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

Ticagrelor hemorrhagic safety in patients with acute coronary syndrome with ST-segment elevation received thrombolytic therapy in daily clinical practice: 30-day observation results

Background. Effective antithrombotic therapy is a necessary condition for maintaining the patency of the infarct-dependent coronary artery during a primary percutaneous coronary intervention. Aim. To compare the safety of ticagrelor use in patients with STEMI after ineffective thrombolytic treatment (TLT) and successfully performed recanalization of infarct-dependent artery (IDA) by PCI, withticagrelor loading dose administered in the time window from TLT to PCI, in comparison with the TREAT study results on the risk of bleeding in the real clinical practice. Methods. A comparative analysis of the results of a 30-day follow-up of 52 patients with acute coronary syndrome with ST-segment elevation who received a thrombolytic therapy with alteplasa and early ticagrelor administration with the ticagrelor group in the TREAT study on the parameters of hemorrhagic safety. Results. Arterial hypertension, dyslipidemia, generalized atherosclerosis, chronic obstructive pulmonary disease and a history of myocardial infarction were significantly more common in the study group. The analysis of the results revealed no significant differences between the groups in the frequency and risk of hemorrhagic complications. Conclusion. There are no significant differences in the frequency of major bleeding according to the TIMI and BARC criteria between the groups, which indicates the safety of early (within 24 hours after thrombolysis) ticagrelor use in the pharmacoinvasive approach in the real clinical practice

Stratigraphy of the Golden Hoard Town of Madzhar. First Observations

The paper presents the first stratigraphic scale for the main Golden Horde center in the North Caucasus - the town of Madzhar. The scale has been developed on the basis of materials obtained during the three field archaeological seasons of 2015–2017, during which the Caffa archaeological expedition within the framework of the State Program of the Republic of Tatarstan “Preservation of the national identity of the Tatar people (2014–2021)” founded three excavation areas (XI–XIII), and two trenches in the territory of the settlement. All cultural strata belong to the Golden Horde period in the history of the town of Madzhar. The developed stratigraphic column of Madzhar settlement includes five main strata: I – 20th – early 21st centuries, II – 1380s–1390s, III – 1340s–1370s, IV – 1300s–1330s, and V – 1260s–1290s

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

First principles calculations of oxygen adsorption on the UN (001) surface

Fabrication, handling and disposal of nuclear fuel materials require comprehensive knowledge of their surface morphology and reactivity. Due to unavoidable contact with air components (even at low partial pressures), UN samples contain considerable amount of oxygen impurities affecting fuel properties. The basic properties of O atoms adsorbed on the UN(001) surface are simulated here combining the two first principles calculation methods based on the plane wave basis set and that of the localized atomic orbitals.Comment: 9 page

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

Ab initio modeling of oxygen impurity atom incorporation into uranium mononitride surface and subsurface vacancies

The incorporation of oxygen atoms has been simulated into either nitrogen or uranium vacancy at the UN(001) surface, sub-surface or central layers. For calculations on the corresponding slab models both the relativistic pseudopotentials and the method of projector augmented-waves (PAW) as implemented in the VASP computer code have been used. The energies of O atom incorporation and solution within the defective UN surface have been calculated and discussed. For different configurations of oxygen ions at vacancies within the UN(001) slab, the calculated density of states and electronic charge re-distribution was analyzed. Considerable energetic preference of O atom incorporation into the N-vacancy as compared to U-vacancy indicates that the observed oxidation of UN is determined mainly by the interaction of oxygen atoms with the surface and sub-surface N vacancies resulting in their capture by the vacancies and formation of O-U bonds with the nearest uranium atoms. Keywords: Density functional calculations, uranium mononitride, surface, defects, N and U vacancie