Natürliche Gleichung der Kurven auf einer allgemeinen Fläche im metrischen Raume

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Bemerkung zur Arbeit von Herrn T. Y. Thomas „A projective theory of affinely connected manifolds”

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Riccati equations and Lie series

Lie series and a special matrix notation for first-order differential operators are used to show that the Lie group properties of matrix Riccati equations arise in a natural way. The Lie series notation makes it evident that the solutions of a matrix Riccati equation are curves in a group of nonlinear transformations that is a generalization of the linear fractional transformations familiar from the classical complex analysis. It is easy to obtain a linear representation of the Lie algebra of the nonlinear group of transformations and then this linearization leads directly to the standard linearization of the matrix Riccati equations. We note that the matrix Riccati equations considered here are of the general rectangular type.     

Bäcklund transformation for KdV-type equations

Classification of KdV-type equations possessing certain type of Bäcklund transformations is given together with the explicit form of the Bäcklund transformations. Besides some well-known equations and their Bäcklund transformations, several new ones are presented.     

Electrochemically initiated intramolecular cyclization of 2-nitro-2′-isothiocyanatobiphenyl

2-Nitro-2′-isothiocyanatobiphenyl was prepared as a new substance, suitable for the investigation of an electrochemically initiated intramolecular cyclization. If it is reduced at a mercury cathode in acidic media an acid catalysed intramolecular follow-up reaction occurs which leads to the formation of 6-mercaptodibenzo (d, f)-(1,3)-diazepin-5-oxide. The rate of the follow-up reaction decreases in neutral or alkaline media and the reduction of the isothiocyanato group also takes place. The main product is here 5,6-dihydrobenzo(c)cinnoline.     

Thermal Stability of Clay/organic Intercalation Complexes

The comparison of thermal stabilities of different organoclay intercalation complexes is presented in this work. Montmorillonite/monomer and montmorillonite/polymer intercalation complexes with similar basal spacings show a pronounced difference in changes of d ₀₀₁ values after 30 min heating. The hydrophilic and/or organophilic surface modification of the starting montmorillonite is an important factor affecting the intercalated amount of organic material and thus the expansion of the sheet silicate structure.This revised version was published online in November 2005 with corrections to the Cover Date.     

Induzierte und eingeborene Konnexion in den (nicht) holonomen Räumen

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