A Kenmotsu Metric as a *-conformal Yamabe Soliton with Torse Forming Potential Vector Field

Acta Mathematica Sinica, English Series - The purpose of the present paper is to deliberate *-conformal Yamabe soliton, whose potential vector field is torse-forming on Kenmotsu manifold. Here, we...     

Electron spin resonance in the photo-excited triplet state of free base porphin in a single crystal of n-octane

E.S.R. experiments have been performed on the lowest triplet state of free base porphin (H₂P) in a n-octane single crystal at 1·3 K. The results demonstrate that the large majority of guest molecules occur in two orientations. While the molecules in these two orientations are coplanar, they have their N-H H-N axes at right angles. The fine structure results show that the two molecular orientations have zero-field splittings that differ by a few per cent in magnitude. Further, the 65 cm^-1 doublet separation which appears in the fluorescence spectrum of H₂P is related to the occurrence of these two orientations.

Resolved hyperfine structure is obtained for the two in-plane canonical orientations of the magnetic field and also when the field bisects the angle between these two directions. From an analysis of the fine structure and hyperfine structure results it is established that the zero-field splitting pattern is described by the parameters (average over the two orientations) the x axis is taken along the N-H H-N direction and z is the out-of-plane axis. From a computer simulation of the hyperfine structure it further follows that this structure is dominated by a high spin density at the methine carbons; with the coupling constants of the C-H fragment proposed by Hirota et al. the methine density is found to be ρ_m = 0·163.

In order to interpret the experimental results the zero-field splitting parameters and spin density distribution have been calculated for the lower triplet states of H₂P on the basis of a set of PPP-SCF-MO-CI calculations. From these calculations it follows that the lowest triplet state must correspond to the excitation e_g ←a _2u in Gouterman's four-orbital model. In terms of the D _2h symmetry of the H₂P molecule the assignment is ³ B _2u (b _3g ←b _1u ). For this assignment the calculations yield .     

On CNC commuting contractive tuples

The characteristic function has been an important tool for studying completely non-unitary contractions on Hilbert spaces. In this note, we consider completely non-coisometric contractive tuples of commuting operators on a Hilbert space H. We show that the characteristic function, which is now an operator-valued analytic function on the open Euclidean unit ball in ℂⁿ, is a complete unitary invariant for such a tuple. We prove that the characteristic function satisfies a natural transformation law under biholomorphic mappings of the unit ball. We also characterize all operator-valued analytic functions which arise as characteristic functions of pure commuting contractive tuples.     

Strong signal of dynamical long-range correlation among target fragments in relativistic and ultra-relativistic nuclear interactions

This paper reports an investigation on the two-particle long-range angular correlation among the target fragments produced in ²⁸Si–AgBr interactions at 14.5 AGeV, ¹⁶O–AgBr interactions at 60 AGeV and ³²S–AgBr interactions at 200 AGeV. The experimental data have been compared with Monte Carlo simulated events to extract dynamical correlation. The data exhibit two-particle long-range correlation in emission angle space at all energies.     

Some new constructions of bivariate Weibull models

In this article, several approaches are advanced towards the construction of bivariate Weibull models from the consideration of failure behaviors of the components of a two-component system. First, a general method of construction of bivariate life models is developed in the setting of random environmental effects. Some new bivariate Weibull models are derived as special cases and added insights are provided for some of the existing ones. In the course of model formulation in terms of the dependence structure, a new bivariate family of life distributions is constructed so as to incorporate both positive and negative quadrant dependence in the same parametric setting, and a bivariate Weibull model is obtained as a special case. Finally, some distributional properties are presented for a bivariate Weibull model derived from the consideration of random hazards.     

Quantitative analysis of triphenylboron in environmental water samples by liquid chromatography/mass spectrometry.

Liquid chromatography/mass spectrometry (LC/MS) has been applied to the analysis of triphenylboron, which has been produced as a substitute for organotin compounds, in water. Although commercial triphenylboron compounds are produced as pyridinyl complexes, the chemical form in water is supposed to be mainly triphenylboron after liberating pyridine. The triphenylborons were extracted from water with an Empore C18 extraction disk under acidic condition, and the extracts were introduced directly into a liquid chromatograph-mass spectrometer equipped with a negative ion electrospray ionization interface. Identification of the compounds was performed with specific ions produced from the triphenylboron, and a quantitative analysis was carried out using the peak areas. The average recoveries from distilled water, seawater and river water at 0.30 ng/ml were 92.3, 100 and 85.3%, respectively. A detection limit of 0.023 ng/ml for triphenylboron was achieved.     

Handling of intrinsic divergence in the orthogonal gradient method of orbital optimization in an MC-SCF framework and geometry optimization in pathological cases: I (propynal in excited states)

It is demonstrated that a generalized version of the orthogonal gradient method of orbital optimization may sometimes encounter a specific divergence problem which may be termed intrinsic to the first order method. Instead of switching over to a more sophisticated second order method one can cure the divergence problem at the first order level itself by suitably tailoring the MC-SCF operator or the MC-SCF energy matrix. Results of complete geometry optimization of propynal in^l,3nπ* and³ππ* states (pathological cases) are reported to demonstrate the usefulness of the method at an INDO-MCSCF level of approximation. The results of structure calculations are further rationalized from generalized quantum chemical bond order indices.