Determination of the anharmonicity constant of oxygen by raman measurements

The hot band ν = 1 → 2 of O₂, which could not be resolved in previous Raman measurements, has been observed by direct scanning of the purely isotropic part of Raman scattered light. A computer simulation of the spectrum confirmed the set of anharmonicity constants given by Babcock and Herzberg.     

Synthesis of isoquinobenzodiazepinediones

1-(2′-Chloroacetylamino)-4,4-dimethyl-1,4-dihydro-3(2H)-isoquinolinone ( 3 ) was cyclised by treatment with sodium hydride in dimethyl sulphoxide containing 0.1 % of water to give 10,10-dimethyl-6,7,9,10-tetrahydro-5H,14bH-isoquino[2,1-d][1,4]benzodiazepine-6,9-dione ( 4 ) in a yield of 80%. In anhydrous dimethyl sulphoxide the main product of the reaction was 5-N-(4,4-dimethyl-1-phenyl-1,4-dihydro-3(2H)-isoquinolinon-1′-yl)isoquino[2,1-d][1,4]benzodiazepine-6,9-dione ( 5 ), which was also prepared by the reaction of 3 with 4 .     

Magnetic properties of a mixed spin-1/2 and spin-3/2 transverse Ising model

A theoretical study of a mixed spin-1/2 and spin-3/2 Ising system with independent transverse fields is presented using an effective field method within the framework of a single-site cluster theory. In this approach the effective field equations are derived using a probability distribution method based on the use of generalized van der Waerden identities accounting exactly for the single-site kinematic relations. The effect of the transverse fields on the critical behaviour is studied. The thermal dependence of the longitudinal and transverse components of the magnetization and its higher moments is also studied.     

Pressure independence of stereomutation and fragmentation in the bis-spirocyclobutanes, anti- and syn-2,9-dicyanodispiro[5.0.5.2]tetradeca-1,8-dienes

Pressure dependent rate constants and volumes of activation for stereomutational interconversions of the cyclobutanes, anti- and syn-2,9-dicyanodispiro[5.0.5.2]tetradeca-1,8-dienes (anti-6 and syn-6), and for their fragmentation to 1-cyano-3-methylenecyclohexene (5) have been determined. Although fragmentations might have been expected to have larger and thus more positive volumes of activation than stereomutation, both processes have essentially identical volumes of activation within experimental uncertainties at 50.1 degrees C over the pressure range, 1-3000 bar: DeltaV(not equal) = (+7.4 to +9.9) +/- 2.0 cm3 mol(-1). While these positive values are consistent with the rate of entry into the hypothetical caldera being determined by breaking the weakest bond in the cyclobutanes, the insensitivity of the product-determining exit channels argues against the obligatory second bond-breaking being a significant factor in fragmentation.     

A priori Schranken für Eigenwerte von Sturm-Liouvilleschen Eigenwertproblemen

By means of a duality principle of the optimal control theory bounds for the eigenvalues of a Sturm-Liouville problem are constructed. They are then compared with the bounds obtained from monotonicity principles.     

Expressing a prime as difference between two numbers containing all the previous primes

We consider the simultaneous equations $$\begin{gathered} p_1^{\alpha _1 } p_2^{\alpha _2 } ...p_n^{\alpha _n } = P_1 P_2 \hfill \\ p_{n + 1} = P_1 - P_2 \hfill \\ \end{gathered} $$ wherep ₁,p ₂,...,p _n+1 are then+1 first primes and α₁,...,α _n ,P ₁,P ₂ are integers. The equations are solved completely forn≦3 and all solutions given under certain restrictions on the α _i 's forn≦9.