Marianne Nofz

Exploration of NMR data of glasses by means of formal concept analysis

Abstract After explaining the mathematical background of formal concept analysis this method was applied to 29 Si-NMR data (chemical shift and full width at half height of the corresponding signals) of 31 calcium-aluminosilicate glasses. Conceptual scaling of the data was necessary to transform the experimental data into a single-valued context. Interpretation of the results was performed on the basis of a structural model ( Q n m units model) for the glasses developed intuitively in a previous work. The results of the formal concept analysis applied to the NMR data and to the composition of the glasses in terms of distinct structural units allowed a confirmation of the Q n m model.

Clustering of 29Si NMR data of aluminosilicate glasses using, k-means and fuzzy c-means — a comparison

Abstract Ehrentreich, F., Nofz, M. and Bartel, H.-G., 1992. Clustering of 29 Si NMR data of aluminosilicate glasses using k -means and fuzzy c -means. Chemometrics and Intelligent Laboratory Systems , 15: 61–73. The results of applying k -means (KM) and fuzzy c -means (FCM) methods of cluster analysis to a set of 29 Si NMR data of calcium aluminosilicate glasses are compared. Hard partitions are obtained as a result of KM cluster analysis, i.e. each object belongs to only one definite cluster. The FCM algorithm optimizes the degree of membership of objects in all the clusters — each object may thus belong to more than one cluster. The results of FCM are influenced by a parameter which controls the ‘degree of fuzziness’. This influence is studied and a method is suggested which makes the manifold of data obtained by FCM convenient and clear. The discussion of the partitions obtained shows that the FCM analysis yields valuable additional information on outliers and hybrids, i.e. less typical members of the clusters. The results of KM and FCM cluster analysis support the interpretation of the 29 Si NMR data on the basis of a structural model for the calcium aluminosilicate glasses.

Application of the Fuzzy-C-Means algorithm to the study of relationships between composition and properties: Physical properties of glasses

SummaryThe opportunities of applying the Fuzzy-C-Means (FCM) algorithm for cluster analysis to study composition-property relations are discussed. Physical properties of 98 aluminosilicate glasses serve as an example. The influences of the initial partition and of the number of clusters chosen are discussed in detail. The FCM algorithm allows to find characteristic members of clusters (these form the “nuclei” of the clusters) and to find outliers of the data set under consideration. Thus the results of the cluster analysis form a basis for a deeper understanding of relations between the composition and properties of the glasses studied.ZusammenfassungEs werden die Möglichkeiten des Fuzzy-C-Means-(FCM)-Algorithmus für Cluster-Analysen zur Untersuchung von Zusammensetzung-Eigenschafts-Relationen diskutiert. Die physikalischen Eigenschaften von 98 Aluminosilikat-Gläsern dienen als Beispiel. Es wird der Einfluß von Anfangsverteilung und Clusteranzahl untersucht. Der FCM-Algorithmus erlaubt das Auffinden von charakteristischen Teilen von Clustern (diese bilden den „Kern“ des Clusters) und auch von Außenseitern des betrachteten Datensatzes. Somit liefern die Ergebnisse der Clusteranalyse die Grundlage für ein tieferes Verständnis der Beziehungen zwischen Zusammensetzung und Eigenschaften von Gläsern.

Investigation of different end partitions obtained during aggregative nonhierarchic cluster analysis of glasses

Abstract The influence of number of clusters and initial partition on the result of a partitioning cluster analysis is discussed. This discussion leads to the development of an algorithm to make full use of the different end partitions found and to construct a generalized partition. The application of this algorithm is demonstrated using the physical properties of glasses as an example of objects which are to be classified.

Eichinvariante Berechnung des Diamagnetismus und der chemischen Verschiebung

The procedure described in1,2 was used to calculate the magnetic susceptibility contributions of C-H bonds to the diamagnetism of various hydrocarbons. It was found a correlation between these C-H-bond contributions and the bond lengths. The transferability of the evaluated C-H-bond susceptibilities from one molecule to another is discussed.

Eichinvariante Berechnung des Diamagnetismus und der chemischen Verschiebung@@@Gauge-invariant calculation of diamagnetism and chemical shift IV: Incrementary calculation of the diamagnetism of unsaturated hydrocarbons: 4. Mitt.: Inkrementre Berechnung des Diamagnetismus ungesttigter Kohlenwasserstoffe

The procedure derived in1–4 was used to calculate the magnetic susceptibilities of a series of unsaturated hydrocarbons (propene, isobutene, 1-butene, cyclohexene, butadiene,trans-1,3,5-hexatriene). The difference δχ between the measured and computed susceptibilities of these molecules is discussed. The discussion shows, that there is no correlation existing between the difference δχ and the presumed delocalisation effects.