Inverse sequences, rooted trees and their end spaces

In this paper we prove that if we consider the standard real metric on simplicial rooted trees then the category Tower-Set of inverse sequences can be described by means of the bounded coarse geometry of the naturally associated trees. Using this we give a geometrical characterization of Mittag-Leffler property in inverse sequences in terms of the metrically proper homotopy type of the corresponding tree and its maximal geodesically complete subtree. We also obtain some consequences in shape theory. In particular we describe some new representations of shape morphisms related to infinite branches in trees.     

Probabilistic matching of planar regions

We analyze a probabilistic algorithm for matching shapes modeled by planar regions under translations and rigid motions (rotation and translation). Given shapes A and B, the algorithm computes a transformation t such that with high probability the area of overlap of t(A) and B is close to maximal. In the case of polygons, we give a time bound that does not depend significantly on the number of vertices, but on perimeter and area of the shapes and, in the case of rigid motions, also on the diameter.     

Computing the Fréchet distance between piecewise smooth curves

We consider the Fréchet distance between two curves which are given as a sequence of m+n curved pieces. If these pieces are sufficiently well-behaved, we can compute the Fréchet distance in O(mnlog(mn)) time. The decision version of the problem can be solved in O(mn) time. The results are based on an analysis of the possible intersection patterns between circles and arcs of bounded curvature.     

LEED structure determination of the Ni(1 1 1)(√3×√3)R30°-Sn surface

Quantitative low energy electron diffraction has been used to determine the structure of the Ni(1 1 1)(√3×√3)R30°-Sn surface phase. The results confirm that the surface layer comprises a substitutional alloy of composition Ni₂Sn as previously found by low energy ion scattering (LEIS), and also shows that there is no stacking fault at the substrate/alloy interface as has been found in (√3×√3)R30°-Sb surface alloys on Ag and Cu(1 1 1). The surface alloy layer is rumpled with the Sn atoms 0.45 ± 0.03 Å higher above the substrate than the surrounding Ni atoms. This rumpling amplitude is almost identical to that previously reported on the basis of the LEIS study. Comparison with similar results for Sn-induced surface alloy phases on Ni(1 0 0) and Ni(1 1 0) shows a clear trend to reduced rumpling with reduced surface atomic layer density, an effect which can be rationalised in terms of the different effects of valence electron charge smoothing at the surface.     

Crystal structure and cation distribution in the solid solution series 2(ZnX)-CuInX2 (X=S, Se, Te)

The solid solution series (2ZnX)_x (CuInX₂)_1−x (X=S, Se, Te) were studied by the combination of laboratory and synchrotron X-ray and by neutron powder diffraction. Within the homologous series the tetragonal distortion ¼-u increases in the sequence S→Se→Te whereas the tetragonal deformation η=c/2a decreases. Besides that, with increasing 2ZnX content in CuInX₂ the anion position parameter u increases as expected. The cation site occupancy in the chalcopyrite type phase of single phase tetragonal samples was obtained by Rietveld analysis of the neutron diffraction data. A non-statistic Zn distribution could be deduced for all three systems. The high temperature in situ diffraction experiments with synchrotron radiation on CuInX₂ powder samples revealed the Cu-In anti-site occupation as the driving force of the temperature dependent phase transition from the chalcopyrite to the zinc-blende type structure.     

An efficient algorithm for strain history tracking in finite element computations of non-Newtonian fluids with integral constitutive equations

A new finite element technique has been developed for employing integral-type constitutive equations in non-Newtonian flow simulations. The present method uses conventional quadrilateral elements for the interpolation of velocity components, so that it can conveniently handle viscoelastic flows with both open and closed streamlines (recirculating regions). A Picard iteration scheme with either flow rate or elasticity increment is used to treat the non-Newtonian stresses as pseudo-body forces, and an efficient and consistent predictor-corrector scheme is adopted for both the particle-tracking and strain tensor calculations. The new method has been used to simulate entry flows of polymer melts in circular abrupt contractions using the K-BKZ integral constitutive model. Results are in very good agreement with existing numerical data. The important question of mesh refinement and convergence for integral models in complex flow at high flow rate has also been addressed, and satisfactory convergence and mesh-independent results are obtained. In addition, the present method is relatively inexpensive and in the meantime can reach higher elasticity levels without numerical instability, compared with the best available similar calculations in the literature.     

石墨炉原子吸收光谱法直接测定铝合金中的痕量铍

本文叙述了痕量铍在铝合金中的重要作用以及石墨炉原子吸收光谱法测定铝合金中痕量铍的方法研究。该方法用硝酸（１＋１）溶解样品。０．１０ｍｇ／ｍＬ以上的铝具有增感效应，铍在０－０．２５μｇ／１００ｍＬ的范围内具有良好线性关系。该方法操作简便、灵敏度高，特征浓度为１．０５×１０￣（－５）μｇ／ｍＬ／１％。相对标准偏差为１．６６％，回收率在９６％－１０２．５％。     

Memory function for dressed particles

This paper is concerned with the calculation of the memory function and derivation of a kinetic equation for one-body phase space correlation functions. The theory uses a one-body additive projection operator and a division of the Liouville operator with an unperturbed part that describes dressed particles. Binary collisions are neglected, for the theory aims at describing the screening and backflow effects of a type contained in the plasma kinetic theory of Balescu and Lenard. We obtain an explicit kinetic equation which is an improvement of these theories for the plasma case, and involves the exact equilibrium pair and triplet distributions. The equation also describes systems with strong short-range forces and shows how the screening effects occur in this case as well. The unifying function is the direct correlation function. The theory is meant to provide understanding for a more complete theory of fluids where a proper account is given of close collisions.Work supported by National Science Foundation, Grant No. GH 35691.     

Beyond mean field approach to the beta decay of medium mass nuclei relevant for nuclear astrophysics

The Gamow-Teller strength distributions for the β decay of the ground state as well as the lowest excited states of the rp-process waiting point nuclei ⁶⁸Se and ⁷²Kr are obtained within the complex Excited Vampir variational approach using realistic effective interactions and a rather large model space. The shape mixing is consistently described for both the states in the even-even parent and the states in the odd-odd daugther nucleus. The influence of the shape mixing accounted by the different effective interactions used and comparison with the available data are presented. The possible influence of the decay of the lowest excited states of the parent nuclei in the astrophysical environment of X-ray bursts is discussed.Gamow-Teller strength distributions, β-decay half-lives, and β-delayed neutron emission probabilities for neutron-rich Zr nuclei are investigated for the first time within the complex Excited Vampir approach using a large model space. Comparison with available data and predictions relevant for the astrophysical r process are presented.