Optimal node disjoint paths on partial 2-trees: A linear algorithm and polyhedral results

We present anO(p · n) algorithm for the problem of finding disjoint simple paths of minimum total length betweenp given pairs of terminals on oriented partial 2-trees withn nodes and positive or negative arc lengths. The algorithm is inO(n) if all terminals are distinct nodes. We characterize the convex hull of the feasible solution set for the casep=2.We gratefully acknowledge the referee's many helpful suggestions to improve the presentation of this paper.     

Zur Bestimmung von Submikromengen von Kohlenstoff in organischen Verbindungen

Analytical and Bioanalytical Chemistry -     

Ein Verfahren zur Schnellbestimmung von Phosphor in Motorölen und Additiven

Analytical and Bioanalytical Chemistry -     

Gas-Chromatographie

Analytical and Bioanalytical Chemistry -     

Milch

Ohne Zusammenfassung     

Amber‐Woody Scent: Alcohols with Divergent Structure Present Common Olfactory Characteristics and Sharp Enantiomer Differentiation

Only one out of the four possible trans isomers of the important perfumery alcohol Norlimbanol^® ( 1 ) possesses a very strong amber‐woody smell, the isomer 1A with (1′R,3S,6′S) absolute configuration. Its enantiomer 1B is almost odorless and devoid of amber‐woody character, whereas the diastereoisomers 1C and 1D are considerably weaker and perceptible only by the most‐sensitive persons. The same is true for a whole series of perceptual analogs of 1 , including β‐alkoxy alcohols. These ethers belong to two structural classes: [(2,2,6‐trimethylcyclohexyl)oxy]‐ (see 3, 4 , and 16 ) or {[2‐(tert‐butyl)cyclohexyl]oxy}alkan‐2‐ol derivatives (see 19 and 20 ; Table). A superimposition model allowing for good overlap of the respective hydroxylated side chains offers a tentative explanation for the shared perceptual characteristics of the two classes (Fig. 5). The lipophilic cyclohexane moieties present only a minimal overlap in this model, suggesting that quite larger molecules might possess the same smell. (S)‐Configured β‐alkoxy alcohols can conveniently be obtained on a larger scale by enantioselective reduction of the corresponding ketones (Scheme 9).     

Über sechsgliedrige Heterocyclen mit Phosphor-, Stickstoff- und Schwefelatomen im Ring

Cyclic sulphurylphosphazochloride (I: formula see ?Inhaltsübersicht”?) reacts with ammonia or methylamine forming the. tetramide(II) and (III), respectively, and with aniline or dimethylamine forming the diamide (IV) resp. (V). The synthesis of the diphenyl derivative (VI) is achieved starting from C₆H₅? PCl₄. (II) gives with PCl₅ the ionic compound (VII).     

Über Phosphorstickstoffverbindungen. XXIX. Reaktionen von Diphenyltrichlorphosphoran mit Stickstoff enthaltenden Verbindungen

The reaction of diphenyltrichlorophosphorane with amides leads to (C₆H₅)₂P(Cl)?N-acyl compounds, whereas with amines salt-like compounds, [(C₆H₅)₂P(Cl)? NHR]Cl, are formed.