非强占FBFS服务规则下Re-entrant Line排队网络的扩散逼近

本文研究了-个非强占静态优先权first-buffer-first-served(FBFS)服务规则下的re-entrant line排队网络.文章首先建立了-个极限定理,后通过分析队长和斜反射映射的关系,建立了队长过程和闲期过程的扩散逼近.     

Bootstrapped confidence bands for percentile lifetime

Summary We propose bootstrapped confidence bands for the percentile lifetime function. Our method is based on a joint approximation of the empirical and quantile processes and their bootstrapped counterparts. Modest simulations support the results. Confidence bands are applied to quantile and median residual lifetimes of tractor rear brakes. Research done while at Carleton University Norman Paterson Centre: also partially supported by NSERC Canada grants of M. Cs?rgő. Research supported in part by a NSERC Canada operating grant. Research done while at Carleton University; also partially supported by NSERC Canada grants of m. Cs?rgő and D. A. Dawson and by an EMR Canada grant of M. Cs?gő. Research supported in part by a United States Department of Agriculture CSRS grant and a United States NSF grant of D. M. Bates, G. Wahba and B. S. Yandell.     

Single identities for lattice theory and for weakly associative lattices

We present a single identity for the variety of all lattices that is much simpler than those previously known to us. We also show that the variety of weakly associative lattices is one-based, and we present a generalized one-based theorem for subvarieties of weakly associative lattices that can be defined with absorption laws. The automated theorem-proving program Otter was used in a substantial way to obtain the results.Presented by S. Burris.Supported by the Office of Scientific Computing, U.S. Department of Energy, under Contract W-31-109-Eng-38.Supported by an operating grant from NSERC of Canada (#A8215).     

Shift-invariant spaces and linear operator equations

In this paper we investigate the structure of finitely generated shift-invariant spaces and solvability of linear operator equations. Fourier trans-forms and semi-convolutions are used to characterize shift-invariant spaces. Criteria are provided for solvability of linear operator equations, including linear partial difference equations and discrete convolution equations. The results are then applied to the study of local shift-invariant spaces. Moreover, the approximation order of a local shift-invariant space is characterized under some mild conditions on the generators. Supported in part by NSERC Canada under Grant OGP 121336.     

Geometry of normed bilinear maps and the 16-square problem

Supported in part by NSERC of Canada     

一类重入型网络在优先服务原则下的扩散近似

本文研究了一类重入型网络在优先服务原则下的扩散近似,运用随机分析方法,证明了标准化队长过程的C-紧性．在优先服务原则下,给出了这类网络的标准化队长过程扩散近似存在的充分条件．     

Automorphisms of split Cayley algebras over real closed fields

Research supported in part by NSERC Canada grant A7251.     

The range of the gradient of a LipschitzC 1-smooth bump in infinite dimensions

If a Banach space has a LipschitzC ¹-smooth bump function, then it admits other bumps of the same smoothness whose gradients exactly fill the dual unit ball and other reasonable figures. This strengthens a result of Azagra and Deville who were able to cover the dual unit ball. Supported in part by NSERC and the Canada Research Chair Programme. Supported in part by grants NATO CRG-973982, GAĈR 201-01-1198, and AV 1019003 (Czech Republic). Supported in part by NATO CRG-973982 and NSERC.     

Eigenvectors and ratio limit theorems for Markov chains and their relatives

Associated to classes of countable discrete Markov chains or, more generally, column-finite nonnegative infinite matrices, and a finite subset of the state space, is a dimension group. In many cases, this dimension group gives information about the nonnegative eigenvectors of the process. Moreover, the study of the nonnegative eigenvectors is, equivalent to the traces on an analytic one parameter family of dimension groups. We pay particular attention to the case that there is at most one nonnegative eigenvector per eigenvalue, giving a number of sufficient conditions. Using the techniques developed here, we also show that under a reasonable set of conditions (principle among them that there be just one nonnegative eigenvector for the spectral radius), a (one-sided) ratio limit theorem holds. Supported in part by an operating grant from NSERC (Canada) and an Isaac Walton Killam Fellowship (Canada Council).     

Graphical methods in first and second-order differentiability theory of integral functionals

We discuss several notions of first and second-order differentiability for integral functionals on a Hilbert space.Supported in part by Deutsche Forschungsgemeinschaft (DFG) and Natural Sciences and Engineering Research Council of Canada (NSERC).     

Extremal Ternary Self-Dual Codes Constructed from Negacirculant Matrices

In this paper, a construction of ternary self-dual codes based on negacirculant matrices is given. As an application, we construct new extremal ternary self-dual codes of lengths 32, 40, 44, 52 and 56. Our approach regenerates all the known extremal self-dual codes of lengths 36, 48, 52 and 64. New extremal ternary quasi-twisted self-dual codes are also constructed. Supported by an NSERC discovery grant and a RTI grant. Supported by an NSERC discovery grant and a RTI grant. A summer student Chinook Scholarship is greatly appreciated.     

Overlarge sets and partial geometries

We extend our earlier work on overlarge sets of Fano planes, obtaining three results of particular interest. We find seven new partial geometries pg(8,7,4) and nine new strongly regular graphs, by means of switching cliques of points with spreads of lines. One of these new strongly regular graphs supports four different partial geometries. Then we give a new construction of the recently discovered eightfold cover of the complete graph K₁₆.Supported by NSERC grant OGP0008651Supported by ARC grant A49130102 and an Australian Senior Research Fellowship     

Rank one transformations with singular spectral type

We show that a certain class of measures arising from generalized Riesz products is singular. In particular, cutting and stacking (i.e. rank one) transformations whose cuts do not grow too rapidly, have singular maximal spectral type. The precise condition is , wherew _h is the number of cuts at stagen. Supported by a Canada NSERC grant. Supported by an NSF grant.     

Ordered sets,pagenumbers and planarity

General bounds for the pagenumber of an ordered set are developed. One bound is derived by first showing that the maximum number of edges in the diagram of a planar ordered setP is 2v(P)-2-ht(P). A construction is given to show that the pagenumber of the product ofn chains is no more than 2n-2. Lastly, some open questions are discussed.Supported in part by NSERC of Canada.Supported by an NSERC Summer Scholarship.     

Optimal markovian couplings and applications

This paper is devoted to studying a new topic: optimal Markovian couplings, mainly for time-continuous Markov processes. The study emphasizes the analysis of the coupling operators rather than the processes. Some constructions of optimal Markovian couplings for Markov chains and diffusions are presented, which are often unexpected. Then, the results are applied to study theL ²-convergence for Markov chains and for a diffusion on compact manifold. The estimate of the convergent rate provided by this method can be sharp. Supported in part by NSFC, the State Education Commission of China, the NSERC operating grant of D.A. Dawson and Centro Vito Volterra.     

Some characterizations of appell andℊ-appell polynomials

Summary Several characterizations are given for the wellknown Appell polynomials and for their basic analogues: the -Appell polynomials defined by Equation (3.3)below. The main results contained in Theorems 1, 2and 3of the present paper, and the applications considered in Section 2,are believed to be new. Some interesting connections with earlier results are also indicated.Supported, in part, by NSERC (Canada) grant A-7353.     

Strong converse inequalities

Techniques are developed to obtain strong converse inequalities for various linear approximation processes. This will establish equivalence between the approximating rate of a certain linear process and the appropriate PeetreK-functional. Approximation processes that will be treated have to be saturated asK-functionals are saturated. These general methods will lead to new results on the various trigonometric polynomial approximation processes, on holomorphic semigroups, on Bernstein polynomials and on other commonly used approximation processes. Supported by NSERC A4816 of Canada.     

Lifting positive elements in C*-algebras

Supported by an NSERC grant, a NATO International Collaboration grant, and an E.W.R.Steacie Fellowship     

A generalized permutahedron

With respect to a fixedn-element ordered setP, thegeneralized permutahedron Perm(P) is the set of all ordered setsP L, whereL is any permutation of the elements of the underlyingn-element set. Considered as a subset of the extension lattice of ann-element set,Perm(P) is cover-preserving. We apply this to deduce, for instance, that, in any finite ordered setP, there is a comparability whose removal will not increase the dimension, and there is a comparability whose addition toP will not increase its dimension.We establish further properties about the extension lattice which seem to be of independent interest, leading for example, to the characterization of those ordered setsP for which this generalized permutahedron is itself a lattice.Presented by J. Sichler.Dedicated to the memory of Alan DaySupported in part by PRC Mathématiques-Informatique (France) and NSERC (Canada).Supported in part by DFG (Germany) and NSERC (Canada).Supported in part by NSERC (Canada).     

Lifting factor maps to resolving maps

We consider Smale spaces, that is, homeomorphisms of a compact metric spaces possessing canonical coordinates of contracting (stable) and expanding (unstable) directions. Examples of such dynamical systems include the basic sets for Smale's Axiom A systems. We also assume that each point of the space is non-wandering and that there is a dense orbit. We show that any almost one-to-one factor map between two such systems may be lifted in a certain sense to a factor map which is injective on the local stable sets (i.e., s-resolving). We derive several corollaries. One is a refinement of Bowen's result that every irreducible Smale space is a factor of an irreducible shift of finite type by an almost one-to-one factor map. We are able to show that there exists such a factor which is the composition of an s-resolving map and a u-resolving map. Supported in part by a grant from NSERC, Canada.