upon as continuum analysis. By contrast discrete analysis is based upon an arbitrary countable subset of X, rather than upon X itself, and all countable subsets are treated alike with a Poisson process used to distinguish among them probabilisticly. The sort of functions appropriate for discrete analysis are the Campbell functions, or, as they are called in the present paper, the random functions of Poisson type. The paper presents an account of the ideas underlying discrete analysis and treats briefly the specifies of representation, stochastic integrals, and duality theory for random functions of Poisson type. It is chiefly concerned, however, with those random functions which occur in connection with the discrete analysis of Brownian motion, (for example, with Gaussian noise). In particular it shows that there is a completely positive map which carries such discrete processes onto an algebraic version of Wiener's Brownian motion process, and that under this map, random functions of Poisson type go over to the appropriate random functions of Wiener type. It also shows that the map carries random variables into noncommuting operators characteristic of quantum theory. 相似文献
An algebra is near-boolean if every two generated subalgebra is a boolean algebra. It is shown that for n ? 4 there is a near-boolean algebra of size n ≡ 4 or 8 (mod 12), that for n ? 16 and n ≡ 4 or 8 (mod 12) there is a near-boolean algebra of size n which is not a boolean algebra, and that the smallest near-boolean algebra which is not a boolean algebra has 16 elements. 相似文献
We construct two d-dimensional independent diffusions , with the same viscosity ν≠0 and the same drift u(x,t)=(pρta(x)v1+(1?p)ρtb(x)v2)/(pρta(x)+(1?p)ρtb(x)), where ρta,ρtb are respectively the density of Xta and Xtb. Here and p∈(0,1) are given. We show that is the unique weak solution of the following pressureless gas system such that as t→0+. To cite this article: A. Dermoune, S. Filali, C. R. Acad. Sci. Paris, Ser. I 337 (2003).相似文献
According to a result of A. Ghizzetti, for any solution y(t) of the differential equation where , (0 ?i ? n ?1, either y(t) = 0 for t ? 1 or there is an integer r with 0 ? r ? n ? 1 such that exists and ≠0. Related results are obtained for difference and differential inequalities. A special case of the former has interesting applications in the study of orthogonal polynomials. 相似文献
A generalized inverse of a linear transformation A: → , where and are arbitrary finite dimensional vector spaces, is defined using only geometrical concepts of linear transformations. The inverse is uniquely defined in terms of specified subspaces ? , ? and a linear transformation N satisfying some conditions. Such an inverse is called the N-inverse. A Moore-Penrose type inverse is obtained by choosing N = 0. Some optimization problems are considered by choosing and as inner product spaces. Our results extend without any major modification of proofs to bounded linear operators with closed range on Hilbert spaces. 相似文献