Curvature and finite domination

Upper bounds obtained by Gromov on the Betti numbers of certain closed Riemannian manifolds are shown to be upper bounds on the minimum number of cells in --spaces dominating such manifolds.

     

Crumpled laminations and manifolds of nonfinite type

Using a group-theoretic construction due to Bestvina and Brady, we build -manifolds which admit partitions into closed, connected -manifolds but which do not have finite homotopy type.

     

Spatial chaotic structure of attractors of reaction-diffusion systems

The dynamics described by a system of reaction-diffusion equations with a nonlinear potential exhibits complicated spatial patterns. These patterns emerge from preservation of homotopy classes of solutions with bounded energies. Chaotically arranged stable patterns exist because of realizability of all elements of a fundamental homotopy group of a fixed degree. This group corresponds to level sets of the potential. The estimates of homotopy complexity of attractors are obtained in terms of geometric characteristics of the potential and other data of the problem.

     

Derivative of the exponential mapping for infinite dimensional lie groups

It is proved that for infinite dimensional Lie groups in the sense of the differential calculus of Frölicher and Kriegl the derivative of the exponential mappings is given by the formula d(exp)(X)Y=d_exp(X)(e) ₀ ¹ Ad_exp(–tX) Y dt, where stands for the left translation ande is the neutral element.This work was supported by the Alexander von Humboldt-Stiftung.     

Geometric modules and Quinn homology theory

LetR be a ring with unit and invariant basis property. In [1], the authors define a functorK(_;R):TOP/LIP _c-LPEP by combining the open cone construction of [7] with a geometric module construction and show this functor is a homology theory. This paper shows that if attention is restricted to objects TOP/LIP _c with a homotopy colimit structure, then the functorK(_;R) is a Quinn homology theory, In particular, for each having a homotopy colimit structure,K(;R) is a homotopy colimit in the category of -spectra. Furthermore, the constituent spectra of this homotopy colimit are obtained naturally from the fibres of .Partially supported by the National Science Foundation under grant number DMS88-03148.Partially supported by the SNF (Denmark) under grant number 11-7792.     

RECENT PROGRESS OF NANO-MECHANICAL MAPPING

 Nano-mechanical mapping by atomic force microscopy has been developed as an useful application to measure mechanical properties of soft materials at nanometer scale. To date, the Hertzian theory was used for analyzing force-distance curves as the simplest model among several contact mechanics between elastic bodies. However, the preexisting methods based on this theory do not consider the adhesive interaction in principle, which cannot be neglected in the ambient condition. A new analytical method was introduced to estimate the elasticity and the adhesive energy simultaneously by means of the JKR theory, describing adhesive contact between elastic materials. Poly(dimethylsiloxane) (PDMS) and isobutylene-co-isoprene rubber (IIR) were analyzed to verify the applicable limit of the JKR analysis. For elastic samples such as PDMS, the force-deformation plots obtained experimentally were consistent with JKR theoretical curves. Meanwhile, for viscoelastic samples, especially for IIR, the experimental plots revealed large deviations from JKR curves depending on scanning velocity and maximum loading force. Some nano-rheological arguments were employed based on the difference between these specimens.     

Characterization of individual atmospheric particles by element mapping in electron probe microanalysis

In this paper procedures for the characterization of individual aerosol particles by element mapping in the electron microprobe are presented. The number, size and qualitative chemical composition of particles is derived from a combination of secondary or backscattered electron images and element distribution maps. Accuracy of the size distribution and reliability of the qualitative analysis procedure were checked with silicate samples. In order to obtain a semi-quantitative estimate of the chemical composition of individual particles the count rates taken from element distribution maps are corrected for matrix and geometric effects using particle ZAF procedures.Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthday     

PHOTOEMISSION WITHIN AND BEYOND THE ONE-STEP MODEL

Photoemission in the vacuum ultraviolet photon regime has proved to be an effective tool for the investigation of valence band surface electronic structure. The interpretation cannot be exclusively confined to the valence bands but has to consider cross sections with realistic final states consistently designed within the one-step model. Therefore especially in the surface sensitive photoemission, several effects hide the final goal of deducing the energetic and wavefunction structure together with microscopic potential parameters through a convincing agreement of calculated with measured spectra. The final states band structure is much less well understood than the valence band structure under consideration. The optical potential, which controls the surface sensitivity through the underlying damping mechanisms, widely relies on empirical assumptions. Furthermore, the photon field is not only strongly influenced but in the vicinity of the plasma frequency also deteriorated by the electronic response. In view of high resolution spectroscopy the accuracy of the data interpretation is affected, and in fact, band-mapping methods are no longer valid. Examples of recent calculations to account for these effects are reviewed.     

冠心病微量元素谱的计算机模式识别

用计算机多元分析研究冠心病微量元素谱，识别冠心病患者与健康者；非线性映射法判别率男性８６．６％，女性９６．２％；ＳＩＭＣＡ差别法正确回判率男性８５．０％，女性８８．３％。     

Computer optimization of separation in gas-solid chromatography,optimization model and computer-modified mapping procedure

Summary This paper proposes an optimization model for gas-solid chromatographic separations in a non-linear programming form and an approximate equation of the plate height for the model. A computer-modified mapping procedure is also described for searching the optimum separation conditions. Just five experiments and about 20 minutes of the computer time are needed to establish the optima of column temperature and of the carrier gas linear velocity. The relative deviation between the predicted and the experimental values was found to be within 20% for the plate heights, and within 1.5% for the retention times.