Singularities of Blaschke normal maps of convex surfaces

We prove that the difference between the numbers of positive swallowtails and negative swallowtails of the Blaschke normal map for a given convex surface in affine space is equal to the Euler number of the subset where the affine shape operator has negative determinant.     

The first halogen-substituted cyclotrigermenes: a unique halogen walk over the three-membered ring skeleton and facial stereoselectivity in the Diels-Alder reaction

Dark red crystals of the halogen-substituted cyclotrigermenes [(tBu3Si)3Ge3X; X = Cl, Br, I] were obtained in good yields by the reaction of [(tBu3Si)3Ge3]+.TTFPB- (TTFPB- = tetrakis(2,3,5,6-tetrafluorophenyl)borate) with potassium halides (KCl, KBr, or KI) in diethyl ether. The crystal structures of the halogen-substituted cyclotrigermenes reveal a cis-bent Ge=Ge double bond, caused by the introduction of the electronegative halogen atom on the sp3 germanium atom of cyclotrigermene. In solution, an intramolecular halogen migration over the three-membered ring skeleton was observed. Facial stereoselectivity in the Diels-Alder reaction of new cyclotrigermenes with 2,3-dimethyl-1,3-butadiene is also reported.     

Structure of dichlorine monoxide as studied by microwave spectroscopy. Determination of equilibrium structure by a modified mass dependence method

The microwave spectra of four isotopic species of dichlorine monoxide (OCl₂) have been observed, and the rotational constants have been obtained. The r_m structure for each isotopic species has been determined by Watson's method. The equilibrium structure has been estimated by taking proper averages of r_m structures to be $\text{r}{}_{\mathrm{e}}\text{(OCl) = 1.69587(7)}\text{A}\text{?}$ and ∠_eClOCl = 110.886(6)°. The general applicability and the merit of the present method for estimating the equilibrium structure are pointed out.     

Intensity of Ar spectral lines in an Ar-O2 glow discharge

Measurements of relative intensities of spectral lines and of plasma parameters have been carried out in an Ar-O₂ d.c. glow discharge under the following conditions: gas pressures of 1, 2 and 3 torr and partial pressures for O₂ of 0, 0.01, 0.02, 0.05 and 0.1 torr. Many of the Ar line intensities decreased when O₂ was added, while some were enhanced. Enhancement of the 6677A and 7504A lines has been most notable. The number density of metastable Ar atoms is decreased when O₂ is added. Upon addition of O₂, the electron temperature is decreased and the electron density increased, except at a gas pressure of 1 torr; the electric field strength in the positive column is also increased.     

Low temperature magnetic properties of trimeric clusters

The degeneracy in the Heisenberg model of the three chromium clusters having D₃ symmetry is split by the antisymmetric exchange interaction. Based on this new energy level scheme, the low temperature behavior of the specific heat and magnetic susceptibility are reexamined.