Solitons generated by self-organization in bismuth germanium oxide single crystals during the interaction with laser beam

We present here the experimental, theoretical, and numerical investigations of Kerr solitons generated by self-organization in black and yellow high quality bismuth germanium oxide (Bi₁₂GeO₂₀) single crystals. A picosecond laser beam of increasing power induces competing cubic and quintic nonlinearities. The numerical evolution of two-dimensional complex cubic-quintic nonlinear Schrödinger equation with measured values of nonlinearities shows the compensation of diffraction by competing cubic and quintic nonlinearities of opposite sign, i.e., the self-generation and stable propagation of solitons. Experiments as well as numerical simulations show higher nonlinearity in the black Bi₁₂GeO₂₀ than in the more transparent yellow one.     

Purified oxygenand nitrogen-modified multi-walled carbon nanotubes as metal-free catalysts for selective olefin hydrogenation

Oxygen-and nitrogen-functionalized carbon nanotubes (OCNTs and NCNTs) were applied as metal-free catalysts in selective olefin hydrogenation. A series of NCNTs was synthesized by NH3 post-treatment of OCNTs. Temperature-programmed desorption, N2 physisorption, Raman spectroscopy, high-resolution transmission electron microscopy and X-ray photoelectron spectroscopy were employed to characterize the surface properties of OCNTs and NCNTs, aiming at a detailed analysis of the type and amount of oxygenand nitrogen-containing groups as well as surface defects. The gas-phase treatments applied for oxygen and nitrogen functionalization at elevated temperatures up to 600 C led to the increase of surface defects, but did not cause structural damages in the bulk. NCNTs showed a clearly higher activity than the pristine CNTs and OCNTs in the hydrogenation of 1,5-cyclooctadiene, and also the selectivity to cyclooctene was higher. The favorable catalytic properties are ascribed to the nitrogen-containing surface functional groups as well as surface defects related to nitrogen species. In contrast, oxygen-containing surface groups and the surface defects caused by oxygen species did not show clear contribution to the hydrogenation catalysis.     

An ω‐categorical structure with amenable automorphism group

We analyse ω‐categorical precompact expansions of particular ω‐categorical structures from the viewpoint of amenability of their automorphism groups.     

Development of a high-speed spectrophotometer for transient measurement of pulverized-coal flame radiation emission

A high-speed spectrophotometer system was developed for the transient measurement of pulverized-coal flame radiation. The system is a grating spectrograph with a single detector instead of a detector array. The position of the four-sided rotatable mirror determines the wavelength of the measured spectral radiation intensity, and the plane grating is mounted in a new arrangement. The system allows repeated measurement of radiation intensity spectra at wavelengths of 2.4–4.0 μm within a period of 1 or less. A desktop combustion system with the ability to vary parameters influencing the combustion of pulverized coal has been designed and assembled.

Experiments performed include steady-state measurement of radiation from a constant-intensity light source and transient measurement of radiation from a pulverized-coal flame.

Preliminary measurements showed that this spectrophotometer is capable of obtaining the desired measurements. Transient measurement of the flame radiation of pulverized coal performed on samples of Yugoslav pulverized coals produced data that comply well with results of other authors.     

Depolarised Rayleigh light scattering in argon layer confined between graphite plains: MD simulation

The interaction-induced light scattering many-body correlation functions and their spectra in a thin argon layer located between two parallel graphite walls have been investigated by molecular dynamics simulation method. The calculations have been performed for three different distances between graphite plates. Our simulations show the increased intensity of the interaction-induced light scattering spectra at low frequencies for argon atoms in confined space, in comparison to the bulk (unconfined) sample. Moreover, we show a substantial dependence of the interaction-induced light scattering correlation functions of argon on the distances between graphite walls, that is, on the density of argon layer. The mean square displacement and related diffusion coefficient of argon atom in the confined space has been also investigated. Moreover, the structural feature of the thin layer has been studied by calculating the argon density profile, perpendicular to the graphite walls. An interesting observation is the development of a fluid phase in the innermost region of the confined argon layer.     

Direct observation of the substitution effects on the hydrogen bridge dynamics in selected Schiff bases--a comparative molecular dynamics study

We have studied substituent effects on the properties of the intramolecular hydrogen bond of some ortho-hydroxy Schiff bases using density functional theory (DFT) based first-principle molecular dynamics (FPMD) and path integral molecular dynamics. The studied compounds possess a strong intramolecular hydrogen bond (r((O???N)) ≤ 2.6 A?), which can be tuned by substitution to either (i) enhance the basicity of the acceptor moiety by induction effects or (ii) decrease the hydrogen bond length through steric repulsion. DFT calculations and FPMD were employed to investigate structural and dynamical properties of the selected molecules, while quantum effects on the structural properties were assessed using path integral FPMD. The simulations were performed in vacuo and in the solid state to study the influence of the environment on the hydrogen bond and spectroscopic properties. We give computational support to the suggestion that induction effects are less effective to tune the intramolecular hydrogen bond properties of the discussed ortho-hydroxy Schiff bases than the steric or the environmental effects.     

Synthesis and binding ability of mono- and tetrasubstituted aminophosphonate Zn-tetraarylporphyrins towards N- and O-containing organic substrates

The 1,6-addition of mono- and tetra-amino 5,10,15,20-tetraphenylporphyrins with dimethyl-(3,5-di-tert-butyl-4-oxocyclohexa-2,5-dienylidenemethyl)phosphonate leads to the corresponding mono- and tetrasubstituted aminophosphonate porphyrin derivatives. The binding ability of their Zn(II)-complexes towards 1,4-diazabicyclo[2,2,2]octane, imidazole, 4-(1H-imidazole-1-yl)benzyl alcohol and 4-(1H-imidazole-1-ylmethyl)benzyl alcohol in toluene was investigated by spectrophotometric and ¹H NMR titration. It has been determined that the monosubstituted Zn-tetraarylporphyrin is involved in a two-point selective binding of 4-(1H-imidazole-1-ylmethyl)benzyl alcohol. Taking into account the fact that this binding is accompanied by a clear and easily identifiable response in the UV–vis spectra of the reaction mixture, this metalloporphyrin could be considered as a molecular optical sensing device for selected bidentate N- and O-containing substrates.     

Multi-channel transformations of 1,3-diarylpropynones under superelectrophilic activation conditions: concurrence of intra- and intermolecular reactions. Experimental and theoretical study

1,3-Diarypropynones undergo concurrent multi-channel transformations in Bronsted (FSO₃H, TfOH) and Bronsted–Lewis (HF–SbF₅, TfOH-SbF₅) superacids, leading intramolecularly to 3-arylindenones, or intermolecularly to 1,3,3-triarylpropenones, and dimeric structures. The outcome depends on the electronic donor-acceptor properties of the substituents in the aromatic rings of the 1,3-diarylpropynones, and on the added aromatic external π-nucleophiles. The orbital energies, atom charges, orbital contributions, and global electrophilicity indices of the cationic intermediates have been calculated by DFT methods to explain these transformations.     

Option Pricing in Subdiffusive Bachelier Model

The earliest model of stock prices based on Brownian diffusion is the Bachelier model. In this paper we propose an extension of the Bachelier model, which reflects the subdiffusive nature of the underlying asset dynamics. The subdiffusive property is manifested by the random (infinitely divisible) periods of time, during which the asset price does not change. We introduce a subdiffusive arithmetic Brownian motion as a model of stock prices with such characteristics. The structure of this process agrees with two-stage scenario underlying the anomalous diffusion mechanism, in which trapping random events are superimposed on the Langevin dynamics. We find the corresponding fractional Fokker-Planck equation governing the probability density function of the introduced process. We construct the corresponding martingale measure and show that the model is incomplete. We derive the formulas for European put and call option prices. We describe explicit algorithms and present some Monte-Carlo simulations for the particular cases of α-stable and tempered α-stable distributions of waiting times.