On cubature formulae with a minimal number of knots

Summary In this paper an approach is outlined to the two-dimensional analogon of the Gaussian quadrature problem. The main results are necessary and sufficient conditions for the existence of cubature formulae which are exact for all polynomials of degree m and which have a minimal number of 1/2k(k+1) knots,k=[m/2]+1. Ifm is odd, similar results are due to I.P. Mysovskikh ([5, 6]) which will be derived in a new way as a special case of the general characterization given here. Furthermore, it will be shown how this characterization can be used to construct minimal formulae of even degree.     

Photolyse von 3-Methyl-2, 1-benzisoxazol (3-Methylanthranil) und 2-Azido-acetophenon in Gegenwart von Schwefelsäure und Benzolderivaten

Photolysis of 3-Methyl-2, 1-benzisoxazole (3-Methylanthranil) and 2-Azido-acetophenone in the Presence of Sulfuric Acid and Benzene Derivatives Irradiation of 3-methylanthranil ( 1 ) in acetonitrile in the presence of sulfuric acid and benzene, toluene, p-xylene, mesitylene or anisole with a mercury high-pressure lamp through a pyrex filter yields beside varying amounts of 2-amino-acetophenone ( 3 ) and 2-amino-5-hydroxy- ( 4a ) and 2-amino-3-hydroxy-acetophenone ( 4b ) the corresponding diphenylamine derivatives 5 (see Table 1). In the case of toluene and anisole mixtures of the corresponding ortho- and para-substituted isomers ( 5b, 5d or 5g, 5i respectively), but no meta-substituted isomers ( 5c or 5h ) are obtained. In addition to these products, the irradiation of 1 in the presence of anisole yields also 2-amino-5-(4′-methoxyphenyl)-acetophenone ( 7 ), 2-amino-3-(4′-methoxyphenyl)-acetophenone ( 8 ) and 2-methoxy-9-methyl-acridine ( 6 ; see Scheme 1). The latter product is also formed thermally by acid catalysis from the diphenylamine derivative 5i . Irradiation of 2-azido-acetophenone ( 2 ) in acetonitrile solution in the presence of sulfuric acid and benzene leads to the formation of 1, 3, 4a, 4b, 5a and 9 (see Table 2). Compounds 3, 4a, 4b and 5a are also obtained after acid catalyzed decomposition of 2 in the presence of benzene. Thus, it is concluded that irradiation of 1 or 2 in the presence of sulfuric acid yields 2-acetyl-phenylnitrenium ions 10 in the singlet ground state which will undergo electrophilic substitution of the aromatic compounds, perhaps via the π-complex 11 (see Scheme 2).     

Photochemische Cycloadditionen von 3-Phenyl-2H-azirinen an Carbonsäurechloride. 35. Mitteilung über Photoreaktionen

Irradiation of 2, 3-diphenyl-2H-azirine ( 1a ) and 1-azido-1-phenyl-propene, the precursor of 2-methyl-3-phenyl-2H-azirine ( 1b ), in benzene, with a high pressure mercury lamp (pyrex filter) in the presence of acid chlorides yields the oxazoles 5a–d (Scheme 2). Photolysis of 2, 2-dimethyl-3-phenyl-2H-azirine ( 1c ) under the same conditions gives after methanolysis the 5-methoxy-2, 2-dimethyl-4-phenyl-3-oxazolines 7a, b, d , while hydrolysis of the reaction mixture leads to the formation of the 1, 2-diketones 8a, c, d (Scheme 4). The suggested reaction path for all these reactions is a 1, 3-dipolar cycloaddition of the photochemically generated benzonitrilemethylides 2 to the carbonyl double bond of the acid chlorides to give the intermediates 4 , followed by either elimination of hydrogen chloride or solvolysis (Schemes 2 and 4). Irradiation of 1c in the presence of acetic acid anhydride leads via the intermediate 9 to the 5-hydroxy-3-oxazoline 10 and the 5-methylidene-3-oxazoline 11 (Scheme 5).     

Thermisches Verhalten von 1,2-Dipropenylbenzolen

1-cis, 2-cis-Dipropenylbenzene (cis, cis- 1 ) isomerises thermally at 215–235° with 1st order kinetics to give trans, cis- 1 and vice versa. At equilibrium 89% trans, cis- and 11% cis, cis- 1 are present. It is shown by thermal rearrangement of cis, cis-2′, 2″-d₂- 1 that the isomerisation is attributable to aromatic [1, 7a]-sigmatropic H-shifts. trans, trans- 1 rearranges thermally at 225–245° to yield 2, 3-dimethyl-1, 2-dihydronaphthalene ( 2 ). The formation of 2 can be visualized by disrotatory ring closure followed by an aromatic [1, 5s]-sigmatropic H-shift. 2 is also formed when, cis, cis- or trans, cis- 1 are heated for 153 h at 225°. Besides 2 a small amount (3%) of 1-ethyl-1, 2-dihydronaphthalene ( 5 ) is formed. The rearrangement of trans, trans- 1 and trans, trans-2′, 2″-d₂- 1 shows a secondary isotope effect k_H/k_D = 0,90.     

Totalsynthese von natürlichem α-Tocopherol. 2. Mitteilung. Aufbau der Seitenkette aus (−)-(S)-3-Methyl-γ-butyrolacton

Total Synthesis of Natural α-Tocopherol A short and efficient route to optically pure (+)-(3 R, 7 R)-trimethyldodecanol ( 14 ) is demonstrated, 14 serving as side chain unit in the preparation of natural vitamin E. The synthesis of 14 is based on the concept of using a single optically active C₅-synthon of suitable configuration and functionalization to introduce both asymmetric centres in 14 . (?)-(S)-3-Methyl-γ-butyrolacton ( 1 ) and ethyl (?)-(S)-4-bromo-3-methylbutyrate ( 2 ), respectively, is used in a sequence of either two Grignard C,C-coupling reactions 5 → 8 and 12 → 13 or two Wittig reactions 17a → 18 and 20 → 21 to achieve this goal. 14 is converted to (2 R, 4′R, 8′R)-α-tocopherol (= vitamin E) by coupling with a chroman unit in known manner. Optical purity of products and intermediates is established.     

Die thermische Umlagerung von 2-(Buta-1′,3′-dienyl)-phenolen in 2-Alkyl-2H-chromene; Beispiele für aromatische [1,7a]- und [1,5s]sigmatropische Wasserstoffverschiebungen

2-(1′-cis,3′-cis-)- and 2-(1′-cis,3′-trans-Penta-1′,3′-dienyl)-phenol (cis, cis- 4 and cis, trans- 4 , cf. scheme 1) rearrange thermally at 85–110° via [1,7 a] hydrogen shifts to yield the o-quinomethide 2 (R ? CH₃) which rapidly cyclises to give 2-ethyl-2H-chromene ( 7 ). The trans formation of cis, cis- and cis, trans- 4 into 7 is accompanied by a thermal cis, trans isomerisation of the 3′ double bond in 4. The isomerisation indicates that [1,7 a] hydrogen shifts in 2 compete with the electrocyclic ring closure of 2 . The isomeric phenols, trans, trans- and trans, cis- 4 , are stable at 85–110° but at 190° rearrange also to form 7 . This rearrangement is induced by a thermal cis, trans isomerisation of the 1′ double bond which occurs via [1, 5s] hydrogen shifts. Deuterium labelling experiments show that the chromene 7 is in equilibrium with the o-quinomethide 2 (R ? CH₃), at 210°. Thus, when 2-benzyl-2H-chromene ( 9 ) or 2-(1′-trans,3′-trans,-4′-phenyl-buta1′,3′-dienyl)-phenol (trans, trans- 6 ) is heated in diglyme solution at >200°, an equilibrium mixture of both compounds (～ 55% 9 and 45% 6 ) is obtained.     

Stationary points in the temperature dependence of electron transfer rates

The temperature dependence of the rate of electron transfer is analyzed in the framework of a molecular theory presented recently, characterized by decoupling the total solvent reorganization energy into two contributions featuring reorganizations of permanent dipoles as well as solvent density. The inclusion of the temperature dependence of liquid density reorganization can give rise to a maximum in the Arrhenius coordinates for electron transfer in the inverted region and for exothermic reactions with small activation barriers as well.     

Kinetik und Mechanismus der Diazotierung, 15. Mitt.: Kinetik der anorganischen Startreaktion der Diazotierung

Zusammenfassung Es werden die Geschwindigkeitskoeffizienten der Primärreaktion der Diazotierung, nämlich der Bildung des Nitrosoacidiumions aus salpetriger Säure und Hydroxoniumion: HNO₂+H₃O⁺H₂O·NO⁺+H₂O bei verschiedenen Temperaturen bestimmt. Die thermodynamischen Aktivierungsgrößen dieser Urreaktion werden daraus errechnet.Die Resultate werden aus der Kinetik der Diazotierung des Anilins in Nitritpufferlösungen und in schwach sauren ungepufferten Lösungen geschöpft, bei welchen nur die beiden anorganischen Urreaktionen HNO₂+H₃O+H₂O·NO⁺+H₂O H₂O·NO⁺+NO_2–N₂O₃+H₂O kinetisch in Erscheinung treten.Originalvortrag vonHermann Schmid beim XVII. Internat. Kongr. Reine u. Angew. Chem. (München, 2. Sept. 1959).     

Rapid determination of microorganisms using a flow-injection system

An automated method for the rapid determination of microorganisms using a flow-injection system is presented. Electrochemical measurement of a mediator reduced by microbial metabolism allowed the determination of fungi and bacteria in a few minutes. The lowest detection limit was 5 × 10⁶ colony-forming units (cfu) ml^?1 for Escherichia coli. Correlation between the flow-injection method and standard microbiological methods was excellent (r = 0.997, n = 4 for Beauveria bassiana; r = 0.997, n = 7 for E. coli). The flow-injection system was applied to the on-line control of an E. coli cultivation.     

Partialsynthesen und Reaktionen von Abietanderivaten (Lanugonen) aus Plectranthus lanuginosus und verwandten Verbindungen

Partial Syntheses and Reactions of Abietanoid Derivatives (Lanugones) from Plectranthus lanuginosus and of Related Compounds Interconversions by partial syntheses of several lanugones establish their absolute configuration at C(15). Unexpected reactions exemplify the unique reactivity of these abietanoic diterpenes, - Lanugone O ( 4 ) was prepared in several steps from (15S)-coleon C ( 8a ; Scheme 2) thus establishing its (15S)-configuration. One of the intermediates, the 12-O-acetyl-6-oxoroyleanone 12 , through acetyl-migration sets up an equilibrium with the vinylogous quinone 13 (Scheme 3). - The chirality at C(15) in the dihydrofuran moiety of lanugone Q ( 16 ) was proven by acid-catalyzed conversion of lanugone O ( 4 ) to 16 . - Instead of the usual nucleophilic attack shown by quinomethanes, lanugone L (1 ) is electrophilically substituted at C(7) by acetic anhydride/pyridine (Scheme 1). - In a homosigmatropic [1,5]-H-shift, lanugone G ( 17 ) in solution is converted to the corresponding allyl substituted royleanone 18 (Scheme 4). - Methanolysis of lanugone J ( 19 ) leads to the expected royleanone 20 having the 2-methoxypropyl side chain ( Scheme 5 ). Similar reactions were found in acetolytic reactions. However, treatment-of spirocoleons with SOCl₂/DMF produces mainly 12-deoxyroyleanones with allyl- and 2-chloropropyl groups, i. e. 19 → 26 and 27 ; 28 → 29 . The possible natural occurrence of these compounds is emphasized.