Determination of rank by augmentation (DRAUG)

Determining the rank of a chemical matrix is the first step in many multivariate, chemometric studies. Rank is defined as the minimum number of linearly independent factors after deletion of factors that contribute to random, nonlinear, uncorrelated errors. Adding a matrix of rank 1 to a data matrix not only increases the rank by one unit but also perturbs the primary factor axes, having little effect on the secondary axes associated with the random errors in the measurements. The primary rank of a data matrix can be determined by comparing the residual variances obtained from principal component analysis (PCA) of the original data matrix to those obtained from an augmented matrix. The ratio of the residual variances between adjacent factor levels represents a Fisher ratio that can be used to distinguish the primary factors (chemical as well as instrumental factors) from the secondary factors (experimental errors). The results gleaned from model studies as well as those from experimental studies are used to illustrate the efficacy of the proposed methodology. The method is independent of the nature of the error distribution. Limitations and precautions are discussed. An algorithm, written in MATLAB format, is included. Copyright © 2011 John Wiley & Sons, Ltd.     

On the reconstruction problem for factorizable homeomorphism groups and foliated manifolds

For a group G of homeomorphisms of a regular topological space X and a subset U⊆X, set . We say that G is a factorizable group of homeomorphisms, if for every open cover U of X, _?U∈UG generates G.

Theorem I. Let G, H be factorizable groups of homeomorphisms of X and Y respectively, and suppose that G, H do not have fixed points. Let φ be an isomorphism between G and H. Then there is a homeomorphism τ between X and Y such thatφ(g)=τ○g○τ−1for everyg∈G.     

A supernodal formulation of vertex colouring with applications in course timetabling

For many problems in scheduling and timetabling, the choice of a mathematical programming formulation is determined by the formulation of the graph colouring component. This paper briefly surveys seven known integer programming formulations of vertex colouring and introduces a new approach using “supernodes”.     

Über einige Summen,die von den Nullstellen der Riemann'schen Zetafunktion abhängen

Ohne Zusammenfassung     

Zur Bestimmung des Schwefels und der Halogene in organischen K?rpern

Ohne Zusammenfassung     

Über den Gebrauch bedingt konvergenter Integrale in der Primzahltheorie

Ohne Zusammenfassung