Spectral parameter power series method for discontinuous coefficients

Let (a,b) be a finite interval and 1/p, q, r be functions from L1(a,b). We show that a general solution (in the weak sense) of the equation (pu')'+qu = zru on (a,b) can be constructed in terms of power series of the spectral parameter z. The series converge uniformly on [a,b] and the corresponding coefficients are constructed by means of a simple recursive procedure. We use this representation to solve different types of eigenvalue problems. Several numerical tests are discussed

Lattices of quasi-equational theories as congruence lattices of semilattices with operators, Part I

We show that for every quasivariety K of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S,+,0,F). As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found.Comment: Presented on International conference "Order, Algebra and Logics", Vanderbilt University, 12-16 June, 2007 25 pages, 2 figure

An amplitude-phase (Ermakov-Lewis) approach for the Jackiw-Pi model of bilayer graphene

In the context of bilayer graphene we use the simple gauge model of Jackiw and Pi to construct its numerical solutions in powers of the bias potential V according to a general scheme due to Kravchenko. Next, using this numerical solutions, we develop the Ermakov-Lewis approach for the same model. This leads us to numerical calculations of the Lewis-Riesenfeld phases that could be of forthcoming experimental interest for bilayer graphene. We also present a generalization of the Ioffe-Korsch nonlinear Darboux transformationComment: FTC, 11 pp, 5 figure

CRISPR-Cas: an adaptive immunity system in prokaryotes

Most of the archaea and numerous bacteria possess an elaborate system of adaptive immunity to mobile genetic elements known as the CRISPR (clustered regularly interspaced short palindromic repeats)-associated system (CRISPR-Cas), which consists of arrays of short repeats interspersed with unique DNA spacers and adjacent operons encompassing CRISPR-associated (cas) genes with predicted and, in some cases, experimentally validated nuclease, helicase, and polymerase activities. The system functions by integrating fragments of alien DNA between the repeats and employing their transcripts to degrade the DNA of the respective invading elements via an RNA interference-like mechanism. The CRISPR-Cas system is a case of apparent Lamarckian inheritance

The impact of the food embargo on con­sumer preferences and cross-border practices in the Kaliningrad region

The Russian food market has been a fascinating subject for researchers investigating food security risks and ways to mitigate them since the embargo was imposed in 2014. The Kaliningrad region, an exclave of Russia, responded more sensitively to the restrictions than any other territory of the country due to the heavy dependence of its food market on imported finished products and raw materials, as well as the transit from Russia via third countries. This study aims to explore how the consumer preferences of Kaliningraders changed in 2014-2021 under the food embargo. The research also investigates changes in the cross-­border mobility of the region's residents with regard to the practice of shopping for groceries in neighbouring countries. The principal method used in the study is survey research. A survey of 1,019 respondents was conducted in September 2021. Additionally, a comparative analysis of average food prices in the region and neighbouring countries from 2012 to 2019 was carried out based on data from Kaliningradstat and the national statistics services in Poland and Lithuania. The ways to obtain embargoed food were systematised using content analysis of social media, advertising and joint purchase services, travel agency websites, regional news portals and blogs. The study found that rising prices for commodity groups falling under the import ban were the most significant change in the regional food market. As a result, the share of Kaliningrad and Belarusian manufacturers in the regional market basket of consumer goods rose dramatically, as the volume and range of products increased and new manufacturers entered the market. At the same time, the dependence of purchases of "sanctioned" goods on non-material reasons (quality, personal preferences) determined Kaliningraders’ continued commitment to the "old" strategies despite significant restrictions