Eine ErweiterungT(V′) des Ordinalzahlensystems 58-0158-0158-01(Λ0) von G. Jäger

Summary This paper gives a recursive generalization of a strong notation system of ordinals, which was devellopped by Jäger [3]. The generalized systemT(V) is based on a hierarchy of Veblen-functions for inaccessible ordinals. The definition ofT(V) assumes the existence of a weak Mahlo-ordinal. The wellordering ofT(V) is provable in a formal system of second order arithmetic with the axiom schema of ₂ ¹ -comprehension in a similar way, as it is proved in [6] for the weaker notation systemT(V).     

A Highly Stereoselective Synthesis of C(11)-Functionalized Aromatic Steroids by an Intramolecular Benzocyclobutene-Olefin -Cycloaddition. Preliminary Communication

The racemic cis-anti-trans-steroids 9 to 11 have been synthesized in a highly stereoselective manner starting from 4-methoxybenzocyclobutene carboxylic acid via the key step 8 → 9 . (cf. Scheme 2).     

Ein v. Staudt-Clausenscher Satz für periodische Bernoullizahlen

Letk, n be relatively prime integers, 1k<n. The numbersB _k ^m =m(i/2) ^m cot^(m–1)(k/n),m2, belong to then-th cyclotomic field. They occur as values of certain simple Dirichlet series at integral arguments and have a natural interpretation as generalized Bernoulli numbers. Therefore the arithmetic properties of these numbers arouse some interest. Ifn is not a prime power,B _k ^m /m is an algebraic integer. In the other case, i.e.n=p ^e ,p prime, the fractional part ofB _k ^m /m resp.B _k ^m is determined in this paper. It is periodic modulop–1 and exhibits a connection between these Bernoulli numbers and the Stirling numbers of the second kind.     

Arbeiten über Phosphorsäure und Thiophosphorsäureester mit einem heterocyclischen Substituenten 9. Mitteilung 1. Aza-Analogie I: Aza-Analoge von Phthalimid-, Benztriazol- und 1,2,3-Benztriazin-4(3H)-on-Derivaten

Aza-analogues of the known pesticidal dithiophosphates 2, 4 and 5 have been prepared by replacing the phthalimide, benzotriazole and 1,2,3-benzotriazin-4(3H)-one moieties resp. in 2 by those of quinolinic acid imide (6), cinchomeronic acid imide (7) and pyrazine-2,3-dicarboxylic acid imide (12), in 4 by 1H-v-triazolo[4,5-b]pyridine (15) and in 5 by pyrido[2,3-e]1,2,3-triazin-4(3H)-one (21). Compared to the known compounds the new esters are less or at best equally pesticidal with an equal or even higher mammalian toxicity.     

The Synthesis of 4b, 5, 12, 12a-Tetrahydro-5, 12-ethano-13H-indeno[2,3-b]anthracenes, 4b, 5, 10, 10a - tetrahydro-5,10-ethano-11H-indeno[2,3-b]naphtalenes and 1,2,3,4,4a, 9a-Hexahydro-1,4-(peri-naphthaleno)-fluorenes

The synthesis of endo- and exo-13-oxo-4b, 5, 12, 12a-tetrahydro-5, 12-ethanoindeno[2,3-b]anthracene ( 23 ; Schemes 1 and 2), exo- and endo-11-oxo-4b, 5, 10, 10a-tetrahydro-5, 10-ethano-indeno[2,3-b]naphthalene ( 31 ; Scheme 3), 1,2,3,4,4a,9a-hexahydro?1,4-(peri-naphthaleno)-fluoren-9-one (36; Scheme 4), and the corresponding hydrocarbons of the stereoisomeric ketone pairs 23 and 36 , is described.     

Semi-preparative liquid-chromatographic separation of all four stereoisomers of α-bisabolol on tribenzoylcellulose

Summary A semi-preparative low-pressure liquid-chromatographic procedure using tribenzoylcellulose has been developed for the separation and isolation of the four -bisabolol stereoisomers. Stereochemical assignments were made by HPLC-polarimeter coupling and by using the authentical isomers. This method can be applied to the quality control of chamomile preparations, as it allows the detection of adulterations resulting from admixtures of synthetic -bisabolol. In addition, the isolation of all four -bisabolol stereoisomers from commercially available synthetic -bisabolol has been made possible.     

Homopolar- and Heteropolar Bond Dissociation Energies and Heats of Formation of Radicals and Ions in the Gas Phase. I. Data on organic molecules

The literature data on heteropolar and homopolar 2-center bond dissociation energies in organic molecules in the gas phase and the corresponding heats of formation of radicals and ions have been critically evaluated. Data for more than 500 bonds are represented in tabular form together with the pertinent literature references. Selected electron affinities and π-bond dissociation energies have also been incorporated. The follow-up paper will discuss some empirical general aspects of these data particularly regarding the effect of structure on the bond dissociation energies.     

Internal rotation and pyramidal inversion in triacylphosphines

MO calculations predict a P-C rotation barrier in triformylphosphine of less than 6 kcal/mol, and an inversion barrier of ca 14 kcal/mol.     

1,3-Oxazolidin-4-ones. Synthesis and configuration of cis and trans isomers

Mixtures of cis and trans 1,3-oxazolidin-4-ones were obtained by cyclodehydration, in the presence of p-toluenesulfonic acid or boron trifluoride etherate, of lactamide and N-methyl-lactamide with aromatic and aliphatic aldehydes. The products were separated by column (silica) chromatography and their configurations were determined.     

Equilibrium interaction of solid surfaces across a polymer melt

Forces across polymer melts are poorly understood despite their importance for adhesion and fabricating composite materials. Using an atomic force microscope (AFM), this interaction was measured for poly(dimethyl siloxane) (PDMS). The structure of the polymer at the surface changed during the first approximately 10 h. Afterward, short-range attractive forces were observed with short-chain PDMS (M(w) = 4200 g/mol). Using PDMS with a molecular weight (M(w) = 18 000 g/mol) above the entanglement limit, we measured a monotonically decaying repulsive force, which indicates that a quasi-immobilized layer had formed at the solid surface. Due to the small radius of curvature of the tip, forces could be measured in equilibrium.