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961.
Giuseppe Mingione 《Journal of Global Optimization》2008,40(1-3):209-223
I will report on some recent developments concerning the problem of estimating the Hausdorff dimension of the singular sets
of solutions to elliptic and variational problems. Emphasis will be given on some open issues. Connections with measure data
problems will be outlined. 相似文献
962.
963.
雷达船目标的模糊智能识别 总被引:2,自引:0,他引:2
模糊集理论和技术给复杂的模糊背景下的模式识别问题提供了一种简易有效的处理手段。基于模糊集理论,定量地分析和处理识别过程中的各种不确定性信息,以提高识别系统的可靠性和智能度,便是我们研究舰船雷达目标识别系统中识别算法的一重要内容。本文通过舰船雷达目标识别这一典型的模糊模式识别问题,系统地论述了模糊模式识别系统的一般性框架、模糊特征抽取和隶属函数的建立、模糊特征选择和匹配分类、层次化模糊分类系统构造等一系列关键性问题。本文提出的各种方法具有通用性,已建立的识别系统在试验中具有良好的目标识别能力。 相似文献
964.
The aim of this paper is to establish both necessary and sufficient conditions for the existence of viable solutions of a higher-order differential inclusion. Higher-order tangent sets are introduced and studied to get such conditions. These tangent sets are analysed in the case of the viable set defined by equality or inequality constraints and viability conditions are rewritten in terms of these constraints. 相似文献
965.
Ignacio Garcia Ursula Molter Roberto Scotto 《Proceedings of the American Mathematical Society》2007,135(10):3151-3161
We estimate the packing measure of Cantor sets associated to non-increasing sequences through their decay. This result, dual to one obtained by Besicovitch and Taylor, allows us to characterize the dimension functions recently found by Cabrelli et al for these sets.
966.
For a function ?(y) = o(y ?1/s ), y → ∞, we prove the existence of vectors ?∈? s admitting, for any ε > 0, infinitely many simultaneous ?(1 + ε-approximations, but not admitting any simultaneous ?-approximations. 相似文献
967.
Xiao Yun CHENG Jian Guo XIA Hou Rong QIN 《数学学报(英文版)》2007,23(5):819-826
Let K2 be the Milnor functor and let Фn (x)∈ Q[X] be the n-th cyclotomic polynomial. Let Gn(Q) denote a subset consisting of elements of the form {a, Фn(a)}, where a ∈ Q^* and {, } denotes the Steinberg symbol in K2Q. J. Browkin proved that Gn(Q) is a subgroup of K2Q if n = 1,2, 3, 4 or 6 and conjectured that Gn(Q) is not a group for any other values of n. This conjecture was confirmed for n =2^T 3S or n = p^r, where p ≥ 5 is a prime number such that h(Q(ζp)) is not divisible by p. In this paper we confirm the conjecture for some n, where n is not of the above forms, more precisely, for n = 15, 21,33, 35, 60 or 105. 相似文献
968.
This article extends a paper of Abraham and Bonnet which generalised the famous Hausdorff characterisation of the class of
scattered linear orders. They gave an inductively defined hierarchy that characterised the class of scattered posets which
do not have infinite incomparability antichains (i.e. have the FAC). We define a larger inductive hierarchy κℌ* which characterises the closure of the class of all κ-well-founded linear orders under inversions, lexicographic sums and FAC weakenings. This includes a broader class of “scattered”
posets that we call κ-scattered. These posets cannot embed any order such that for every two subsets of size < κ, one being strictly less than the other, there is an element in between. If a linear order has this property and has size
κ it is unique and called ℚ(κ). Partial orders such that for every a < b the set {x: a < x < b} has size ≥ κ are called weakly κ-dense, and posets that do not have a weakly κ-dense subset are called strongly κ-scattered. We prove that κℌ* includes all strongly κ-scattered FAC posets and is included in the class of all FAC κ-scattered posets. For κ = ℵ0 the notions of scattered and strongly scattered coincide and our hierarchy is exactly aug(ℌ) from the Abraham-Bonnet theorem.
The authors warmly thank Uri Abraham for his many useful suggestions and comments. Mirna Džamonja thanks EPSRC for their support
on an EPSRC Advanced Fellowship. 相似文献
969.
Guang Gong 《Discrete Applied Mathematics》2006,154(18):2590-2598
Let p be a prime, q=pm and Fq be the finite field with q elements. In this paper, we will consider q-ary sequences of period qn-1 for q>2 and study their various balance properties: symbol-balance, difference-balance, and two-tuple-balance properties. The array structure of the sequences is introduced, and various implications between these balance properties and the array structure are proved. Specifically, we prove that if a q-ary sequence of period qn-1 is difference-balanced and has the “cyclic” array structure then it is two-tuple-balanced. We conjecture that a difference-balanced q-ary sequence of period qn-1 must have the cyclic array structure. The conjecture is confirmed with respect to all of the known q-ary sequences which are difference-balanced, in particular, which have the ideal two-level autocorrelation function when q=p. 相似文献
970.
We analyze a polling system with multiple stations (queues) attended by a cycling server, in which a setup occurs only when the queue that is polled by the server has one or more customers present. Although such systems are appropriate for modeling numerous manufacturing and telecommunication systems, their analysis is not well developed in the literature. We provide an exact analysis for the 2 station model and present two approximation schemes to determine the mean station waiting times for models with 3 or more stations. We show that some approximate models which have been proposed in the literature for providing upper bounds on the mean station waiting times do not always yield upper bounds. Extensive numerical tests indicate that a simple average of the two approximation schemes yields a close estimate of the true mean station waiting time. This average-of-approximations procedure appears to be robust for a large range of parameter values.Research supported in part by the Natural Sciences and Engineering Research Council of Canada under grant OGP0045904.Research supported in part by the National Science Foundation under grant DMI-9500471. 相似文献