Crowns,cutsets, and valuable partial orders

We consider the problem of recognizing those partial orders which admit a valuation: this is a linear-algebraic condition which arises naturally in an algebraic/geometric context. We show that a partial order has at most one valuation (which is integer-valued) and present various structural conditions which are either necessary or sufficient for a partial order to be valuable. The first main result is a reduction theorem which allows us to restrict attention to those partial orders which do not have a bounded cutset. We use this and a theorem of Kelly and Rival to prove the second main result: that every contraction of a bounded partial order is fibre-valuable if and only if the partial order is a dismantlable lattice. This result has a geometric interpretation.This research was supported by the Natural Sciences and Engineering Research Council of Canada under operating grant OGP0105392.     

The divergence theorem and the Laplacian in Minkowski space

Let (X, B) be a Minkowski space (finite-dimensional Banach space) with unit ball B. Using a Minkowski definition of unit normal to a hypersurface, a Minkowski analogue of Euclidean divergence is defined. We show that the divergence theorem holds. Using the Minkowski divergence, a Minkowski Laplacian is defined. We prove that this Laplacian is a second-order, constant-coefficient, elliptic, differential operator. Furthermore, the symbol of this Laplacian is computed and used to associate a natural Euclidean structure with (X, B).Supported, in part, by NSERC Operating Grant #4066.     

氢化－原子吸收法测定钢铁中砷量

本文应用连续蒸汽产生系统的氢化－原子吸收法，以王水溶解试样，加硫酸驱除过量硝酸。采用邻菲啉有效地掩蔽干扰元素，在适当的盐酸酸度和硼氢化钾浓度下，测定钢铁中砷量。采用本法准确度与精确度均能获满意结果，方法简便、快速。     

One-dimensional perturbations of the shift

The structure of isometries on a Hilbert space are well studied. In this paper we study contractions which are one-dimensional perturbations of isometries, in particular, perturbations of the shift operator onH ².     

Excitation of analytes and enhancement of emission intensities in a d.c. plasma jet: a critical review leading to proposed mechanistic models

Experimental data and theoretical criteria are used to critically review existing models for analyte emission enhancement in the 3-electrode d.c. plasma (DCP). The analytical zone is characterized as a non-optically thin recombining plasma in partial thermodynamic equilibrium (PTE). Spectrochemical excitation the authors ascribe largely to: (1) argon resonance line radiative transport; (2) inversion of optically pumped argon states; (3) inversion of analyte populations by Franck-Condon collisions with argon; (4) energy cascading in analytes via a multitude of channels. Adding an easily ionized element (EIE): (1) induces additional resonance line radiative transfer; (2) raises electron densities in cooler, analyte-rich plasma margins; (3) locally increases argon optical absorption cross sections via Stark broadening; (4) redistributes ohmic heating. Coupling between the proposed mechanisms is non-linear. Relationships between radiative transfer and collisional redistribution and (1) background suppression by EIE and (2) analyte emission enhancement by helium are also examined. Similarities between DCP and inductively coupled plasma (ICP) excitation mechanisms are noted and practical implications are addressed.     

Multiple points of trajectories of multiparameter fractional Brownian motion

Consider 0<α<1 and the Gaussian process Y(t) on ℝ ^N with covariance E(Y(s)Y(t))=|t|^2α+|s|^2α−|t−s|^2α, where |t| is the Euclidean norm of t. Consider independent copies X ¹,…,X ^d of Y and␣the process X(t)=(X ¹(t),…,X ^d (t)) valued in ℝ ^d . When kN≤␣(k−1)αd, we show that the trajectories of X do not have k-multiple points. If N<αd and kN>(k−1)αd, the set of k-multiple points of the trajectories X is a countable union of sets of finite Hausdorff measure associated with the function ϕ(ɛ)=ɛ ^{k N /α−( k −1) d} (loglog(1/ɛ)) ^k . If N=αd, we show that the set of k-multiple points of the trajectories of X is a countable union of sets of finite Hausdorff measure associated with the function ϕ(ɛ)=ɛ ^d (log(1/ɛ) logloglog 1/ɛ) ^k . (This includes the case k=1.) Received: 20 May 1997 / Revised version: 15 May 1998     

What must and what need not be contained in a graph of uncountable chromatic number?

We investigate the following problem: What countable graphs must a graph of uncountable chromatic number contain? We define two graphsΓ andΔ which are very similar and we show thatΓ is contained in every graph of uncountable chromatic number, whileΔ is (consistently) not.