A graph G = (V,E) is a threshold graph if there is a mapping a : V → R+ and a positive real number S such that a(v) < S for all v ∈ V and (v, w) ∈ E if and only if a(v) + a(w) ≥ S. It is well known that G can be partitioned into a clique K and a stable set I. Threshold graphs constitute a very important and well studied class in graph theory and graph algorithms, since they have applications in...

We investigate detailed relationships between the set W of all infinite “reduced” sequences of elements of a canonical generating set of an arbitrary affine Weyl group and the set B of all infinite sets having a certain “biconvex” property in a positive root system ∆+ of the corresponding untwisted affine Lie algebra g. The study is related to the classification of convex orders on ∆+, which ar...

abstract Various rewriting mechanisms can be thought of as functions mapping words w to nite sets of words W. The adult language of (; !) is the set of words w which are xed points of , i.e. (w) = fwg, and reachable from a start word or axiom !, i.e. w 2 n (!) for some n 2 N 0. Interestingly, for systems without the table mechanism, the degree of parallelism does not aaect the generative capaci...

we extend Painlevé’s determinateness theorem from the theory of ordinary differential equations in the complex domain allowing more general ’multiple-valued’ Cauchy’s problems. We study C0−continuability (near singularities) of solutions. Foreword and preliminaries In this paper we slightly improve Painlevé’s determinateness theorem (see [HIL], th.3.3.1), investigating the C0−continuability of ...

One of the main methods of examining non-normal operators, acting on Hilbert spaces, is the theory of contractions. This area of operator theory was developed by Béla Sz.-Nagy and Ciprian Foias from the dilation theorem of Sz.-Nagy. Sz.-Nagy and Foias classi ed the contractions according to their asymptotic behaviour. They got strong structural results in the case when the contraction and its a...

Understanding the anisotropy of thermal and electrical properties carbon fibers is important for many applications, but transverse transport are difficult to measure. We apply time-domain thermoreflectance (TDTR) mapping determine spatial variations in conductivity different radial positions two polyacrylonitrile (PAN)-based fibers, IM7 AS4 fibers. Single-point TDTR measurements longitudinal co...

We characterize spaces W such that the W -nullification functor PW , applied to any BGL(R), gives BGL(R) . Let X be a pointed space and X the Quillen plus-construction on X with respect to the maximal perfect subgroup of π1X. If W is a pointed CW-complex, let PW (X) denote the W -nullification of X. (Recall that PWX is up to homotopy the initial space Y under X which is W -null in the sense tha...

For a ring R, Hilbert’s Tenth Problem HTP (R) is the set of polynomial equations over R, in several variables, with solutions in R. We view HTP as an operator, mapping each set W of prime numbers to HTP (Z[W−1]), which is naturally viewed as a set of polynomials in Z[X1, X2, . . .]. For W = ∅, it is a famous result of Matiyasevich, Davis, Putnam, and Robinson that the jump ∅′ is Turing-equivale...