On Higher Derivatives as Constraints in Field Theory: a Geometric Perspective

We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.Comment: 7 page

Genoese domain in the Crimea (the second half of 14th century)

Copyright © 2015 by Sochi State University. The article describes the domain of the Genoese republic in the Crimea in the middle of the 14th century. During this period, the Genoese possessions in the northern Black Sea region consist of one major city Caffa. In the second half of 14th century in the city was reaches the highest point of development. During the second half of the 14th - the first half of 15th centuries Caffa played a leading role in marchand and political life of the Black Sea region. After 1365 the administration of Caffa passes from the defense to the captures of the land previously depending from the Golden Horde. As a result, creates a new political entity on the Crimean Black Sea coast - a system of cities, castles and villages, subject to Genoa, called the Genoes? Gazaria and covered the all coastline including the settlement of the South Coast of Crimea, Soldaya (Sudak), Cembalo (Balaclava) and Vosporo (Bosporus, Kerch)

Structural and thermodynamic insight into the process of “weak” dimerization of the ErbB4 transmembrane domain by solution NMR

AbstractSpecific helix–helix interactions between the single-span transmembrane domains of receptor tyrosine kinases are believed to be important for their lateral dimerization and signal transduction. Establishing structure–function relationships requires precise structural-dynamic information about this class of biologically significant bitopic membrane proteins. ErbB4 is a ubiquitously expressed member of the HER/ErbB family of growth factor receptor tyrosine kinases that is essential for the normal development of various adult and fetal human tissues and plays a role in the pathobiology of the organism. The dimerization of the ErbB4 transmembrane domain in membrane-mimicking lipid bicelles was investigated by solution NMR. In a bicellar DMPC/DHPC environment, the ErbB4 membrane-spanning α-helices (651–678)2 form a right-handed parallel dimer through the N-terminal double GG4-like motif A655GxxGG660 in a fashion that is believed to permit proper kinase domain activation. During helix association, the dimer subunits undergo a structural adjustment (slight bending) with the formation of a network of inter-monomeric polar contacts. The quantitative analysis of the observed monomer–dimer equilibrium provides insights into the kinetics and thermodynamics of the folding process of the helical transmembrane domain in the model environment that may be directly relevant to the process that occurs in biological membranes. The lipid bicelles occupied by a single ErbB4 transmembrane domain behave as a true (“ideal”) solvent for the peptide, while multiply occupied bicelles are more similar to the ordered lipid microdomains of cellular membranes and appear to provide substantial entropic enhancement of the weak helix–helix interactions, which may be critical for membrane protein activity

The Solkhat's war and its reflection in the fortification of Caffa

A relationship between two political entities - the Golden Horde and the Commune of caffa in the 6o's-8o's of the 14th century is discussed in this article. The authors examine the emergence of powerfiui fortifications on the Black Sea coast and the transformation of the town landscape which had been influenced by the conflict between these states. The military conflict called the Solkhat's war resulted in the victory of Genoa Republic. The Golden Horde lost its coastal territory of Southern Crimea. A system of towns, villages and fortresses was created in subordination to the town of affa. The lands of the peninsula which belonged to Golden Horde and Byzantine were cut offfrom the harbours and, as a consequence, from receiving large incomes on sea trade. The last one became a monopoly of Genoa

Hierarchy of Conservation Laws of Diffusion--Convection Equations

We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such systems. We also revise the notion of linear dependence of conservation laws and define the notion of local dependence of potentials. To construct conservation laws, we develop and apply the most direct method which is effective to use in the case of two independent variables. Admitting possibility of dependence of conserved vectors on a number of potentials, we generalize the iteration procedure proposed by Bluman and Doran-Wu for finding nonlocal (potential) conservation laws. As an example, we completely classify potential conservation laws (including arbitrary order local ones) of diffusion--convection equations with respect to the equivalence group and construct an exhaustive list of locally inequivalent potential systems corresponding to these equations.Comment: 24 page

Jacobi multipliers, non-local symmetries and nonlinear oscillators

Constants of motion, Lagrangians and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last multiplier allows us to find Lagrangian descriptions and constants of the motion. An application of the jet bundle formulation of symmetries of differential equations is presented in the second part of the paper. After a short review of the general formalism, the particular case of non-local symmetries is studied in detail by making use of an extended formalism. The theory is related to some results previously obtained by Krasil'shchi, Vinogradov and coworkers. Finally the existence of non-local symmetries for such two nonlinear oscillators is proved.Comment: 20 page

Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics

Many human infections with viruses such as human immunodeficiency virus type 1 (HIV--1) are characterized by low numbers of founder viruses for which the random effects and discrete nature of populations have a strong effect on the dynamics, e.g., extinction versus spread. It remains to be established whether HIV transmission is a stochastic process on the whole. In this study, we consider the simplest (so-called, 'consensus') virus dynamics model and develop a computational methodology for building an equivalent stochastic model based on Markov Chain accounting for random interactions between the components. The model is used to study the evolution of the probability densities for the virus and target cell populations. It predicts the probability of infection spread as a function of the number of the transmitted viruses. A hybrid algorithm is suggested to compute efficiently the dynamics in state space domain characterized by a mix of small and large species densities

Determination of a type of adaptation strategy as a method of estimation of effectiveness of intensive therapy

The research included data on the postoperative treatment of 120 patients after one-side total hip replacement. In 40 patients of clinical comparison group we used traditional program of postoperative intensive therapy. Program of intensive treatment in main group consisted of 80 patients was optimized. Higher clinical effectiveness of intensive therapy in patients of main group was proved by significant decrease of duration of staying in Intensive Care Unit. Significant intergroup differences were revealed only at the comparison of index of consumption of oxygen by myocardium that characterizes type of adaptation reaction. At that realization of adaptation by resistant (active) type testified to the attempts of an organism to achieve adaptation and, consequently, to the insufficient effectiveness of program of postoperative intensive therapy. Achieved data allows to conclude about possibility of an estimation of general effectiveness of the program of postoperative intensive therapy with use of determination of the type of adaptation strategy

Potential Conservation Laws

We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially depend on potential variables. This statement provides a significant generalization of results of the recent paper by Bluman, Cheviakov and Ivanova [J. Math. Phys., 2006, V.47, 113505]. Moreover, we present extensions to gauged potential systems, Abelian and general coverings and general foliated systems of differential equations. An example illustrating possible applications of proved statements is considered. A special version of the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are proposed as new tools for the investigation of potential conservation laws.Comment: 36 pages, extended versio