Über die periodischen Transformationen der Kugel

Ohne Zusammenfassung     

How to statistically analyze nano exposure measurement results: using an ARIMA time series approach

Measurement strategies for exposure to nano-sized particles differ from traditional integrated sampling methods for exposure assessment by the use of real-time instruments. The resulting measurement series is a time series, where typically the sequential measurements are not independent from each other but show a pattern of autocorrelation. This article addresses the statistical difficulties when analyzing real-time measurements for exposure assessment to manufactured nano objects. To account for autocorrelation patterns, Autoregressive Integrated Moving Average (ARIMA) models are proposed. A simulation study shows the pitfalls of using a standard t-test and the application of ARIMA models is illustrated with three real-data examples. Some practical suggestions for the data analysis of real-time exposure measurements conclude this article.     

Synthesis of a Fluorescent Naphthalenic Ligand of Melatonin Receptors

Abstract: The synthesis of a fluorescent naphthalenic derivative, as a potential ligand of melatonin receptors is described through a multisteps procedure from 1-(2-acetylaminoethyl)-7-methoxynaphthalene.     

Empirical analysis of self-adaptive differential evolution

Differential evolution (DE) is generally considered as a reliable, accurate, robust and fast optimization technique. DE has been successfully applied to solve a wide range of numerical optimization problems. However, the user is required to set the values of the control parameters of DE for each problem. Such parameter tuning is a time consuming task. In this paper, a self-adaptive DE (SDE) algorithm which eliminates the need for manual tuning of control parameters is empirically analyzed. The performance of SDE is investigated and compared with other well-known approaches. The experiments conducted show that SDE generally outperform other DE algorithms in all the benchmark functions. Moreover, the performance of SDE using the ring neighborhood topology is investigated.     

Zur Analysis Situs

Ohne ZusammenfassungMit 2 Tafeln     

On q-analogues and stability theorems

In this survey recent results about q-analogues of some classical theorems in extremal set theory are collected. They are related to determining the chromatic number of the q-analogues of Kneser graphs. For the proof one needs results on the number of 0-secant subspaces of point sets, so in the second part of the paper recent results on the structure of point sets having few 0-secant subspaces are discussed. Our attention is focussed on the planar case, where various stability results are given.     

Improved variable reduction in partial least squares modelling based on predictive-property-ranked variables and adaptation of partial least squares complexity

The calibration performance of partial least squares for one response variable (PLS1) can be improved by elimination of uninformative variables. Many methods are based on so-called predictive variable properties, which are functions of various PLS-model parameters, and which may change during the variable reduction process. In these methods variable reduction is made on the variables ranked in descending order for a given variable property. The methods start with full spectrum modelling. Iteratively, until a specified number of remaining variables is reached, the variable with the smallest property value is eliminated; a new PLS model is calculated, followed by a renewed ranking of the variables. The Stepwise Variable Reduction methods using Predictive-Property-Ranked Variables are denoted as SVR-PPRV. In the existing SVR-PPRV methods the PLS model complexity is kept constant during the variable reduction process. In this study, three new SVR-PPRV methods are proposed, in which a possibility for decreasing the PLS model complexity during the variable reduction process is build in. Therefore we denote our methods as PPRVR-CAM methods (Predictive-Property-Ranked Variable Reduction with Complexity Adapted Models). The selective and predictive abilities of the new methods are investigated and tested, using the absolute PLS regression coefficients as predictive property. They were compared with two modifications of existing SVR-PPRV methods (with constant PLS model complexity) and with two reference methods: uninformative variable elimination followed by either a genetic algorithm for PLS (UVE-GA-PLS) or an interval PLS (UVE-iPLS). The performance of the methods is investigated in conjunction with two data sets from near-infrared sources (NIR) and one simulated set. The selective and predictive performances of the variable reduction methods are compared statistically using the Wilcoxon signed rank test. The three newly developed PPRVR-CAM methods were able to retain significantly smaller numbers of informative variables than the existing SVR-PPRV, UVE-GA-PLS and UVE-iPLS methods without loss of prediction ability. Contrary to UVE-GA-PLS and UVE-iPLS, there is no variability in the number of retained variables in each PPRV(R) method. Renewed variable ranking, after deletion of a variable, followed by remodelling, combined with the possibility to decrease the PLS model complexity, is beneficial. A preferred PPRVR-CAM method is proposed.     

Solvatochromic rotaxane molecular shuttles

A strongly fluorescent bistable rotaxane is described in which the relative position of the macrocyclic ring with respect to a solvatochromic fluorophore gives a strong response in the spectral domain.     

SL2-modules of small homological dimension

Let V _n be the SL₂-module of binary forms of degree n and let V = V_n1 ???V_np V = {V_{{n_1}}} \oplus \cdots \oplus {V_{{n_p}}} . We consider the algebra R = O(V)^{\textS\textL₂} R = \mathcal{O}{(V)^{{\text{S}}{{\text{L}}_2}}} of polynomial functions on V invariant under the action of SL₂. The measure of the intricacy of these algebras is the length of their chains of syzygies, called homological dimension hd R. Popov gave in 1983 a classification of the cases in which hd R ≤ 10 for a single binary form (p = 1) or hd R ≤ 3 for a system of two or more binary forms (p > 1). We extend Popov’s result and determine for p = 1 the cases with hd R ≤ 100, and for p > 1 those with hd R ≤ 15. In these cases we give a set of homogeneous parameters and a set of generators for the algebra R.     

A Consistent BGK-Type Model for Gas Mixtures

We introduce a relaxation collision operator for a mixture of gases which satisfies several fundamental properties. Different BGK type collision operators for gas mixtures have been introduced earlier but none of them could satisfy all the basic physical properties: positivity, correct exchange coefficients, entropy inequality, indifferentiability principle. We show that all those properties are verified for our model, and we derive its Navier–Stokes limit by a Chapman–Enskog expansion.