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81.
82.
83.
J. Arvesú L. L. Littlejohn F. Marcellán 《Journal of Computational Analysis and Applications》2002,4(4):363-387
In this paper, we further develop the left-definite and right-definite spectral theory associated with the self-adjoint differential operator A in L2(-1,1), generated from the classical second-order Legendre differential equation, having the sequence of Legendre polynomials as eigenfunctions. Specifically, we determine the first three left-definite spaces associated with the pair (L2(-1,1),A). As a consequence of these results, we determine the explicit domain of both the associated left-definite operator A1, first observed by Everitt, and the self-adjoint operator A1/2. In addition, we give a new characterization of the domain D(A) of A and, as a corollary, we present a new proof of the Everitt-Mari result which gives optimal global smoothness of functions in D(A). 相似文献
84.
A. V. Arhangel'skii R. Z. Buzyakova 《Proceedings of the American Mathematical Society》1999,127(8):2449-2458
We prove that the cardinality of every first countable linearly Lindelöf Tychonoff space does not exceed , and every strongly discretely Lindelöf Tychonoff space of countable tightness is Lindelöf.
85.
王文胜 《浙江大学学报(理学版)》1999,26(1)
本文对id多指标随机变量序列{Xk;k∈Nd}(d≥2)的部分和Sn=∑k≤nXk及H(t)↑+∞,(t→+∞),提出并讨论了Порохоров的3个问题(d≥2),并讨论了多指标随机变量和的完全收敛性. 相似文献
86.
Consider a closed Jackson type network in which each queue has a single exponential server. Assume that N customers are moving among k queues. We establish simple closed form bounds on the network throughput (both lower and upper), which are sharper than those that are currently available. Numerical evaluation indicates that the improvements are significant. 相似文献
87.
Let N denote the set of natural numbers and let P =(N
k
, ) be a countably infinite poset on the k-dimensional lattice N
k
. Given x N
k
, we write max(x) (min(x)) for the maximum (minimum) coordinate of x. Let
be the directed-incomparability graph of P which is defined to be the graph with vertex set equal to N
k
and edge set equal to the set of all (x, y) such that max(x) max(y) and x and y not comparable in P. For any subset D N
k
, we let P
D
and
D
denote the restrictions of P and
to D. Points x N
k
with min(x) = 0 will be called boundary points. We define a geometrically natural notion of when a point is interior to P or
relative to the lattice N
k
, and an analogous notion of monotone interior with respect to
or
D
. We wish to identify situations where most of these interior points are exposed to the boundary of the lattice or, in the case of monotone interior points, not concealed very much from the boundary. All of these ideas restrict to finite sublattices F
k
and/or infinite sublattices E
k
of N
k
. Our main result shows that for any poset P and any arbitarily large integer M > 0, there is an F E with F = M where, relative to the sublattices F
k
E
k
, the ideal situation of total exposure of interior points and very little concealment of monotone interior points must occur. Precisely, we prove that for any P =(N
k
, ) and any integer M > 0, there is an infinite E N and a finite D F
k
with F E and F = M such that (1) every interior vertex of P
E
k
or
E
k
is exposed and (2) there is a fixed set C E, C k
k
, such that every monotone-interior point of
D
belonging to F
k
has its monotone concealment in the set C. In addition, we show that if P
1 =(N
k
, 1),..., P
r
=(N
k
,
r
) is any sequence of posets, then we can find E,D, and F so that the properties (1) and (2) described above hold simultaneously for each P
i
. We note that the main point of (2) is that the bound k
k
depends only on the dimension of the lattice and not on the poset P. Statement (1) is derived from classical Ramsey theory while (2) is derived from a recent powerful extension of Ramsey theory due to H. Friedman and shown by Friedman to be independent of ZFC, the usual axioms of set theory. The fact that our result is proved as a corollary to a combinatorial theorem that is known to be independent of the usual axioms of mathematics does not, of course, mean that it cannot be proved using ZFC (we just couldn"t find such a proof). This puts our geometrically natural combinatorial result in a somewhat unusual position with regard to the axioms of mathematics. 相似文献
88.
Sheila Sundaram 《Journal of Algebraic Combinatorics》1999,9(3):251-269
We present a class of subposets of the partition lattice
n
with the following property: The order complex is homotopy equivalent to the order complex of
n
– 1, and the S
n
-module structure of the homology coincides with a recently discovered lifting of the S
n
– 1-action on the homology of
n
– 1. This is the Whitehouse representation on Robinson's space of fully-grown trees, and has also appeared in work of Getzler and Kapranov, Mathieu, Hanlon and Stanley, and Babson et al.One example is the subposet P
n
n
– 1 of the lattice of set partitions
n
, obtained by removing all elements with a unique nontrivial block. More generally, for 2 k n – 1, let Q
n
k
denote the subposet of the partition lattice
n
obtained by removing all elements with a unique nontrivial block of size equal to k, and let P
n
k
=
i = 2
k
Q
n
i
. We show that P
n
k
is Cohen-Macaulay, and that P
n
k
and Q
n
k
are both homotopy equivalent to a wedge of spheres of dimension (n – 4), with Betti number
. The posets Q
n
k
are neither shellable nor Cohen-Macaulay. We show that the S
n
-module structure of the homology generalises the Whitehouse module in a simple way.We also present a short proof of the well-known result that rank-selection in a poset preserves the Cohen-Macaulay property. 相似文献
89.
Maria Angeles Gil 《Annals of the Institute of Statistical Mathematics》1988,40(4):627-639
The absence of exactness in the observation of the outcomes of a random experiment always entails a loss of information about the experimental distribution. This intuitive assertion will be formally proved in this paper by using a mathematical model involving the notions of fuzzy information and fuzzy information system (as intended by Tanaka, Okuda and Asai) and Zadeh's probabilistic definition. On the basis of this model we are first going to consider a family of measures of information enclosing some well-known measures, such as those defined by Kagan, Kullback-Leibler and Matusita, and then to establish methods for removing the loss of information due to fuzziness by increasing suitably the number of experimental observations. 相似文献
90.
无限维Heisenberg代数的导子代数和全形 总被引:2,自引:0,他引:2
给出了无维Heisrberg代数的全形和全形的导子代数Der(s)证明(s)不是一个完备李代数,但Der(s)是一个完备李代数。 相似文献