Operators with bounded conjugation orbits

For a bounded invertible operator on a complex Banach space let be the set of operators in for which Suppose that and is in A bound is given on in terms of the spectral radius of the commutator. Replacing the condition in by the weaker condition as for every 0$">, an extension of the Deddens-Stampfli-Williams results on the commutant of is given.

     

Molybdenum and tungsten complexes of biquinoline. Crystal structure of W(CO)4(2,2′-biquinoline)

M(CO)₆ (M = Mo and W) reacts with 2,2-biquinoline (biq) to yield tetracarbonyl derivatives M(CO)₄(biq). Crystals suitable for X-ray structure determination of W(CO)₄(biq) were isolated from benzene solution. The u.v.–vis. spectra of the complexes exhibited visible transitions due to metal-to-ligand charge-transfers. Electrochemical investigation of the complexes showed some irreversible, reversible and quasi-reversible redox reactions due to tautomeric interconversions through electron transfer. The thermal properties of the complexes were also investigated using the thermogravimetric technique.     

A nonlinear problem having a continuous locus of singular points and no multiple solutions

The boundary-value problem ?z″ = (z² ? t²)z′, ? > 0, z(? 1) = α, z(0) = β, t? [?1, 0], has been shown to have a solution, and moreover, depending on the choice of α and β, multiple solutions to it exist. We consider the more general equation f(z, t)z″ = (z^r ? t^s)z′ for a particular non-negative function f(z, t), and integrate the equation exactly. Depending on α and β, we find that either there are no solutions, or that only unique solutions exist. The conclusion is that the presence of a continuous locus of singular points, given by z^r = t^s, does not necessarily produce multiple solutions.     

NMR studies in the heterocyclic series. XVIII—Carbon-13 NMR study of azolium salts. Attempted correlation of chemical shifts with calculated charge densities

The carbon-13 chemical shifts and the ¹J(CH) coupling constants for 18 azolium salts (di-N-methyl-pyrazolium, -indazolium, -benzimidazolium and -benzotriazolium iodides) have been determined and assigned. The chemical shifts are discussed as a function of substituent effects, positive charge introduction and total electronic density (calculated by the CNDO/2 method). The general problem of correlations between chemical shifts and total charge densities in azoles is discussed. A statistical approach shows that these correlations are of poor quality.     

Two-wavelength and power-balanced oscillation of a CO2 laser for application to differential absorption measurements

A new technique of alternate two-wavelength oscillation of a CO₂ laser is discussed for application to various differential absorption spectroscopic measurements. Power-balanced, two-adjacent branch oscillation using a single CO₂ laser was achieved by modulating the angle of a mirror inside the laser cavity and adjusting automatically the cavity length. The two-wavelength modulation frequency was extended up to about 1.2 kHz. Line tuning and power modulation characteristics were studied. The laser was used in long-path differential absorption measurements of ethylene air pollution molecules to demonstrate the capability of this power-balanced, two-wavelength oscillation method. The minimum detectable absorption was nearly 1×10^–3 in a short-path cell experiment and 3×10^–3 in a long-path experiment.     

Crystal Structures of Bis[aquachlorotriphenyltin(Ⅳ)] dihydrate·1,4,7,10,13,16-hexacyclooctadecane bis[aquachlorotriphenyltin(Ⅳ)]·1,4,7,10,13,16-hexacyclooct-adecane (3/1) and Bis[aquatrifluoroacetatotriphenyltin(Ⅳ)] dihydrate·1,4,7,10,13,16-hexacyclooctad

In the crystal structures of the centrosymmetric isostructural co-crystals, bis[aqua- hlorotriphenyltin]dihydrate(1,4,7,10,13,16-hexacyclooctadecane-bis[aquachlorotriphenyltin(Ⅳ)]a 1,4,7,10,13,16-hexacyclooctadecane (3/1) 1 and bis[aquatrifluoroacetatotriphenyltin] dihydrateb 1,4,7,10,13,16-hexacyclooctadecane-bis[aquatrifluoroacetatotriphenyltin(IV)](1,4,7,10,13,16- hexacyclooctadecane(3/1) 2, the crown ether interacts with the triphenyltin unit through both the coordinated and lattice water molecules in one molecular entity, but only through the coordinated water molecule in the other. The tin atoms are five-coordinate in trans-trigonal bipyramidal environments. Compound 1 is refined on 204 variables and 4665 I > 3((I) reflections to R = 0.055, and compound 2 on 233 variables and 5721 I > 3((I) reflections to R = 0.052. For crystal 1: C192H244Cl8O38Sn8, fw = 4392.99, trigonal, R, a = 27.391(1), c = 23.007(1) A。, V = 14948(1) A。3, Z = 3, Dc = 1.464 g/cm3, F(000) = 6708 and μ = 1.162 mm－1; and for 2: C208H244F24O54Sn8, fw = 5013.55, trigonal, R, a = 28.775(1), c = 23.289(1) A。, V = 16699(1) A。3, Z = 3, Dc = 1.496 g/cm3, F(000) = 7620 and μ = 0.978 mm－1.     

Studies on 5-aminoisoxazole derivatives: Synthesis of some new fused isoxazoles

Several new fused isoxazole derivatives could be obtained utilising 5-amino-4-ethoxycarbonyl-3-ethoxycarbonylmethyl and 5-amino-4-cyano-3-trichloromethyl-isoxazoles as starting components.

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Untersuchungen an 5-Aminoisoxazol-Derivaten: Synthese einiger neuer kondensierter Isoxazole

Zusammenfassung Es konnten einigen neue Isoxazolderivate über 5-Amino-4-ethoxycarbonyl-3-ethoxycarbonylmethyl-und 5-Amino-4-cyano-3-trichlormethyl-isoxazol als Ausgangsverbindungen erhalten werden.

     

Steady state creep during transformation in Cd-Zn alloys

Apparent steady-state creep of Cd-2 wt. % Zn and Cd-17·4 wt. %Zn alloys has been studied under different constant stresses ranging from 6·4 MPa to 12·7 MPa, near the transformation temperature of 483 K. The strain rate of the steady-state creep for both compositions has shown two temperature regions of deformation, the low-temperature region (below 483 K) and the high-temperature region above this temperature. The stress exponent m' was found to change from 4·7 to 2 for Cd-2 wt. % Zn and from 3·1 to 2·4 for Cd-17·4 wt. % Zn alloys. The activation energies in the temperature region below the transformation temperature have been found to be 84 kJ/mole for Cd-2 wt. % Zn and 70 kJ/mole for Cd-17·4 wt. % Zn alloys characterizing the mechanism of volume self-diffusion in Cd.