The generalized beta- and F-distributions in statistical modelling

The univariate generalized beta- and generalized F-distributions are frequently in recent statistical modellings and applications. They have richer properties than the standard beta- and Snedecor F-distributions and provide more flexibility than these distributions, of which they are natural extensions. Their connection with the Gauss hypergeometric function and Lauricella functions leads to further generalizations and important properties. This article gives a unified and up-to-date treatment of these two generalized distributions using only simple arguments. Proofs are given for some original results and a complete reference to their source is provided for established ones. The important problem of parameter estimation is also studied.     

Thee + e −→¯nn cross section predicted remarkably larger than thee + e −→¯pp one

It is shown that all global analyses of nucleon electromagnetic form factor data predict the electron-positron annihilation into neutron-antineutron cross section (for which there are no data till now) to be in a finite energy region substantially larger than the electron-positron annihilation into the proton-antiproton one.Dedicated to the memory of M. Gmitro.     

Aldo Cossu’s Work in Finite Geometry

A survey of the contributions of Aldo Cossu in finite geometry is given. Dedicated to the memory of Professor Aldo Cossu     

The first bismuth(III)-catalyzed guanylation of thioureas

This work describes the first catalytic bismuth-promoted synthesis of polysubstituted guanidines in good yields through the guanylation reaction of N-benzoyl or N-phenylthioureas with primary and secondary amines, but now employing equimolar amounts of each organic reagent. Both bismuth iodine and bismuth nitrate were efficient as inorganic thiophiles at only 5 mol % in relation to substrates, being the first example of inorganic thiophiles acting in guanylation at catalytic levels.     

Tiled Orders and Frobenius Rings

Mathematical Notes -     

J-aggregates of pseudoisocyanine with long alkyl substituents in thin films: Synthesis, spectral properties, and thermal stability

The formation and properties of J-aggregates in thin solid films of pseudoisocyanines with long N-alkyl groups, obtained by centrifuging from solutions in organic solvents, were studied. It is shown for the first time that nonsymmetric cyanine dyes, containing a C₂H₅ group at one nitrogen atom and a C₁₀H₂₁, C₁₅H₃₁, or C₁₈H₃₇ group at another nitrogen atom, spontaneously form J-aggregates stable at room temperature and pressing a narrow absorption band with a half-width at half maximum of 200 cm^?1. The thermal stability of J-aggregates in thin films of pseudoisocyanines with alkyl substituents decreases in the following order: C₂H₅-C₂H₅> C₂H₅-C₆H₁₃>C₂H₅-C₁₈H₃₇>C₂H₅-C₁₀H₂₁>C₂H₅-C₁₅H₃₁. By introducing 1-octadecyl-2-methylquinolinium iodide in the film, it was found that the J-aggregates studied consist of a small number (2–4) of dye molecules.     

An attempt on the calculation of relativistic potential energy curves: Noble gas difluorides

Total energy SCF calculations were performed for noble gas difluorides in a relativistic procedure and compared with analogous non-relativistic calculations. The discrete variational method with numerical basis functions was used. Rather smooth potential energy curves could be obtained. The theoretical Kr-F and Xe-F bond distances were calculated to be 3.5 a.u. and 3.6 a.u. which should be compared with the experimental values of 3.54 a.u. and 3.7 a.u. Although the dissociation energies are off by a factor of about five it was found that ArF₂ may be a stable molecule. Theoretical ionization energies for the outer levels reproduce the experimental values for KrF₂ and XeF₂ to within 2 eV.     

Reaction of 2-formyl-1,3-cyclohexanediones with cyanoacetamide

Chemistry of Heterocyclic Compounds -