Theory of spin-peierls transitions in chains of exchange clusters

A theoretical approach to the analysis of magnetostructural phase transitions of chain polymeric heterospin complexes is suggested. The approach is based on a model of the spin-Peierls transition in chains of exchange clusters. The chain elasticity parameter is found to be a main factor determining the order of phase transition.     

Option Pricing Under Jump-Diffusion Processes with Regime Switching

We study an incomplete market model, based on jump-diffusion processes with parameters that are switched at random times. The set of equivalent martingale measures is determined. An analogue of the fundamental equation for the option price is derived. In the case of the two-state hidden Markov process we obtain explicit formulae for the option prices. Furthermore, we numerically compare the results corresponding to different equivalent martingale measures.     

Efficient synthetic route toward biologically active γ-carboline derivatives

An efficient and short route was established for the synthesis of anti-bovine viral diarrhea virus agents, namely 4-methyl-γ-carboline (SK4M) 1, 3-methyl-γ-carboline (SK3M) 2, 5-methyl-γ-carboline (SK5M) 3, and a new γ-carboline derivative 4, using thermal electrocyclization reaction as a key step. The evaluation of cytotoxicity of compound 4 against human cervical cancer cell line HeLa and leukemic cell line HL-60 furnished CC₅₀ value of 19.5 and 18.8 µM respectively.     

Mixed Convection in a Ventilated Cavity Filled with a Triangular Porous Layer

Accurate prediction of the macroscopic flow parameters needed to describe flow in porous media relies on a good knowledge of flow field distribution at a much smaller scale—in the pore spaces. The extent of the inertial effect in the pore spaces cannot be underestimated yet is often ignored in large-scale simulations of fluid flow. We present a multiscale method for solving Oseen’s approximation of incompressible flow in the pore spaces amid non-periodic grain patterns. The method is based on the multiscale finite element method [MsFEM Hou and Wu in J Comput Phys 134:169–189, 1997)] and is built in the vein of Crouzeix and Raviart elements (Crouzeix and Raviart in Math Model Numer Anal 7:33–75, 1973). Simulations of inertial flow in highly non-periodic settings are conducted and presented. Convergence studies in terms of numerical errors relative to the reference solution are given to demonstrate the accuracy of our method. The weakly enforced continuity across coarse element edges is shown to maintain accurate solutions in the vicinity of the grains without the need for any oversampling methods. The penalisation method is employed to allow a complicated grain pattern to be modelled using a simple Cartesian mesh. This work is a stepping stone towards solving the more complicated Navier–Stokes equations with a nonlinear inertial term.     

Two-Dimensional Topological Strings Revisited

The topological string of the type A with a two-dimensional target space is studied, an explicit formula for the string partition function is found and the target space field theory reproducing this partition function is proposed. This field theory has an infinite set of additional deformations overlooked by the standard definition of the topological string. It can be in turn coupled to gravity, thereby realizing the “worldsheets for worldsheets” idea. We also exhibit the wave function nature of the string partition function and suggest a new relation to quantum integrable systems.     

Correlation between properties of a solid sample and laser-induced plasma parameters

To investigate the influence of mechanical properties of a solid sample on the laser-induced plasma parameters (temperature and mass ablated) a number of aluminum–lithium alloys and lithium ferrites with different microstructure and composition have been studied. The specific approach to estimate excitation temperature for low-resolution emission spectra has been developed. The main limitations of this approach were discussed on the basis of comparison with the energy width of several multiplets. Overall uncertainties for temperature calculation were evaluated by taking into account the accuracy of Einstein's coefficients and errors of the proposed multiplets method. The temporal evolution of laser plasma during the evaporation of these materials was studied. Extremely high value of the Li I excitation temperature has been estimated to be T > 10⁵ K for the annealed ferrite ablation, in contrast to the temperature T  1.5 · 10⁴ K for non-annealed ferrite. Only for ablation of annealed ferrite the Li II emission line at 548.4 nm was observed. It means that this laser-induced plasma was the hottest. In the case of alloys, the temperature calculated by using Li I transitions was proportional to the microhardness of the solid samples. The negative correlation between crater volume/opto-acoustic signal and alloy microhardness was observed. At the first pulses the mechanical properties of the alloys didn't correlate with the ablated mass, while the maximal correlation coefficients were observed after ablation by 10 or 50 consequent laser pulses.     

Reduction of the matrix influence on analytical signal in laser-enhanced ionization spectrometry with laser sampling

The novel approach using a slope of correlation line (laser-enhanced ionization of lithium versus laser-induced plasma emission of aluminum) as analytical signal was proposed for reduction of matrix interferences in laser-enhanced ionization spectrometric determination of Li with laser sampling.     

Microfluorescence analysis of nanostructuring inhomogeneity in optical fibers with embedded gallium oxide nanocrystals

A spectroscopic protocol is proposed to implement confocal microfluorescence imaging to the analysis of microinhomogeneity in the nanocrystallization of the core of fibers belonging to a new kind of broadband fiber amplifier based on glass with embedded nanocrystals. Nanocrystallization, crucial for achieving an adequate light emission efficiency of transition metal ions in these materials, has to be as homogeneous as possible in the fiber to assure optical amplification. This requirement calls for a sensitive method for monitoring nanostructuring in oxide glasses. Here we show that mapping microfluorescence excited at 633 nm by a He-Ne laser may give a useful tool in this regard, thanks to quasi-resonant excitation of coordination defects typical of germanosilicate materials, such as nonbridging oxygens and charged Ge-O-Ge sites, whose fluorescence are shown to undergo spectral modifications when nanocrystals form into the glass. The method has been positively checked on prototypes of optical fibers--preventively characterized by means of scanning electron microscopy and energy dispersive spectroscopy--fabricated from preforms of Ni-doped Li?O-Na?O-Sb?O?-Ga?O?-GeO?-SiO? glass in silica cladding and subjected to heat treatment to activate gallium oxide nanocrystal growth. The method indeed enables not only the mapping of the crystallization degree but also the identification of drawing-induced defects in the fiber cladding.     

An option pricing model based on jump telegraph processes

A new class of financial market models is developed. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets may admit an arbitrage opportunity, the model under consideration is arbitrage-free and complete if directions of jumps in stock prices are in a certain correspondence with their velocity and interest rate behaviour. An analog of the Black-Scholes fundamental differential equation is derived, but, in contrast with the Black-Scholes model, this equation is hyperbolic. Explicit formulas for prices of European options are obtained using perfect and quantile hedging. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)