On Properties of Rectangular Hyperbolas

This paper improves an old theorem about a rectangular hyperbola : its centre lies on the pedal circle of any point on with respect to any triangle inscribed in . We also prove that an analogous result holds for Cevian circles. These results are used to obtain new characterisations of the Feuerbach, Jarabek, and Kiepert hyperbolas of a triangle.     

On the efficiency of small-angle Čerenkov second harmonic generation in optical waveguides

It is well known that in the non-depleted pump approximation, the efficiency of a second harmonic generation (SHG) of a guided mode in a non-linear optical waveguide increases quadratically with the interaction length (P ₂ L ²), and linearly (P ₂ L) in the erenkov regime. The efficiency of the erenkov SHG in the waveguide with a non-linear substrate and linear guiding layer is known to be strongly peaked at a particular pump wavelength and a particular waveguide thickness, with the erenkov angle approaching zero. The known theory predicts an infinite efficiency value at the peak, however. In this contribution, a simple integral expression for the SHG efficiency in the erenkov regime is derived. For large erenkov angles and interaction lengths it yields the expected P ₂ L dependence, while in the limit of small erenkov angles the dependence is found to have the form of P L ^3/2, possessing also a finite value at the efficiency peak. The condition determining the accurate position of the efficiency peak in the waveguide thickness–pump wavelength plane is given, too.     

Spectral study on the molecular orientation of a tetracationic porphyrin dye on the surface of layered silicates

Tetracationic porphyrin dyes TMPyP and ZnPyP were intercalated into hydrophobized layered silicate films of three smectites. The smectites represented the layered silicate specimens of high (Fluorohectorite, Corning; FHT), medium (Kunipia F montmorillonite; KF) and low layer charge (Laponite, Laporte; LAP). The molecular orientations of the dye cations were studied by means of linearly-polarized ultraviolet-visible (UV-VIS) spectroscopy. The spectral analysis and consequent calculations of tilting angles of the transition moments at the wavelengths of Soret band transitions were in the range of 25°-35°. The determined angles indicated molecular orientation of the dye cations being almost parallel to the surface of the silicates. Slightly higher values (above 35°), determined for a FHT film, indicated either a slightly tilted orientation of the dye cations or the change of molecular comformation after the intercalation of the dye. Presented at 5-th International Conference Solid State Surfaces and Interfaces, November 19–24, 2006, Smolenice Castle, Slovakia     

DC conductivity of amorphous germanium

A critical review of the phonon-assisted hopping theory of the dc conductivity σ is given. It is argued that the current theories either contain uncontrollable approximations, or they yield the result of the same order of magnitude as the approximations used or they may also lead to temperature dependence of σ other than that described by the Mott law. For the simplest usually accepted model of amorphous Ge (a-Ge), the low-temperature asymptote of σ is obtained in the form of a power law. In the experimental part of the work, careful measurements from 300 down to 8 K are reported, both for the pure and the gold-doped a-Ge films. Since the results of such measurements yield a straight line in a wide interval of temperature both in the log σ versus $\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>4</mtext>}}$ and log σ versus log T scale, the power law appears to be equally well justified as the Mott law, both from the point of view of theory and that of experiment.     

Activity of polymer supported cobalt catalyst in the Bray-Liebhafsky oscillator

The infuence of poly-4-vinylpyridine-co-divinylbenzene-Co²⁺ catalyst on the Bray-Liebhafsky (BL) oscillator used as the matrix for establishing catalyst’s activity was analyzed. The addition of the catalyst do not change the dynamics of the reaction in the BL matrix, but the periods of the oscillatory evolution as well as the preoscillatory period (τ₁) and the duration from the beginning of the reaction to the end of the oscillatory state (τ_end). All experimental results are simulated satisfactory. The article is published in the original.     

General variable neighborhood search for the continuous optimization

We suggest a new heuristic for solving unconstrained continuous optimization problems. It is based on a generalized version of the variable neighborhood search metaheuristic. Different neighborhoods and distributions, induced from different metrics are ranked and used to get random points in the shaking step. We also propose VNS for solving constrained optimization problems. The constraints are handled using exterior point penalty functions within an algorithm that combines sequential and exact penalty transformations. The extensive computer analysis that includes the comparison with genetic algorithm and some other approaches on standard test functions are given. With our approach we obtain encouraging results.     

Enantioseparations of non-benzenoid and oligo-Tröger’s bases by HPLC on Whelk O1 column

The separation of enantiomers of several ‘bis- and tris-Tröger’s bases’ by HPLC on commercially available chiral stationary phase Whelk O1 is described for the first time. The observed structure–enantioselectivity relationships are in agreement with the previously established molecular recognition model. For all ‘bis- and tris-Tröger’s bases’ studied, satisfactory to excellent enantioselectivities were observed.     

Two-phase formation of nitrophenols at the radiolysis of nitrobenzene-water emulsions

Two-phase additivity rule for radiation yields of p-nitrophenol, m-nitrophenol and p-nitrosophenol has been demonstrated. The data of partial radiation yields indicated that the nitrobenzene phase is by several times more reactive than a water phase /H₂O, 3M HNO₃ or 1.5M H₂SO₄/ in respect of nitrophenols formation.