Thermal and acoustic effects in optical phase conjugation in Rhodamine 6G solutions with nanosecond pulses

Thermally induced phase conjugation by degenerate four-wave mixing in solutions of Rhodamine 6G in ethanol in the weak absorption region, low-reflectivity regime, and nonosecond time domain is reported. Evidence of oscillatory acoustic modes in the nonlinear medium is presented and existing theories are shown to explain satisfactorily the experimental results.     

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.     

Ablation of poly(methyl methacrylate) and poly(2-hydroxyethyl methacrylate) by 308, 222 and 193 nm excimer-laser radiation

Data on the ablation of Poly(Methyl MetAcylate) (PMMA) and Poly(2-Hydroxyethyl MetAcylate) (PHEMA) with 0%, 1% and 20% of Ethylene Glycol DiMethAcrylate (EGDMA) as crosslinking monomer by 193, 222 and 308 nm laser radiation are presented. Direct photoetching of PMMA at 308 nm is demonstrated for laser fluences ranging from 2 to 18 J/cm². The ablation rate of PHEMA is lower than the corresponding to PMMA and decreases when the amount of EGDMA increases. The determination of the absorbed energy density required to initiate significant ablation suggests that the photoetching mechanism is similar for all the polymers studied and is a function of the irradiation wavelength. The Beer-Lambert law, the Srinivasan, Smrtic and Babu (SSB) theory and the kinetic model of the moving interface are used to analyze the experimental results. It is shown that only the moving interface theory fits well the etch rate for all the selected polymers at the three radiation wavelengths.     

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.