Relative Oscillation Theory for Dirac Operators

We develop relative oscillation theory for one-dimensional Dirac operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the number of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established. As an application we extend a result by K.M. Schmidt on the finiteness/infiniteness of the number of eigenvalues in essential spectral gaps of perturbed periodic Dirac operators.Comment: 13 page

Trigonometric version of quantum-classical duality in integrable systems

We extend the quantum-classical duality to the trigonometric (hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars-Schneider model and the inhomogeneous twisted XXZ spin chain on N sites. Similarly to the rational version, the spin chain data fixes a certain Lagrangian submanifold in the phase space of the classical integrable system. The inhomogeneity parameters are equal to the coordinates of particles while the velocities of classical particles are proportional to the eigenvalues of the spin chain Hamiltonians (residues of the properly normalized transfer matrix). In the rational version of the duality, the action variables of the Ruijsenaars-Schneider model are equal to the twist parameters with some multiplicities defined by quantum (occupation) numbers. In contrast to the rational version, in the trigonometric case there is a splitting of the spectrum of action variables (eigenvalues of the classical Lax matrix). The limit corresponding to the classical Calogero-Sutherland system and quantum trigonometric Gaudin model is also described as well as the XX limit to free fermions.Comment: 14 page

Encapsulation of metallic iron magnetic nanoparticles by polyacrylamide in water suspensions

Received: 28.06.2017; accepted: 24.07.2017; published: 20.10.2017.Theoretical consideration of the factors of the stability of metallic iron magnetic nanoparticles (MNPs) in water suspensions was done using extended DLVO (Derjaguin-Landau-Verwey-Overbeek) approach based on the balance among Van der Waals, electrostatic, magnetic and steric interactions. Magnetic and steric interactions dominate over other in suspensions of Fe MNPs. To test the theory Fe MNPs with average diameter 84 nm were synthesized by electrical explosion of wire and encapsulated by polyacrylamide in water suspension to provide steric repulsion. It was shown that encapsulation resulted in the efficient diminishing of the aggregation of metallic iron MNPs in water

Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function

We develop an analog of classical oscillation theory for Sturm-Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the finiteness of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established.Comment: 26 page

Enhanced 2D plotting method for scanning probe microscopy imaging

An enhanced 2D plotting method for scanning probe microscopy imaging implementing a gradient-based value mapping for pseudocolor images and its application to studies of epitaxial layer surface morphology is presented. It is demonstrated that this method is capable of revealing the finest features on growth surfaces. Presence of elementary growth steps on the surface of flat-topped hillocks found on Hg₀.₈Cd₀.₂Te LPE-grown epitaxial layers, examples of cooperative effects of screw dislocations on PbTe and Hg₁₋xCdxTe epilayer growth as well as atypical surface morphology of PbTe epilayers are discussed

Studies of changes in the structure of vermiculite as a filler of building materials by the method of electron microscopy

In this article, construction materials are considered, which are used as a lightweight aggregate for concretes and mortars as well as for thermal insulation designs. Particular attention is paid to materials based on expanded vermiculite. The methods of using vermiculite in construction are analyzed. The study is carried out by electron microscopy of vermiculite crystals burnt traditionally and treated with chemical solutions (fired at 400 ° C). Based on the above study, the developed method for baking vermiculite can be considered the most suitable for technological parameters and operational requirements for use in the construction industry

Pesticides reduce regional biodiversity of stream invertebrates

The biodiversity crisis is one of the greatest challenges facing humanity, but our understanding of the drivers remains limited. Thus, after decades of studies and regulation efforts, it remains unknown whether to what degree and at what concentrations modern agricultural pesticides cause regional-scale species losses. We analyzed the effects of pesticides on the regional taxa richness of stream invertebrates in Europe (Germany and France) and Australia (southern Victoria). Pesticides caused statistically significant effects on both the species and family richness in both regions, with losses in taxa up to 42% of the recorded taxonomic pools. Furthermore, the effects in Europe were detected at concentrations that current legislation considers environmentally protective. Thus, the current ecological risk assessment of pesticides falls short of protecting biodiversity, and new approaches linking ecology and ecotoxicology are needed

Iron oxide nanoparticles fabricated by electric explosion of wire: Focus on magnetic nanofluids

Nanoparticles of iron oxides (MNPs) were prepared using the electric explosion of wire technique (EEW). The main focus was on the fabrication of de-aggregated spherical nanoparticles with a narrow size distribution. According to XRD the major crystalline phase was magnetite with an average diameter of MNPs, depending on the fraction. Further separation of air-dry EEW nanoparticles was performed in aqueous suspensions. In order to provide the stability of magnetite suspension in water, we found the optimum concentration of the electrostatic stabilizer (sodium citrate and optimum pH level) based on zeta-potential measurements. The stable suspensions still contained a substantial fraction of aggregates which were disintegrated by the excessive ultrasound treatment. The separation of the large particles out of the suspension was performed by centrifuging. The structural features, magnetic properties and microwave absorption of MNPs and their aqueous solutions confirm that we were able to obtain an ensemble in which the magnetic contributions come from the spherical MNPs. The particle size distribution in fractionated samples was narrow and they showed a similar behaviour to that expected of the superparamagnetic ensemble. Maximum obtained concentration was as high as 5 % of magnetic material (by weight). Designed assembly of de-aggregated nanoparticles is an example of on-purpose developed magnetic nanofluid. Copyright © 2012 Author(s)

Wpływ cyfryzacji na międzynarodowe bezpieczeństwo finansowe w warunkach zrównoważonego rozwoju

The implementation of digital technologies in financial security allows you to automate and accelerate the processes of ensuring security. Electronic monitoring and analytics systems can quickly identify suspicious transactions and vulnerabilities, facilitating a prompt response to threats. That is why the topic of the current research is relevant and timely. The purpose of the study is to present the main components of the digitization process of international financial security in the context of sustainable development, with an emphasis on the formation of a comprehensive methodological approach to the analysis of the issue. The methods used in this research include the observation method to identify the main features of the digitization process of international financial security, the forecasting method to identify the main trends in the development of digital security, and the methods of analysis, synthesis, deduction, and induction to visually present the results of the research. Additionally, the graphic method is utilized to display a comprehensive methodological approach and illustrate the research results. During the course of the research, the basic components of the process of digitizing financial security were analysed, and an assessment of strengths and weaknesses was conducted. Additionally, opportunities and threats related to the process of digitizing international financial security were determined. The priority areas for the digitization of international financial security in the context of sustainable development have been identified. The main results of the study include the development of a comprehensive methodological approach to the process of digitalizing international financial security under conditions of sustainable development. The study also yields the following conclusions regarding the development of digitization: the utilization of analytical tools and artificial intelligence in financial security improves the accuracy of detecting fraud, money laundering, and other financial crimes; digital technologies facilitate access to financial services in remote and less developed regions; digital technologies enable cost optimization for ensuring financial security through automation and efficient resource utilization.Wdrożenie technologii cyfrowych w kontekście bezpieczeństwa finansowego pozwala zautomatyzować i przyspieszyć procesy zapewnienia bezpieczeństwa. Elektroniczne systemy monitorowania i analizy potrafią szybko identyfikować podejrzane transakcje i luki, ułatwiając szybką reakcję na zagrożenia. Dlatego tematyka artykułu  jest istotna i aktualna. Celem jest przedstawienie głównych elementów procesu cyfryzacji międzynarodowego bezpieczeństwa finansowego w kontekście zrównoważonego rozwoju, z naciskiem na ukształtowanie kompleksowego podejścia metodologicznego do analizy. W artykule wykorzystano następujące metody:  obserwacyjną, służącą identyfikacji głównych cech procesu cyfryzacji międzynarodowego bezpieczeństwa finansowego, metodę prognostyczną służącą identyfikacji głównych trendów rozwoju bezpieczeństwa cyfrowego oraz metody analizy, syntezy, dedukcji oraz indukcja wizualnej prezentacji wyników badań. Dodatkowo, metoda graficzna służy zobrazowaniu kompleksowego podejścia metodologicznego i zilustrowaniu wyników badań. W toku badań dokonano analizy podstawowych elementów procesu cyfryzacji bezpieczeństwa finansowego oraz dokonano oceny mocnych i słabych stron. Dodatkowo określono szanse i zagrożenia związane z procesem cyfryzacji międzynarodowego bezpieczeństwa finansowego. Zidentyfikowano priorytetowe obszary cyfryzacji międzynarodowego bezpieczeństwa finansowego w kontekście zrównoważonego rozwoju. Do głównych wyników badania należy opracowanie kompleksowego podejścia metodologicznego do procesu cyfryzacji międzynarodowego bezpieczeństwa finansowego w warunkach zrównoważonego rozwoju. Z badania wynikają także następujące wnioski dotyczące rozwoju cyfryzacji: wykorzystanie narzędzi analitycznych i sztucznej inteligencji w bezpieczeństwie finansowym poprawia skuteczność wykrywania oszustw, prania pieniędzy i innych przestępstw finansowych; technologie cyfrowe ułatwiają dostęp do usług finansowych w odległych i słabiej rozwiniętych regionach; technologie cyfrowe umożliwiają optymalizację kosztów w celu zapewnienia bezpieczeństwa finansowego poprzez automatyzację i efektywne wykorzystanie zasobów