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.     

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     

Transitive Quasi-Uniformities and Topogenous Orders

The purpose of the present paper is to show that the concept of topogenous order, introduced in [1] and discussed in detail in [2], can be useful in answering questions concerning transitive quasi-uniformities.     

Low cost bifunctional initiators for bidirectional living cationic polymerization of olefins. I. isobutylene

We describe the discovery of novel low cost bifunctional initiators 2,4,7,9‐tetramethyl‐tricyclo[6.2.0.0³⁶]deca‐1(8),2,6‐triene‐4,9‐diol (bBCB‐diOH) and 4,9‐dichloro,2,4,7,9‐tetramethyl‐tricyclo[6.2.0.0³⁶]deca‐1(8),2,6‐triene (bBCB‐diCl), for living cationic bidirectional polymerization of olefins, for example, isobutylene. bBCB‐diOH was quantitatively synthesized in one step by UV radiation of commercially available diacetyl durene (DAD) and bBCB‐diCl by hydrochlorination of bBCB‐diOH. These molecules, in conjunction with TiCl₄ coinitiator, initiate the living polymerization of isobutylene. Livingness was demonstrated by linear conversion versus molecular weight (MW) plots and narrow MW distributions. Polymerizations are slower than those initiated by the universally used “hindered” bifunctional initiator 5‐tert‐butyl‐1,3‐bis(1‐chloro‐1‐methyl)benzene and are suitable for rate studies. Herein, we report the synthesis, by the use of bBCB‐diCl, of relatively low MW (M _n < 3000 g mol^?1) allyl‐telechelic polyisobutylene (PIB) used for the synthesis of PIB‐based polyurethanes and that of relatively high MW (M _n > 30,000) living PIB telechelics for the synthesis of thermoplastic elastomers. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55 , 3716–3724     

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.     

Low-temperature, solution processing of TiO2 thin films and fabrication of multilayer dielectric optical elements

High-quality TiO₂ thin films have been deposited from aqueous titanium-peroxo solutions via spin coating. The effects of precursor solution pH on the crystallization behavior, morphology, density, and refractive index of the films are reported. From X-ray diffraction measurements, the amorphous as-deposited films are found to crystallize in the anatase phase at 250 °C. Surface and cross-section SEM images reveal that films deposited from an acidic precursor are more uniform and denser than those deposited from a basic precursor. X-ray reflectivity measurements show that films with smooth surfaces and high densities (up to 87% of single-crystal anatase) can be produced at temperatures as low as 300 °C. Measured densities are consistent with high refractive indices at 633 nm of 2.24 and 2.11 for films derived from acidic and basic precursors, respectively. The uniformity and dense nature of the films have allowed fabrication of multilayer dielectric optical elements with thermal processing at only 300 °C. The distributed Bragg reflector with four bilayers exhibits a reflectance of 92% and a stop band width of 150 nm. The optical microcavity has a quality factor of 20. The optical properties of all elements agree well with theoretical models, indicating good optical quality. Use of the precursor chemistry for direct photopatterning of TiO₂ films without a polymer resist is also demonstrated.