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.     

Numerical study of chaotic oscillations in the electron beam with virtual cathode in the external non-uniform magnetic fields

In this Letter the results of theoretical investigations of the chaotic microwave oscillator based on the electron beam with a virtual cathode are presented. Nonlinear non-stationary processes in these electron systems are studied by means of numerical analysis of 2.5D model. It was discovered that the non-uniform external magnetic field value controls the dynamical regime of oscillations in the virtual cathode oscillator. The processes of the chaotization of output microwave radiation are described and interpreted from the point of view of the formation and interaction of electron structures (bunches) in the electron beams. The numerical results have shown that the investigated electron system with virtual cathode could be considered as a promising controlled source of wideband chaotic oscillations in the microwave range.     

Quasi-optical ferrite devices for millimeter and submillimeter wave bands

Main features of the development of quasi-optical ferrite devices, using Faraday effect, are considered. Properties of a polarizing divider and a ferrite rotator of a polarization plane are analysed with standpoint of minimum losses. A matching method, based on an utilization of the rotator element in a form of the multilayers ferrite structure, which can be adjusted independently for right-handed and left-handed cyrcularly polarized waves, is suggested. It is shown, that this method allows to obtain a total matching in a quasi-optical transmission line. Results of an investigation of quasi-optical ferrite devices for the oversized round waveguide withH ₁₁ mode are presented.     

Notes on entropic characteristics of quantum channels

One of most important issues in quantum information theory concerns transmission of information through noisy quantum channels. We discuss a few channel characteristics expressed by means of generalized entropies. Such characteristics can often be treated in line with more usual treatment based on the von Neumann entropies. For any channel, we show that the q-average output entropy of degree q ≥ 1 is bounded from above by the q-entropy of the input density matrix. The concavity properties of the (q, s)-entropy exchange are considered. Fano type quantum bounds on the (q, s)-entropy exchange are derived. We also give upper bounds on the map (q, s)-entropies in terms of the output entropy, corresponding to the completely mixed input.     

Cosmological perturbations in SFT inspired non-local scalar field models

We clearly and consistently supersymmetrize the celebrated horizontality condition to derive the off-shell nilpotent and absolutely anticommuting Becchi?CRouet?CStora?CTyutin (BRST) and anti-BRST symmetry transformations for the supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. For the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our system, we consider the present theory on a (1,2)-dimensional supermanifold parameterized by an even (bosonic) variable (??) and a pair of odd (fermionic) variables ?? and $\bar{\theta}$ (with $\theta^{2} = \bar{\theta}^{2} = 0$ , $\theta\bar{\theta}+ \bar{\theta}\theta= 0$ ) of the Grassmann algebra. One of the most important and novel features of our present investigation is the derivation of (anti-)BRST invariant Curci?CFerrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-)BRST transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system. These observations are completely new results for this model.     

Enzyme biosensors based on ion-selective field-effect transistors

The key theoretical principles of the work on ion-selective field-effect transistor connected with their application in bioanalytical practice, some specifics of modern microtechnologies for their creation, and measurement schemes with set-ups are discussed. The achievements in the creation of enzyme biosensors based on ion-selective field-effect transistors and prospects for their application are described in detail.     

Selective halogenation at the pnictogen atom in Lewis-acid/base-stabilised phosphanylboranes and arsanylboranes

The halogenation of Lewis-acid/base-stabilised phosphanylboranes () and arsanylboranes () with CX(4) (X = Cl, Br) leads selectively to the substitution of both protons at the pentel atom and the new compounds [(CO)(5)W(X(2)PBH(2).NMe(3))] (: X = Cl, : X = Br) and [(CO)(5)W(X(2)AsBH(2).NMe(3))] (: X = Cl, : X = Br), respectively, are obtained. The new products were comprehensively characterised by spectroscopic methods and by X-ray crystallography. While compounds and show an antiperiplanar arrangement of the Lewis acid (W(CO)(5)) and the Lewis base (NMe(3)) in the solid state, a synclinal arrangement in and , respectively, was observed. Computational calculations of the optimised antiperiplanar and synclinal geometries of the compounds and in the gas phase slightly favour the antiperiplanar arrangement of the Lewis acid and the Lewis base for both compounds.