Micro raman spectroscopy on a single carbon fibre under stress

An example is given for the application of Raman spectroscopy in material characterization. Raman spectra of carbonaceous materials obtained with the microscope attachment have been used to study orientation of graphite planes in a single carbon fibre under stress with a lateral resolution of 1 m.Dedicated to Professor Dr. H. Kriegsmann on the occasion of his 70th birthday     

4-Manifold topology I: Subexponential groups

The technical lemma underlying the 5-dimensional topologicals-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating ₁-null immersions of disks. These conjectures are theorems precisely for those fundamental groups (good groups) where the ₁-null disk lemma (NDL) holds. We expand the class of known good groups to all groups of subexponential growth and those that can be formed from these by a finite number of application of two operations: (1) extension and (2) direct limit. The finitely generated groups in this class are amenable and no amenable group is known to lie outside this class.Oblatum 20-II-1995 & 26-V-1995The first author is supported by the IHES, the Guggenheim foundation and the NSF.The second author is supported by the IHES and the Humboldt foundation.     

A constrained matching problem

We show that certain manpower scheduling problems can be modeled as the following constrained matching problem. Given an undirected graphG = (V,E) with edge weights and a digraphD = (V,A). AMaster/Slave-matching (MS-matching) ofG with respect toD is a matching ofG such that for each arc (u, v) A for which the nodeu is matched, the nodev is matched, too. TheMS-Matching Problem is the problem of finding a maximum-weight MS-matching. Letk(D) be the maximum size of a (weakly) connected component ofD. We prove that MS-matching is an NP-hard problem even ifG is bipartite andk(D) 3. Moreover, we show that in the relevant special case wherek(D) 2, the MS-Matching Problem can be transformed to the ordinary Matching Problem.This research was supported by Grant 03-KL7PAS-6 of the German Federal Ministry of Research and Technology.     

Partial regularity for certain classes of polyconvex functionals related to nonlinear elasticity

Consider the variational integral where Ω⊂ℝ ⁿ andp≥n≥2. H: (0, ∞)→[0, ∞) is a smooth convex function such that . We approximateJ by a sequence of regularized functionalsJ _δ whose minimizers converge strongly to anJ-minimizing function and prove partial regularity results forJ _δ-minimizers.     

Representations of double coset hypergroups and induced representations

The principal goal of this paper is to investigate the representation theory of double coset hypergroups. IfK=G//H is a double coset hypergroup, representations ofK can canonically be obtained from those ofG. However, not every representation ofK originates from this construction in general, i.e., extends to a representation ofG. Properties of this construction are discussed, and as the main result it turns out that extending representations ofK is compatible with the inducing process (as introduced in [7]). It follows that a representation weakly contained in the left-regular representation ofK always admits an extension toG. Furthermore, we realize the Gelfand pair (where are a local field andR its ring of integers) as a polynomial hypergroup on ℕ₀ and characterize the (proper) subset of its dual consisting of extensible representations.     

Packing random intervals

Summary Letn random intervalsI ₁, ...,I _n be chosen by selecting endpoints independently from the uniform distribution on [0.1]. Apacking is a pairwise disjoint subset of the intervals; itswasted space is the Lebesgue measure of the points of [0,1] not covered by the packing. In any set of intervals the packing with least wasted space is computationally easy to find; but its expected wasted space in the random case is not obvious. We show that with high probability for largen, this best packing has wasted space . It turns out that if the endpoints 0 and 1 are identified, so that the problem is now one of packing random arcs in a unit-circumference circle, then optimal wasted space is reduced toO(1/n). Interestingly, there is a striking difference between thesizes of the best packings: about logn intervals in the unit interval case, but usually only one or two arcs in the circle case.     

Decomposing the complete graph into cycles of many lengths

For all oddv 3 the complete graph onvK _v vertices can be decomposed intov – 2 edge disjoint cycles whose lengths are 3, 3, 4, 5,...,v – 1. Also, for all oddv 7,K _v can be decomposed intov – 3 edge disjoint cycles whose lengths are 3, 4,...,v – 4,v – 2,v – 1,v. Research supported by Australian Research Council grant A49130102