Note – Uncrossing a Family of Set-Pairs

Frank and Jordán [1] proved an important min-max result on covering a crossing family of set-pairs. As an application, among others they can solve the unweighted node-connectivity augmentation problem for directed graphs in polynomial time. In this paper, we show how to solve the dual packing problem in polynomial time. To decompose a fractional dual optimum as a convex combination of integer vertices, besides the ellipsoid method, we use a polynomial-time algorithm for uncrossing a family of set-pairs. Our main result is this uncrossing algorithm. Received November 9, 1998 / Revised October 18, 1999     

Existence Results for Quasistatic Contact Problems with Coulomb Friction

We prove the existence of a solution for an elastic frictional, quasistatic, contact problem with a Signorini non-penetration condition and a local Coulomb friction law. The problem is formulated as a time-dependent variational problem and is solved by the aid of an established shifting technique used to obtain increased regularity at the contact surface. The analysis is carried out by the aid of auxiliary problems involving regularized friction terms and a so-called normal compliance penalization technique. \par Accepted 15 May 2000. Online publication 6 October 2000.     

NOTE – On Minimizing Symmetric Set Functions

u, v ) of nodes such that the star of v is a minimum cut separating u and v. Nagamochi and Ibaraki showed that the last two nodes of a ``max-back order' form such a pair and used this fact to develop an elegant min-cut algorithm. M. Queyranne extended this approach to minimize symmetric submodular functions. With the help of a short and simple proof, here we show that the same algorithm works for an even more general class of set functions. Received December 16, 1998     

Atom trap trace analysis

A new method of ultrasensitive isotope trace analysis has been developed. This method, based on the technique of laser manipulation of neutral atoms, has been used to count individual ⁸⁵Kr and ⁸¹Kr atoms present in a natural krypton gas sample with isotopic abundances in the range of 10⁻¹¹ and 10⁻¹³, respectively. The method is free of contamination from other isotopes and elements, and can be applied to many different isotope tracers for a wide range of applications. This revised version was published online in August 2006 with corrections to the Cover Date.     

Counting Radio-Krypton Atoms with a Laser

Because of their unique chemical and physical properties, long-lived rare krypton radioisotopes, ⁸⁵Kr and ⁸¹Kr, are ideal tracers for environmental samples, including air, groundwater and ice. Atom trap trace analysis (ATTA) is a new laser-based method for counting both ⁸⁵Kr and ⁸¹Kr atoms with the abundance as low as 10^-14 with micro-liters (STP) krypton gas. The entire system for rare radio-krypton measurement built at Hefei is presented, including the atom trap trace analysis instrument and sampling apparatus of gas extraction from water and krypton purification. Atmospheric⁸⁵Kr concentrations at different places in China were measured, showing a range of 1.3-1.6 Bq/m³, consistent with the northern hemispheric baseline. As a demonstration of the system, some shallow and deep groundwater samples in north and south China were sampled and dated.     

A coalgebraic approach to quasigroup permutation representations

The paper identifies the class of all permutation representations of a given finite quasigroup as a covariety of coalgebras. Each permutation representation decomposes as a sum of homomorphic images of homogeneous spaces. For a group, permutation representations in the present sense specialise to the classical concept. Burnside's Lemma, with a new proof, is extended from groups to quasigroups. Received March 13, 2002; accepted in final form September 18, 2002. RID="h1" ID="h1"This paper was written while the author was a guest of the Institute of Mathematics and Information Sciences at Warsaw University of Technology, on Faculty Professional Development Assignment from Iowa State University.     

Minimum edge ranking spanning trees of split graphs

Given a graph G, the minimum edge ranking spanning tree problem (MERST) is to find a spanning tree of G whose edge ranking is minimum. However, this problem is known to be NP-hard for general graphs. In this paper, we show that the problem MERST has a polynomial time algorithm for split graphs, which have useful applications in practice. The result is also significant in the sense that this is a first non-trivial graph class for which the problem MERST is found to be polynomially solvable. We also show that the problem MERST for threshold graphs can be solved in linear time, where threshold graphs are known to be split.     

Space-charge effects in liquid metal ion sources of different geometries

The current work considers the effect of geometry, other than the ideal Taylor cone, on space charge and axial fields of liquid metal ion sources. Solutions of the spacecharge equation for the concentric sphere and hyperboloidal-planar models of a liquid emitter demonstrate a rather dramatic dependence of the space charge and axial fields on the geometry of the emitting surface.This research was supported in part by the NATO Research Grants Division, Grant No. 1902, Scientific Affairs Division, Brussels, BelgiumAltoona Campus     

Phonon scattering and interstitial clusters in γ-irradiated LiF

The thermal conductivity of pure and Mg-doped LiF single crystals irradiated at room temperature in a Co⁶⁰ source (3–780 Mrad) was measured between 60mK and 70 K. Several phonon scattering mechanisms for extended defects are reviewed and it is shown that experimental results can be understood in terms of two types of interstitial clusters: (a) small spherical clusters whose number density and size depend on the residual impurity content; and (b) large non-spherical clusters of toroïdal shape with a major radius of several hundred Å and minor radius of some tens of Å. For increasing dose, the major radius decreases, the minor radius increases and the rings become increasingly opaque possibly due to the associated strain field.