Symmetric invariant cocycles on the duals of q-deformations

We prove that for q∈C^? not a nontrivial root of unity any symmetric invariant 2-cocycle for a completion of Uqg is the coboundary of a central element. Equivalently, a Drinfeld twist relating the coproducts on completions of Uqg and Ug is unique up to coboundary of a central element. As an application we show that the spectral triple we defined in an earlier paper for the q-deformation of a simply connected semisimple compact Lie group G does not depend on any choices up to unitary equivalence.     

Net Spaces and Boundedness of Integral Operators

In this paper we introduce new functional spaces which we call net spaces. Using their properties, necessary and sufficient conditions for the integral operators to be of strong or weak type are obtained. Estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.     

Notes on the Kazhdan–Lusztig Theorem on Equivalence of the Drinfeld Category and the Category of $\boldsymbol{U}_{\!\boldsymbol q}{\boldsymbol {\mathfrak g}}$-Modules

We discuss the proof of Kazhdan and Lusztig of the equivalence of the Drinfeld category \({\mathcal D}({\mathfrak g},\hbar)\) of \({\mathfrak g}\)-modules and the category of finite dimensional \(U_q{\mathfrak g}\)-modules, \(q=e^{\pi i\hbar}\), for \(\hbar\in{\mathbb C}\setminus{\mathbb Q}^*\). Aiming at operator algebraists the result is formulated as the existence for each \(\hbar\in i{\mathbb R}\) of a normalized unitary 2-cochain \({\mathcal F}\) on the dual \(\hat G\) of a compact simple Lie group G such that the convolution algebra of G with the coproduct twisted by \({\mathcal F}\) is *-isomorphic to the convolution algebra of the q-deformation G _q of G, while the coboundary of \({\mathcal F}^{-1}\) coincides with Drinfeld’s KZ-associator defined via monodromy of the Knizhnik–Zamolodchikov equations.     

Extended Lagrangian approach for the defocusing nonlinear Schrödinger equation

We study the defocusing nonlinear Schrödinger (NLS) equation written in hydrodynamic form through the Madelung transform. From the mathematical point of view, the hydrodynamic form can be seen as the Euler–Lagrange equations for a Lagrangian submitted to a differential constraint corresponding to the mass conservation law. The dispersive nature of the NLS equation poses some major numerical challenges. The idea is to introduce a two‐parameter family of extended Lagrangians, depending on a greater number of variables, whose Euler–Lagrange equations are hyperbolic and accurately approximate NLS equation in a certain limit. The corresponding hyperbolic equations are studied and solved numerically using Godunov‐type methods. Comparison of exact and asymptotic solutions to the one‐dimensional cubic NLS equation (“gray” solitons and dispersive shocks) and the corresponding numerical solutions to the extended system was performed. A very good accuracy of such a hyperbolic approximation was observed.     

Rosin Derivatives as a Platform for the Antiviral Drug Design

The increased complexity due to the emergence and rapid spread of new viral infections prompts researchers to search for potential antiviral and protective agents for mucous membranes among various natural objects, for example, plant raw materials, their individual components, as well as the products of their chemical modification. Due to their structure, resin acids are valuable raw materials of natural origin to synthesize various bioactive substances. Therefore, the purpose of this study was to confirm the possibility of using resin acid derivatives for the drug design. As a result, we studied the cytotoxicity and biological activity of resin acid derivatives. It was shown that a slight decrease in the viral load in the supernatants was observed upon stimulation of cells (II) compared with the control. When using PASS-online modeling (Prediction of Activity Spectra for Substances), the prediction of the biological activity spectrum showed that compound (I) is capable of exhibiting antiviral activity against the influenza virus. The use of the SWISS-ADME webserver to reveal the drug-like properties of compounds did not directly indicate the presence of antiviral activity. These results indicate the potential of resin acid derivatives as a starting point for extensive research in the study of biological activity.     

Automatized System for Measuring the Surface Density of Current Carriers and Electrical Permittivity of Conducting Materials

An automatised system for analyzing the electron topography of a conducting surface (semiconductors, metals, ferrites or conductor ceramics) is represented. The function of the system is based on the recently observed surface photo-charge effect. The investigation is express and contactless. The system allows visualisations of different formations on the surface such as defects, ion-implanted areas, etc. on a computer screen. The structure of the system is described. The results from investigations with GaP and Cu are reported.     

Contactless Spectroscopy of Deep Levels in Semiconducting Materials: Gaas

Abstract

The surface photo voltage (SPV) and photocurrent (PC) transients as a result of the excitation by the short high-intensity light pulses from semiconductor's intrinsic absorption spectral region are investigated in semi-insulating GaAs. It is shown that the mathematical convolution of SPV transients and arbitrary form double-pulse integrator (lock-in, double-boxcar) in a wide temperature range allows to receive the deep-level (DL) spectrum without the need to form electrical contacts to the crystal investigated. The use of such a procedure while scanning the crystal surface with a light spot at a temperature, corresponding to some DL maximum in the spectrum, makes possible the con tactless determination of this DL density distribution profile along the scanning direction.     

Preparation of a macrocrystalline pressure calibrant SrB4O7:Sm 2+ suitable for the HP-HT powder diffraction

A new simplified synthesis of monocrystalline chips of SrB₄O₇: Sm²⁺ pressure calibrant, well-suited for the diamond anvil cell (DAC) powder diffraction experiments, is proposed. It consists of ordinary solid-state synthesis of fine-grained SrB₄O₇: Sm²⁺ and subsequent annealing near melting temperature. The obtained material was characterized and tested in HP-HT DAC experiment.     

Surface modes in metal–insulator composites with strong interaction of metal particles

We theoretically examine plasmonic resonance excited between two close metallic grains embedded into a dielectric matrix. The grains sizes are assumed to be much less than the wavelength of the electromagnetic wave in the dielectric medium and the grain’s separation is assumed to be much smaller than the grains sizes. A qualitative scheme is developed that enables one to estimate frequency of the plasmonic resonance and value of the field enhancement inside the gap. Our general arguments are confirmed by rigorous analytic solution of the problem for simplest geometry—two identical spherical grains.