On reproducing kernels and quantization of states

Quantization of a mechanical system with the phase space a Kähler manifold is studied. It is shown that the calculation of the Feynman path integral for such a system is equivalent to finding the reproducing kernel function. The proposed approach is applied to a scalar massive conformal particle interacting with an external field which is described by deformation of a Hermitian line bundle structure.     

Integrable Hamiltonian systems related to the Hilbert–Schmidt ideal

By the application of the coinduction method as well as the Magri method to the ideal of real Hilbert–Schmidt operators we construct the hierarchies of integrable Hamiltonian systems on Banach Lie–Poisson spaces which consist of such types of operators. We also discuss their algebraic and analytic properties and solve them in dimensions, N=2,3,4$N=2,3,4$.     

Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes

Spatial resonances leading to superlattice hexagonal patterns, known as "black-eyes," and superposition patterns combining stripes and/or spots are studied in a reaction-diffusion model of two interacting Turing modes with different wavelengths. A three-phase oscillatory interlacing hexagonal lattice pattern is also found, and its appearance is attributed to resonance between a Turing mode and its subharmonic.     

Flow injection chemiluminescence determination of the total phenolics levels in plant-derived beverages using soluble manganese(IV)

This study established a flow injection (FI) methodology for the determination of the total phenolic content in plant-derived beverages based on soluble manganese(IV) chemiluminescence (CL) detection. It was found that mixing polyphenols with acidic soluble manganese(IV) in the presence of formaldehyde evoked chemiluminescence. Based on this finding, a new FI-CL method was developed for the estimation of the total content of phenolic compounds (expressed as milligrams of gallic acid equivalent per litre of drink) in a variety of wine, tea and fruit juice samples. The proposed method is sensitive with a detection limit of 0.02 ng mL⁻¹ (gallic acid), offers a wide linear dynamic range (0.5-400 ng mL⁻¹) and high sample throughput (247 samples h⁻¹). The relative standard deviation for 15 measurements was 3.8% for 2 ng mL⁻¹ and 0.45% for 10 ng mL⁻¹ of gallic acid. Analysis of 36 different samples showed that the results obtained by the proposed FI-CL method correlate highly with those obtained by spectrophotometric methods commonly used for the evaluation of the total phenolic/antioxidant level. However, the FI-CL method was found to be far simpler, more rapid and selective, with almost no interference from non-phenolic components of the samples examined.     

Efficient synthesis of the core structure of muraymycin and caprazamycin nucleoside antibiotics based on a stereochemically revised sulfur ylide reaction

The reaction of protected uridine 5′-aldehydes with sulfur ylides has been reinvestigated. Further transformation of the resulting epoxide product provided a compound of which a single crystal for X-ray diffraction was obtained. As a consequence from the elucidated structure, the stereochemical configuration of the epoxide furnished by the sulfur ylide reaction was revised. Based on these results, an efficient synthesis of the core structure of the naturally occurring muraymycin and caprazamycin nucleoside antibiotics was developed.     

Hermitean Oscillator-like Realizations of Classical Algebras and Superalgebras in Hilbert Space with Positive Definite Metric

The hermitean oscillator-like realizations of classical algebras in terms of bosonic and fermionic creation and annihilation operators are given. The hermitean realizations of classical superalgebras using boson-fermion oscillators are explicitely described. The assumption of positive definite metric in a Hilbert space of the oscillators states is exploited. Due to this fact, the realizations of superalgebras in the Hilbert space can be constructed only for: the real orthosymplectic superalgebra osp (N; 2M; R); the unitary compact superalgebra su (N; M); the unitary noncompact one SU(N; K, M); and the quaternionic unitary superalgebra uu_α(N; M; H).     

Bethe Subalgebras in Hecke Algebra and Gaudin models

The generating function for elements of the Bethe subalgebra of the Hecke algebra is constructed as Sklyanin’s transfer-matrix operator for the Hecke chain. We show that in a special classical limit ${q \to 1}$ the Hamiltonians of the Gaudin model can be derived from the transfer-matrix operator of the Hecke chain. We construct a non-local analog of the Gaudin Hamiltonians in the case of the Hecke algebras.     

Dynamic mechanism of photochemical induction of turing superlattices in the chlorine dioxide-iodine-malonic acid reaction-diffusion system

We study the mechanism of development of superlattice Turing structures from photochemically generated hexagonal patterns of spots with wavelengths several times larger than the characteristic wavelength of the Turing patterns that spontaneously develop in the nonilluminated system. Comparison of the experiment with numerical simulations shows that interaction of the photochemical periodic forcing with the Turing instability results in generation of multiple resonant triplets of wave vectors, which are harmonics of the external forcing. Some of these harmonics are situated within the Turing instability band and are therefore able to maintain their amplitude as the system evolves and after illumination ceases, while photochemically generated harmonics outside the Turing band tend to decay.     

A holomorphic field theory

Starting from conformal kinematics we show that the complex Minkowski space as a model of time-space is as good as the real one. A holomorphic field theory is constructed on and it is shown that real field theory is a linear approximation of the holomorphic one.