Directed triangles in directed graphs

We show that each directed graph (with no parallel arcs) on n vertices, each with indegree and outdegree at least n/twhere t=2.888997… contains a directed circuit of length at most 3.     

lα-hydroxy previtamin D3, and its selective formation from 1-keto previtamin D3

An efficient method for the preparation of crystalline α-hydroxy previtamin D₃ is described. Also the stereoselective reduction of 1-keto previtamin $\text{9}$ is discussed; it was observed that with aluminum hydride $\text{7}$ is the most abundant product. This stands in contrast with previously reported LiAlH₄ and NaBH₄ mediated reductions.     

Iridoids : on the synthesis and structure of specionin

Recently, structure $\text{8b}$ has been assigned to the iridoid specionin. In the present letter the total synthesis of $\text{8b}$ is described. Comparison of spectral data reveals that the final product is not identical with natural specionin. Therefore the original structural assignment of specionin must be revised.     

The total synthesis of 1-oxygenated eudesmane sesquiterpenes : (±) dihydroreynosin and (±) 1-oxocostic acid

The total synthesis of (±) dihydroreynosin $\text{1}$ and of (±) 1-oxocostic acid $\text{2}$ (R = H) are illustrative examples for a short entry into 1-oxygenated eudesmanes via an easily accessible key intermediate $\text{7}$.     

The synthesis of functionalized cis'-bicyclo ¦3.3.0¦octanes

A number of polyfunctionalized cis-bicycio ¦3.3.0¦octanes have been synthesized starting from the tricyclic key intermediate $\text{5}$ which was obtained by the intramolecular cyclopropanation reaction of the diazo keto ester $\text{4}$. Selected stereocontrolled transformations of $\text{5}$ using nucleophiles and electrophiles have been studied for the preparation of the title compounds.     

Hydroxylation and epoxidation studies of some 3,4-dialkylcyclopentenes

The hydroxylation and the epoxidation of the cis and trans isomers of 3,4-dimethylcyclopentene and 4-t-butyl-3-methylcyclopentene have been studied. The stereoselectivity was studied as a function of the basic conformation of the individual cyclopentenes; the conformations were determined by ¹H NMR spectroscopy.     

Synthesis of new vitamin D3 analogues with a decalin-type CD-ring

Vitamin D analogues, characterized by a decalin CD-ring fragment are described.     

The chemical ionization mass spectra of 2-tert-butyl-substituted 1,3-cycloalkanediol diacetates and dimethyl ethers

The chemical ionization (CI) mass spectra of the 2-tert-butyl-substituted 1,3-cyclopentane- and 1,3-cyclohexanediol diacetates and dimethyl ethers have been determined using isobutane and methane as reagent gases. From the differences in the spectra of these compounds, it clearly follows that steric and conformational effects are expresssed in the CI mass spectra. The relative impact of these effects, however, is strongly dependent on diol derivatization and 2-alkyl substitution.     

Retroaldol-aldol isomerization of perhydroazulenic hydroxyketones

The retroaldol-aldol isomerization of the epimeric hydroxyketones $\text{3}$ and $\text{5}$ was found to yield predominantly $\text{4}$ and $\text{6}$, respectively, under kinetic conditions in the presence of chelating lithium cations. In hydroxylic medium $\text{4}$ is the preferred kinetic product. Under equilibration conditions $\text{4}$ and $\text{5}$ predominate.