On a class of three-dimensional integrable Lagrangians

We characterize non-degenerate Lagrangians of the form $\int f(u_x, u_y, u_t) dx dy dt$ such that the corresponding Euler-Lagrange equations $(f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})_t=0$ are integrable by the method of hydrodynamic reductions. The integrability conditions constitute an over-determined system of fourth order PDEs for the Lagrangian density $f$, which is in involution and possess interesting differential-geometric properties. The moduli space of integrable Lagrangians, factorized by the action of a natural equivalence group, is three-dimensional. Familiar examples include the dispersionless Kadomtsev-Petviashvili (dKP) and the Boyer-Finley Lagrangians, $f=u_x^3/3+u_y^2-u_xu_t$ and $f=u_x^2+u_y^2-2e^{u_t}$, respectively. A complete description of integrable cubic and quartic Lagrangians is obtained. Up to the equivalence transformations, the list of integrable cubic Lagrangians reduces to three examples, $f=u_xu_yu_t, f=u_x^2u_y+u_yu_t, and f=u_x^3/3+u_y^2-u_xu_t ({\rm dKP}).$ There exists a unique integrable quartic Lagrangian, $f=u_x^4+2u_x^2u_t-u_xu_y-u_t^2.$ We conjecture that these examples exhaust the list of integrable polynomial Lagrangians which are essentially three-dimensional (it was verified that there exist no polynomial integrable Lagrangians of degree five). We prove that the Euler-Lagrange equations are integrable by the method of hydrodynamic reductions if and only if they possess a scalar pseudopotential playing the role of a dispersionless `Lax pair'. MSC: 35Q58, 37K05, 37K10, 37K25. Keywords: Multi-dimensional Dispersionless Integrable Systems, Hydrodynamic Reductions, Pseudopotentials.Comment: 12 pages A4 format, standard Latex 2e. In the file progs.tar we include the programs needed for computations performed in the paper. Read 1-README first. The new version includes two new section

THE STUDY OF THE ANTIOXIDANT ACTIVITY OF 2-AMINOTHIAZOLES CONTAINING A DITERPENE FRAGMENT BY CHEMILUMINESCENCE

Presently the focus is on developing both synthetic and natural compounds like antioxidants that act at different levels and that can be possibly used to reduce damage caused by oxidative stress. Among these, biologically important compounds with a wide spectrum of action (antitumor, antioxidant and antioxidant activity) are aminothiazoles

Policentricity as a way to sustainable development of the city (The case-study of the city of kazan)

© SGEM 2017. The article is devoted to the study of the polycentric city structure. The large area of the city combined with territorial-functional differentiation, growing interest of the population in recreation, leisure time, family rest, and the desire to attract tourists are all components of the emerging polycentricity of city life. Polycentricity of city structure assumes the formation of not one but several local centers on the basis of socio-ecological functions in combination with economic activities of a post-industrial nature (trade, entertainment, creative industries, education). Polycentricity allows creating a general brand of the city consisted of local brands, thereby increasing the attractiveness of the urban environment due to its diversity in different areas. The City of of Kazan has an area of more than 600 sq.km and a population of more than 1.2 million people. In administrative terms, the city is divided into seven districts. The historical center of the The City of Kazan has historical and cultural significance - the Kazan Kremlin (UNESCO site) - and natural sites - the Kaban lakes, the embankments of the Kazanka and Volga rivers. The analysis of the territorial differentiation of the city and the functional-territorial characteristics of the administrative districts of Kazan with the use of cartographic and statistical methods is carried out. It is shown that for each district there is a potential for the formation of a center on the base of existing social and environmental factors, and for the city as a whole - a polycentric territorial structure. The importance of creating pedestrian accessibility of these centers and the formation of walking and pedestrian networks of the districts is determined, taking into account the preservation of the region's uniqueness, expressed through existing environmental objects, natural objects, social functions, which is generally the basis of the sustainable development of the city

Actual demographic processes in the Republic of Tatarstan

© 2015, Mediterranean Center of Social and Educational Research. All rights reserved. This article analyzes the current demographic characteristics of the Republic of Tatarstan. The key indicators of the demographic situation, such as the indicators of natural (birth and death rate) and migration of population have an uncertain future. Demographic indicators are influenced by a number of different factors which can be hard to predict. At the same time the demographic characteristics of the population have highly significant implications for economic and social development of any area in a long term perspective. Demographic characteristics and trends analysis is one of the most important points in understanding the demographic future of certain region and the country as a whole. Tatarstan is one of the most socioeconomically developed regions in Russia. In recent years birth rate exceeds its deaths rate in the republic and the urban population increases annually

On Soliton-type Solutions of Equations Associated with N-component Systems

The algebraic geometric approach to $N$-component systems of nonlinear integrable PDE's is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink transitions and multi-peaked soliton solutions is carried out. Transformations are used to connect these solutions to several other equations that model physical phenomena in fluid dynamics and nonlinear optics.Comment: 43 pages, 16 figure

S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies

We introduce an S-function formulation for the recently found r-th dispersionless modified KP and r-th dispersionless Dym hierarchies, giving also a connection of these $S$-functions with the Orlov functions of the hierarchies. Then, we discuss a reduction scheme for the hierarchies that together with the $S$-function formulation leads to hodograph systems for the associated solutions. We consider also the connection of these reductions with those of the dispersionless KP hierarchy and with hydrodynamic type systems. In particular, for the 1-component and 2-component reduction we derive, for both hierarchies, ample sets of examples of explicit solutions.Comment: 35 pages, uses AMS-Latex, Hyperref, Geometry, Array and Babel package

Transfer Hydrogenation of Carbonyl Groups, Imines and N‐Heterocycles Catalyzed by Simple, Bipyridine‐Based MnI Complexes

Utilization of hydroxy‐substituted bipyridine ligands in transition metal catalysis mimicking [Fe]‐hydrogenase has been shown to be a promising approach in developing new catalysts for hydrogenation. For example, MnI complexes with 6,6′‐dihydroxy‐2,2′‐bipyridine ligand have been previously shown to be active catalysts for CO2 hydrogenation. In this work, simple bipyridine‐based Mn catalysts were developed that act as active catalysts for transfer hydrogenation of ketones, aldehydes and imines. For the first time, Mn‐catalyzed transfer hydrogenation of N ‐heterocycles was reported. The highest catalytic activity among complexes with variously substituted ligands was observed for the complex bearing two OH groups in bipyridine. Deuterium labeling experiments suggest a monohydride pathway

Instability of two interacting, quasi-monochromatic waves in shallow water

We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation. Using a multiple-scale technique two defocusing coupled Nonlinear Schr\"odinger equations are derived. We show analytically that plane wave solutions of such a system can be unstable to small perturbations. This surprising result suggests the existence of a new energy exchange mechanism which could influence the behaviour of ocean waves in shallow water.Comment: 4 pages, 2 figure

Recent advances in genetics of aggressive behavior

One of the most important problems of modern neurobiology and medicine is an understanding of the mechanisms of normal and pathological behavior of a person. Aggressive behavior is an integral part of the human psyche. However, environmental risk factors, mental illness and somatic diseases can lead to increased aggression to be the biological basis of antisocial behavior in a human society. An important role in development of aggressive behavior belongs to the hereditary factors that may be linked to abnormal functioning of neurotransmitter systems in the brain yet the underlying genetic mechanisms remain unclear, which is due to a large number of single nucleotide polymorphisms, insertions and deletions in the structure of genes that encode the components of the neurotransmitter systems. The most studied candidate genes for aggressive behavior are serotonergic (TPH1, TPH2, HTR2A, SLC6A4) and dopaminergic (DRD4, SLC6A3) system genes, as well as the serotonin or catecholamine metabolizing enzyme genes (COMT, MAOA). In addition, there is evidence that the hypothalamic-pituitary system genes (OXT, OXTR, AVPR1A, AVPR1B), the sex hormone receptors genes (ER1, AR), neurotrophin (BDNF) and neuronal apoptosis genes (CASP3, BAX) may also be involved in development of aggressive behavior. The results of Genome-Wide Association Studies (GWAS) have demonstrated that FYN, LRRTM4, NTM, CDH13, DYRK1A and other genes are involved in regulation of aggressive behavior. These and other evidence suggest that genetic predisposition to aggressive behavior may be a very complex process

Longitudinal genetic studies of cognitive characteristics

The present review describes longitudinal studies of cognitive traits and functions determining the causes of their variations and their possible correction to prevent cognitive impairment. The present study reviews the involvement of such environmental factors as nutrition, prenatal maternal stress, social isolation and others in cognitive functioning. The role of epigenetic factors in the implementation of environmental effects in cognitive characteristics is revealed. Considering the epigenome significance, several studies were focused on the design of substances affecting methylation and histone modification, which can be used for the treatment of cognitive disorders. The appropriate correction of epigenetic factors related to environmental differences in cognitive abilities requires to determine the mechanisms of chromatin modifications and variations in DNA methylation. Transposons representing stress-sensitive DNA elements appeared to mediate the environmental influence on epigenetic modifications. They can explain the mechanism of transgenerational transfer of information on cognitive abilities. Recently, large-scale meta-analyses based on the results of studies, which identified genetic associations with various cognitive traits, were carried out. As a result, the role of genes actively expressed in the brain, such as BDNF, COMT, CADM2, CYP2D6, APBA1, CHRNA7, PDE1C, PDE4B, and PDE4D in cognitive abilities was revealed. The association between cognitive functioning and genes, which have been previously involved in developing psychiatric disorders (MEF2C, CYP2D6, FAM109B, SEPT3, NAGA, TCF20, NDUFA6 genes), was revealed, thus indicating the role of the similar mechanisms of genetic and neural networks in both normal cognition and cognitive impairment. An important role in both processes belongs to common epigenetic factors. The genes involved in DNA methylation (DNMT1, DNMT3B, and FTO), histone modifications (CREBBP, CUL4B, EHMT1, EP300, EZH2, HLCS, HUWE1, KAT6B, KMT2A, KMT2D, KMT2C, NSD1, WHSC1, and UBE2A) and chromatin remodeling (ACTB, ARID1A, ARID1B, ATRX, CHD2, CHD7, CHD8, SMARCA2, SMARCA4, SMARCB1, SMARCE1, SRCAP, and SS18L1) are associated with increased risk of psychiatric diseases with cognitive deficiency together with normal cognitive functioning. The data on the correlation between transgenerational epigenetic inheritance of cognitive abilities and the insert of transposable elements in intergenic regions is discussed. Transposons regulate genes functioning in the brain due to the processing of their transcripts into non-coding RNAs. The content, quantity and arrangement of transposable elements in human genome, which do not affect changes in nucleotide sequences of protein encoding genes, but affect their expression, can be transmitted to the next generation