Construction of the Barut–Girardello quasi coherent states for the Morse potential

The Morse oscillator (MO) potential occupies a privileged place among the anharmonic oscillator potentials due to its applications in quantum mechanics to diatomic or polyatomic molecules, spectroscopy and so on. For this potential some kinds of coherent states (especially of the Klauder–Perelomov and Gazeau–Klauder kinds) have been constructed previously. In this paper we construct the coherent states of the Barut–Girardello kind (BG-CSs) for the MO potential, which have received less attention in the scientific literature. We obtain these CSs and demonstrate that they fulfil all conditions required by the coherent state. The Mandel parameter for the pure BG-CSs and Husimi’s and P$P$-quasi distribution functions (for the mixed-thermal states) are also presented. Finally, we show that all obtained results for the BG-CSs of MO tend, in the harmonic limit, to the corresponding results for the coherent states of the one dimensional harmonic oscillator (CSs for the HO-1D).     

Cogalois extensions via strongly graded fields

G-radicalG-Kneser and G-Cogalois extensions were introduced in [2]. In this paper we shall study some properties of these extensions by using techniques of graded rings theory.     

The wedderburn-malcev theorem for comodule algebras

Let H be a Hopf algebra over a field k. Under some assumptions on H we state and prove a generalization of the Wedderburn-Malcev theorem for i7-comodule algebras. We show that our version of this theorem holds for a large enough class of Hopf algebras, such as coordinate rings of completely reducible affine algebraic groups, finite dimensional Hopf algebras over fields of characteristic 0 and group algebras. Some dual results are also included.     

On Canonical Ideals of One-Dimensional Local Analytically Irreducible Rings

A characterization is given for certain canonical ideals of local one-dimensional commutative rings with identity under the assumption of analytical irreducibility. This extends both a known result characterizing the case when the ring itself is a canonical ideal (i.e., it is a Gorenstein ring), and another one which is a general characterization of canonical ideals but under the further assumption of residual rationality.     

The synthesis and characterization of melamine based Schiff bases and its trinuclear [salen/salophenFe(III)] and [salen/salophenCr(III)] capped complexes

Four new trinuclear Fe(III) and Cr(III) complexes involving tetradentate Schiff bases N, N′-bis(salicylidene)ethylenediamine-(salenH₂) or bis(salicylidene)-o-phenylenediamine-(salophen H₂) with 2,4,6-tris(4-carboxybenzimino)-1,3,5-triazine have been synthesized and characterized by means of elemental analysis, ¹H NMR, FT-IR spectroscopy, LC-MS, thermal analyses and magnetic susceptibility measurements. The complexes have also been characterized as low-spin distorted octahedral Fe(III) and Cr(III) bridged by COO^? group.     

Bundle pricing of inventories with stochastic demand

We consider a retailer selling a fixed inventory of two perishable products over a finite horizon. Assuming Poisson arrivals and a bivariate reservation price distribution, we determine the optimal product and bundle prices that maximize the expected revenue. Our results indicate that the performances of mixed bundling, pure bundling and unbundled sales strategies heavily depend on the parameters of the demand process and the initial inventory levels. Bundling appears to be most effective with negatively correlated reservation prices and high starting inventory levels. When the starting inventory levels are equal and in excess of average demand, most of the benefits of bundling can be achieved through pure bundling. However, the mixed bundling strategy dominates the other two when the starting inventory levels are not equal. We also observe that an incorrect modeling of the reservation prices may lead to significant losses. The model is extended to allow for price changes during the selling horizon. It is shown that offering price bundles mid-season may be more effective than changing individual product prices.     

Propagators and renormalization transformations for lattice gauge theories. II

We continue the studies of the Paper I and extend the results of this paper to operators defined by restrictions on different scales, or by renormalization transformations of different orders.Research supported in part by the National Science Foundation under Grant PHY-82-03669     

Variation of the Kβ/Kα intensity ratios of Ti, V and Cr in halogen compounds versus excitation energy in the interval 5.5-12.1 keV

The K/K intensity ratios for Ti, V and Cr in halogen (F and Cl) compounds were investigated. Measurements were carried out at ten different energies in the 5.5-12.1 keV interval by using the secondary excitation method. K X-rays emitted by the samples were counted by a Si(Li) detector with a resolution of 160 eV at 5.9 keV. It was observed that the measured values are getting closer to the theoretical values with increasing excitation energy. Values obtained were compared with the theoretical ones for pure elements.     

Spaces of regular gauge field configurations on a lattice and gauge fixing conditions

We consider spaces of lattice gauge field configurations satisfying gauge invariant regularity conditions, and intersections of these spaces with a surface given by gauge fixing conditions. We prove that if these conditions are chosen properly then configurations belonging to the intersection are small and regular.Research supported in part by the National Science Foundation under Grant PHY-82-03669