Description: This article discusses an abstract index theorem on non-compact Riemannian manifolds. Abstract: We prove an abstract index theorem for essentially self-adjoint Fredholm supersymmetric first-order elliptic differential operators on Hermitian vector bundles over complete oriented Riemannian manifolds. According to our main result the supersymmetric L2-index of such an operator can be expressed as the sum of a "local contribution" (the familiar Atiyah-Singer index form, suitably restricted to and integrated over a finite region) and a "boundary contribution" (which depends only on the restriction of the operator at large distances). This is done by splicing together local parametrices and Green's operators defined "at infinity". The result yields (in fact is equivalent to) a generalisation of the relative index theorem of Gromov and Lawson.

Description: This article discusses the effect of solvent polarity on the fluorescence emission fine structures of coronene derivatives. Abstract: The fluorescence properties of coronene (Co), benzo[a]coronene (BCo), naphtho[2,3-a]coronene (NCo), dibenzo[a,j]coronene (DCo), naphtho[1,2,3,4-ghi]perylene, benzo[pqr]naphtho[8,1,2-bcd]perylene and dibenzo[cd,lm]perylene dissolved in solvents of varying polarity are reported. Measurements indicated that the emission intensities of the four coronene derivatives depended on solvent polarity. The Co, BCo and NCo scales have been defined as the ratio of the fluorescence intensities of bands I and III of the vibronic spectra. Band III of dibenzo[a,j]coronene was not clearly identifiable in all the solvents studied, and the DCo scale was therefore defined as the intensity ratio of band I and IV. Emission intensity ratios of the three perylene derivatives remained nearly constant, irrespective of solvent polarity.

Description: This article discusses the enthalpy of solvation correlations for organic solutes and gases dissolved in 2-propanol, 2-butanol, 2-methyl-1-propanol and ethanol. Abstract: Data have been assembled from the published literature on the enthalpies of solvation for 91 organic vapors and gaseous solutes in 2-propanol, for 73 gaseous compounds in 2-butanol, for 85 gaseous compounds in 2-methyl-1-propanol and for 128 gaseous compounds in ethanol. It is shown that an Abraham solvation equation with five descriptors can be used to correlate the experimental solvation enthalpies to within standard deviations of 2.24 kJ/mole, 1.99 kJ/mole, 1.73 kJ/mole and 2.54 kJ/mole for 2-propanol, 2-butanol, 2-methyl-1-propanol and ethanol, respectively. The derived correlations provide very accurate mathematical descriptions of the measured enthalpy of solvation data at 298 K, which in the case of ethanol span a range of 136 kJ/mole. Division of the experimental values into a training set and a test set shows that there is no bias in predictions, and that the predictive capability of the correlations is better than 3.5 kJ/mole.

Description: This article discusses the transfer of neutral molecules, ions and ionic species from water to benzonitrile; comparison with nitrobenzene. Equations have been constructed for the transfer of 64 neutral solutes from water and from the gas phase to the solvent benzonitrile. The equations contain five descriptors and can be used to predict further values of the water-benzonitrile and gas-benzonitrile partition coefficients for a wide range of solutes. The water-benzonitrile equation has been extended to include ions and ionic species derived from acids by loss of a proton and bases by acceptance of a proton. Only two further descriptors are needed, one for anions and one for cations. A previous equation for transfer of neutral solutes from water to nitrobenzene has also been extended to include ions and ionic species. Comparison of the equations for transfer to benzonitrile and to nitrobenzene shows that the two solvents behave quite similarly, although benzonitrile as a solvent is a stronger hydrogen bond base.

Description: This article discusses the enthalpy of solvation correlations for organic solutes and gases dissolved in 1-propanol and tetrahydrofuran. Abstract: Data have been assembled from the published literature on the enthalpies of solvation for 103 organic vapors and gaseous solutes in 1-propanol and for 86 gaseous compounds in tetrahydrofuran. It is shown that an Abraham solvation equation with five descriptors can be used to correlate the experimental solvation enthalpies to within standard deviations of 2.35 kJ/mole and 2.10 kJ/mole for 1-propanol and tetrahydrofuran, respectively. The derived correlations provide very accurate mathematical descriptions of the measured enthalpy of solvation data at 298 K, which in the case of 1-propanol span a range of 119 kJ/mole. Division of the experimental values into a training set and a test set shows that there is no bias in predictions, and that the predictive capability of the correlations is better than 3.5 kJ/mole.