Theorie der ChiralitÄtsfunktionen

The pseudoscalar properties of chiral molecules are object of an algebraic theory, provided a proper definition of molecule-classes is given. The analysis of the phenomenon of chirality on those classes leads to some specific features of the representation theory for chiralty functions, to a new lattice-structure of partions, to properties of permutation groups connected therewith and, finally, gives an insight into the structure of approximate points of view for chirality functions. Thus the present paper includes pure mathematical aspects. Mathematical theorems which will be stated and proved without essential reference to physics will be found in the appendix. The paper itself presents the physical phenomenon in the first place and concepts which are offered by the mathematical formalism like chirality-order, chirality-index, chirality-numbers, qualitative completeness, shortened AnsÄtze, active and inactive partitions of ligands etc. give rise to a systematicism, to an insight and to answering questions concerning the measurement of properties related to chirality of molecules. The co- and contravariant point of view for the transformation behaviour of functions, for instance, gives us two possible interpretations in the case of chirality functions. We may understand components of functions belonging to irreducible representations of \(\mathfrak{S}_n \) as chirality functions for component mixtures of isomers. Thereby projection operators get a physical interpretation as ensembleoperators for mixtures of isomers. Chap. 12 drafts applications of the theory given in this paper. First convincing comparisons of experimental data for rotatory power of allene derivatives with theoretical values on the basis of approximations according to methods given in 8–11 are available and their publication is under preparation [4]. Also, mathematical consequences from the definition of the partition-lattice given in Chapter 6 will be pursued as far as they are not be found in the present paper.     

Enantio- and stereoselective syntheses of the dihydroxyoctadienoic acid framents of the roridins and trichoverrins

Syntheses of protected versions of the dihydroxyoctadienoic acid fragments corresponding to roridin A and trichoverrin B are described.     

Two diophantine systems

The problem of finding rational integers, satisfying the Diophantine system of § 2, seems at first difficult. But these difficulties are surpassed, if we use the well-known Birck's identity-which we note in § 2-and the solutions of the system (1) of §.A method of solving the last system is given in the §.