On a diophantine problem of P. Erdös

Research supported in part by Grant 4055 from the Hungarian National Foundation for Scientific Research and by Kereskedelmi és Hitelbank Rt. Universitas Foundation.     

Electronic structure and spectra of tetrathiotetracene and related molecules

The electronic spectra of tetrathiotetracene (TTT) and of its mono- and dipositive ions have been calculated by the Pariser-Parr-Pople (PPP) method. Furthermore, the band polarizations of the first two bands of TTT have been measured. A reasonable band assignment is given using a new set of PPP parameters based on spectral data of a naphthalene derivative containing similar typical weak S-S bond. Other physical parameters as ionization potential, disproportionation energy, S-S bond length and net π-charges are discussed.     

Multiplication Groups of Topological Loops

In this brief survey, we discuss the following question: Which Lie groups can occur as the multiplication groups Mult(L) of connected topological loops L? We describe correspondences between the structure of the group Mult(L) and the structure of the loop L.     

Kinetic study on the homogeneous esterification of acetic acid with isoamyl alcohol

The liquid‐phase esterification of acetic acid and isoamyl alcohol has been studied to develop a kinetic model using a sequential experimental design based on the divergence criterion. Data come from batch reactor experiments, performed in the temperature range of 316–363 K. Discrimination among 36 possible kinetic models, written in terms of activity, mole fractions, and molar densities, is possible through the deviance information criterion, as estimated by a Markov chain Monte Carlo technique. The obtained results indicate a negligible heat of reaction and a clear autocatalytic effect of acetic acid on the esterification rate. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 45: 10–18, 2013     

On Barycentric Interpolation. II (Grünwald–Marcinkiewicz type Theorems)

Grünwald–Marcinkiewicz type theorems with respect to barycentric Lagrange interpolation based on equidistant and Chebyshev node-sytems in [–1, 1] are proved. It turns out that the results are very similar to the ones known for the classical Lagrange interpolation.     

Bounds on Malapportionment

Uniformly sized constituencies give voters similar influence on election outcomes. When constituencies are set up, seats are allocated to the administrative units, such as states or counties, using apportionment methods. According to the impossibility result of Balinski and Young, none of the methods satisfying basic monotonicity properties assign a rounded proportional number of seats (the Hare-quota). We study the malapportionment of constituencies and provide a simple bound as a function of the house size for an important class of divisor methods, a popular, monotonic family of techniques.     

Simultaneous Extensions of Topogenities

Let (X,) be a topological space, X _i X for i I, and < _i be a topogenity on X _i . We look for a topogenity < on X such that is the topology induced by < and <|X _i =< _i for i I.     

Effect of gamma-radiation in vinylpyrrolidone

The effects of gamma-irradiation in purified N-vinylpyrrolidone monomer have been studied. Dependence of crosslinking and water swelling ability upon the administered dose of ionizing radiation have been documented.