On automorphism groups of affine surfaces

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic groups. At the same time, they can be studied from the viewpoint of the combinatorial group theory, so we put a special accent on group-theoretical aspects (ind-groups, amalgams, etc.). We provide different approaches to classification, prove certain new results, and attract attention to several open problems.Comment: Proposition 2.10 from the previous version (published in Algebraic Varieties and Automorphism Groups, ASPM 75) deleted. There is a mistake in the proof kindly indicated by J.-P. Furter; the validity of the result remains open. This does not affect the rest of the pape

The constitutional principle of proportionality in foreign and Russian law: a theoretical and practical analysis

O artigo é dedicado a um estudo jurídico comparativo do princípio europeu da proporcionalidade e do método americano de ponderar interesses, suas origens, características comuns e distintivas, fundamentos socioculturais e históricos, a aplicação do princípio da proporcionalidade na ordem jurídica russa. Historicamente, as origens (raízes) do princípio europeu da proporcionalidade remontam à doutrina administrativa-jurídica alemã, e o método americano de ponderação como princípio inicial está associado ao direito privado e só mais tarde foi estendido à esfera do direito público. O artigo avalia o impacto desses princípios na doutrina russa e na prática de aplicação da lei.Objetivo: O objetivo principal do artigo é identificar as características gerais e distintivas do princípio europeu de proporcionalidade e o método americano de equilibrar interesses, a fim de compreender, com base nisso, o modelo jurídico russo para garantir o equilíbrio de interesses públicos e privados.Tarefas: explorar os fundamentos históricos, socioculturais e doutrinários da gênese do princípio europeu da proporcionalidade e do método americano de ponderar interesses; identificar características comuns e especiais características desses métodos; mostrar a influência desses métodos na doutrina russa e na prática da aplicação da lei; comparar o princípio russo de equilíbrio entre interesses públicos e privados com o princípio europeu de proporcionalidade; formular recomendações e sugestões para melhorar as práticas de aplicação da lei na Rússia.Métodos: histórico e jurídico, lógico, formal e jurídico, sistêmico e estrutural, método de pesquisa jurídica intersetorial, método de análise de sistemas.Discussão: o princípio europeu da proporcionalidade e o método americano de ponderar interesses, embora não pertençam a novos fenômenos do pensamento jurídico, no entanto, devido à sua importância fundamental, tanto nos níveis constitucionais quanto em outros setores do desenvolvimento do direito, estão constantemente no centro do campo de visão do pensamento jurídico. no exterior, bem como na Rússia. O surgimento de várias abordagens para entender a provisão legal da balança de interesses privados e públicos está causando discussões animadas, às vezes bastante acentuadas, no campo científico. O artigo enfoca as características históricas, socioculturais, políticas e legais do desenvolvimento do princípio europeu da proporcionalidade e o método americano de equilibrar interesses, o que leva a uma interação e convergência próximas, bem como a necessidade de sua pesquisa científica conjunta, o que pode dar um efeito teórico e prático significativo.Conclusão: o artigo afirma que as características distintivas do princípio europeu da proporcionalidade e do método americano de ponderação de interesses não são de natureza paradigmática essencial, o que nos permite concluir que, neste caso, não há fundamento para uma oposição fundamental entre si dos modelos construtivos acima mencionados como métodos de compreensão jurídica. realidade, bem como meios legais para garantir um equilíbrio de interesses públicos e privados. O desenvolvimento do princípio europeu da proporcionalidade tem um impacto significativo na formação do pensamento e das práticas políticas e jurídicas russas no campo da interação entre direito privado e público, garantindo uma combinação orgânica de interesses privados e públicos, o que se reflete na posição jurídica formulada pelo Tribunal Constitucional da Federação da Rússia sobre o princípio de garantir proporcionalidade. observância, equilíbrio de interesses privados e públicos na implementação da regulamentação legal das relações públicas.The article is devoted to a comparative legal study of the European principle of proportionality and the American method of weighing interests, their origins, common and distinctive features, socio-cultural and historical foundations, the application of the principle of proportionality in the Russian legal order. Historically, the origins (roots) of the European principle of proportionality go back to the German administrative-legal doctrine, and the American method of weighing as an initial principle is associated with private law and only later was extended to the public law sphere. The article assesses the impact of these principles on the Russian legal doctrine and law enforcement practice.Purpose: The main purpose of the article is to identify the general and distinctive features of the European principle of proportionality and the American method of balancing interests in order to comprehend on this basis the Russian legal model for ensuring the balance of private and public interests. Tasks: to explore the historical, socio-cultural, doctrinal foundations of the genesis of the European principle of proportionality and the American method of weighing interests; to identify the common and special features characteristic of these methods; to show the influence of these methods on Russian doctrine and law enforcement practice; compare the Russian principle of balance between private and public interests with the European principle of proportionality; formulate recommendations and suggestions for improving Russian law enforcement practice.Methods: historical and legal, logical, formal and legal, systemic and structural, method of interdisciplinary legal research, method of system analysis.Discussion: the European principle of proportionality and the American method of weighing interests, although they do not belong to new phenomena of legal thought, nevertheless, due to their fundamental importance both at the constitutional and other sectoral levels of development of law, are constantly in the center of the field of vision of legal thought abroad, as well as in Russia. The emergence of various approaches to understanding the legal provision of the balance of private and public interests is causing lively, sometimes quite sharp, discussions in the scientific field. The article focuses on the historical, socio-cultural, political and legal features of the development of the European principle of proportionality and the American method of balancing interests, which leads to both close interaction and convergence, as well as the need for their joint scientific research, which can give a significant theoretical and practical effect.Conclusion: the article states that the distinctive features of the European principle of proportionality and the American method of weighing interests are not of an essential, paradigmatic nature, which allows us to conclude that in this case there are no grounds for a fundamental opposition to each other of the above-named constructive models as methods of understanding legal reality, as well as legal means of ensuring a balance of private and public interests. The development of the European principle of proportionality has a significant impact and impact on the formation of Russian political and legal thought and practice in the field of interaction between private and public law, ensuring an organic combination of private and public interests, which is reflected in the legal position formulated by the Constitutional Court of the Russian Federation concerning the principle of ensuring proportional observance, balance of private and public interests in the implementation of legal regulation of public relations

Tricolor Technique for Visualization of Spatial Variations of Polydisperse Dust in Gas-Dust Flows

The aim of this work is to construct an algorithm for visualizing a polydisperse phase of solid particles (dust) in an inhomogeneous flow of a two-phase gas-dust mixture that would allow us to see, within one plot, the degree of polydispersity of the dust phase and the difference in the spatial distributions of individual fractions of dust particles in the computational domain. The developed technique allows us to reproduce concentrations from one to three fractions of dust particles in each cell in the computational domain. Each of the three fractions of dust particles is mapped to one of the main channels of the RGB palette. The intensity of the color shade is set to be proportional to the relative concentration of dust particles in this fraction. The final image for a polydisperse mixture is obtained by adding images in each of the three color channels. To visualize the degree of polydispersity, I propose depicting the spatial distribution of the entropy of the dust mixture. The definition of the entropy of a mixture is generalized to take into account the states of a mixture with zero number of particles in the mixture. They correspond to dust-free sections of the computational domain (voids). The proposed method for visualizing the polydispersity of a mixture of particles is demonstrated using the example of dynamic numerical modeling of the spatial features of dust structures formed in turbulent gas-dust flows and in flows with shock waves

Hadronic structure aspects of K+→π−+l1++l2+K^+\to \pi^-+ l^{+}_1 + l^{+}_2 decays

As is known from previous studies the lepton number violating decays $K^+\to \pi^- + l^{+}_1 + l^{+}_2$ have good prospects to probe new physics beyond the Standard Model and provide valuable information on neutrino masses and mixing. We analyze these processes with an emphasis on their hadronic structure aspects applying relativistic constituent quark model. We conclude that the previously ignored contribution associated with the t-channel Majorana neutrino exchange is comparable with the s-channel one in a wide range of neutrino masses. We also estimated model independent absolute upper bounds on neutrino contribution to these decays.Comment: 15 pages, 1 figure. Version to appear in PRD, normalization factor in Eq. (25) is correcte

5-(Sulfamoyl)thien-2-yl 1,3-oxazole inhibitors of carbonic anhydrase II with hydrophilic periphery

Hydrophilic derivatives of an earlier described series of carbonic anhydrase inhibitors have been designed, prepared and profiled against a panel of carbonic anhydrase isoforms, including the glaucoma-related hCA II. For all hydrophilic derivatives, computational prediction of intraocular permeability routes showed the predominance of conjunctival rather than corneal absorption. The potentially reactive primary or secondary amine periphery of these compounds makes them suitable candidates for bioconjugation to polymeric drug carriers. As was shown previously, the most active hCA II inhibitor is efficacious in alleviating intraocular pressure in normotensive rabbits with efficacy matching that of dorzolamide.Peer reviewe

Coherent spin dynamics of electrons and holes in CsPbBr3_3 perovskite crystals

The lead halide perovskites demonstrate huge potential for optoelectronic applications, high energy radiation detectors, light emitting devices and solar energy harvesting. Those materials exhibit strong spin-orbit coupling enabling efficient optical orientation of carrier spins in perovskite-based devices with performance controlled by a magnetic field. Perovskites are promising for spintronics due to substantial bulk and structure inversion asymmetry, however, their spin properties are not studied in detail. Here we show that elaborated time-resolved spectroscopy involving strong magnetic fields can be successfully used for perovskites. We perform a comprehensive study of high-quality CsPbBr$_3$ crystals by measuring the exciton and charge carrier $g$-factors, spin relaxation times and hyperfine interaction of carrier and nuclear spins by means of coherent spin dynamics. Owing to their "inverted" band structure, perovskites represent appealing model systems for semiconductor spintronics exploiting the valence band hole spins, while in conventional semiconductors the conduction band electrons are considered for spin functionality.Comment: 8 pages, 3 figures + supplementary informatio

Finite-element study of the customized implant for revision hip replacement

This work examines a biomechanical system consisting of the hip endoprosthesis and bones of the pelvic region of a person under a load corresponding to the equilibrium of a person in double-supported state. An assessment of the strength of a customised endoprosthesis has been carried out based on the analysis of the stress-strain state of the finite element model of the “skeleton – hip prosthesis” system when tightening the screws and when the system is subjected the person's weight; dangerous areas of the pelvic bone with high level of stresses have been identified. As recommendations, optimization of the location and number of screws used in order to create a more uniform stress distribution is proposed