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 -     

Two-photon laser spectroscopy of the muonium 1S–2S transition

The 1² S _1/2(F=1)?2² S _1/2(F=1) energy interval in muonium has been investigated by Doppler-free two-photon laser spectroscopy. The transition was observed by uniquely identifying and counting the muons released after the photoionization of the 2S state by the same laser field. The measured transition frequency of 2455 528016(58)(43) MHz is in good agreement with QED calculations. The experiment can be interpreted as a test of the Lamb shift contributions at the 1% level. The method is also well suited for a precise determination of the mass of the positive muon in a muoniumhydrogen isotope shift measurement.     

Milch

Ohne Zusammenfassung     

π-Electron hyperconjugation in organic molecules and ions

The extent of energetic stabilization by alkyl groups with -electron systems via hyperconjugation is investigated theoretically by MINDO molecular orbital calculations. In neutral hydrocarbons, this stabilization represents about 4 % of the effective C-C bond energy, and is additive in the number of alkyl groups present. Calculations for conjugated, polar, and ionic molecules are also discussed.

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Zusammenfassung Das Ausma\ der energetischen Stabilisierung von -Elektronen-Systemen mit Alkylgruppen durch Hyperkonjugation wird theoretisch durch MINDO-MO-Berechnungen untersucht. In neutralen Kohlenwasserstoffen betrÄgt diese Stabilisierung etwa 4% der effektiven C-C Bindungsenergie und ist additiv entsprechend der Zahl der vorhandenen Alkylgruppen. Berechnungen für konjugierte, polare und ionische Moleküle werden ebenfalls diskutiert.

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Résumé La méthode des orbitales moléculaires MINDO est utilisée pour calculer le degré de stabilisation par hyperconjugaison entre des groupements alkyles et des systèmes d'électrons . Dans des hydrocarbures neutres cette stabilisation représente environ 4% de l'énergie effective de la liason C-C; elle est additive par rapport au nombre de groupements alkyles. On discute aussi des calculs effectués pour des molécules conjuguées polaires ou ioniques.

     

Reaction kinetics and critical phenomena: rates of some first order gas evolution reactions in binary solvents with a consolute point

We have measured the rate of carbon dioxide evolution in the aniline catalyzed decomposition of acetone dicarboxylic acid in a mixture of isobutyric acid + water near its consolute point. Within a temperature interval of 1 degrees C, which included the critical solution temperature, the first-order rate constant oscillated in magnitude by about 10% as it passed through three complete cycles of slowing down followed by speeding up. Whereas we can find no ready explanation for the speeding up, we suggest that, because the mixture contained no inert components, the slowing down should belong to the Griffiths-Wheeler class of strong critical effects [Phys. Rev. A 1970, 2, 1047]. As a check on this conclusion, we have measured the rate of the SN1 decomposition of benzene diazonium tetrafluoroborate in 2-butoxyethanol + water near the lower critical solution temperature and also the rate of the acid-catalyzed decomposition of ethyl diazoacetate in isobutyric acid + water near the upper critical solution temperature. Both of these reactions evolve nitrogen. In the first reaction, 2-butoxyethanol is inert, whereas in the second, isobutyric acid is inert. In both cases, because there was one inert component, we regarded the response of the rate constant to temperature in the critical region to be representative of the Griffiths-Wheeler class of weak critical effects. Within our accuracy of measurement of about 2% in the rate constant and about 1 mK in the temperature, we could detect no effect of the critical point on the rates of either of these reactions, suggesting that a weak effect may be too small to be seen with our experimental apparatus. The successful observation of a critical effect in the rate of decomposition of acetone dicarboxylic acid proves, however, that kinetic critical phenomena are observable in heterogeneous reactions.     

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).