Lattice Dynamics in the Half-Space, II. Energy Transport Equation

We consider the lattice dynamics in the half-space. The initial data are random according to a probability measure which enforces slow spatial variation on the linear scale $\varepsilon^{-1}$. We establish two time regimes. For times of order $\varepsilon^{-\gamma}$, $0<\gamma<1$, locally the measure converges to a Gaussian measure which is time stationary with a covariance inherited from the initial measure (non-Gaussian, in general). For times of order $\varepsilon^{-1}$, this covariance changes in time and is governed by a semiclassical transport equation.Comment: 35 page

Four dimensional Lie symmetry algebras and fourth order ordinary differential equations

Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is described.Comment: 12 page

Parameter estimation in pair hidden Markov models

This paper deals with parameter estimation in pair hidden Markov models (pair-HMMs). We first provide a rigorous formalism for these models and discuss possible definitions of likelihoods. The model being biologically motivated, some restrictions with respect to the full parameter space naturally occur. Existence of two different Information divergence rates is established and divergence property (namely positivity at values different from the true one) is shown under additional assumptions. This yields consistency for the parameter in parametrization schemes for which the divergence property holds. Simulations illustrate different cases which are not covered by our results.Comment: corrected typo

Pluripolarity of Graphs of Denjoy Quasianalytic Functions of Several Variables

In this paper we prove pluripolarity of graphs of Denjoy quasianalytic functions of several variables on the spanning se

New deformability characteristics of zirconia-based plasma-sprayed thermal barrier coatings at low loads

© 2017, Pleiades Publishing, Ltd. A new approach to determining the residual stresses and the energy characteristics of the deformability of zirconia-based thermal barrier coatings is described. This approach consists in the formation of a deformation hysteresis in the elastic range of deformation during four-point static bending and in estimating the energy density of relaxation of the elastic strain in the coatings

Revised GLE database : Fluences of solar energetic particles as measured by the neutron-monitor network since 1956

Aims. Continuous measurements of ground-based neutron monitors (NMs) form the main data source for studying high-energy high-intensity solar energetic particle (SEP) events that are called ground-level enhancements (GLEs). All available data are collected in the International GLE Database (IGLED), which provides formal NM count-rate increases above the constant pre-increase level which is due to galactic cosmic rays (GCR). This data set is used to reconstruct the energy spectra of GLE events. However, the assumption of a constant GCR background level throughout GLE events is often invalid. Here we thoroughly revise the IGLED and provide a data set of detrended NM count-rate increases that accounts for the variable GCR background. Methods. The formal GLE count-rate increases were corrected for the variable GCR background, which may vary significantly during GLE events. The corresponding integral omnidirectional fluences of SEPs were reconstructed for all GLEs with sufficient strength from the detrended data using the effective rigidity method. Results. The database of the detrended NM count rate is revised for GLE events since 1956. Integral omnidirectional fluences were estimated for 58 GLE events and parametrised for 52 sufficiently strong events using the modified Ellison-Ramaty spectral shape. Conclusions. The IGLED was revised to account for the variable GCR background. Integral omnidirectional fluences reconstructed for most of GLE events were added to IGLED. This forms the basis for more precise studies of parameters of SEP events and thus for solar and space physics.Peer reviewe

Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves

Two-frequency Wigner distribution is introduced to capture the asymptotic behavior of the space-frequency correlation of paraxial waves in the radiative transfer limits. The scaling limits give rises to deterministic transport-like equations. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker-Planck-like differential equation in the phase space. The solutions to these equations have a probabilistic representation which can be simulated by Monte Carlo method. When the medium fluctuates more rapidly in the longitudinal direction, the corresponding Fokker-Planck-like equation can be solved exactly.Comment: typos correcte

Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis

Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM equation. It gives us the possibility to describe an optimal system of subalgebras and correspondingly the set of invariant solutions to the model. In this way we can describe the complete set of possible reductions of the nonlinear RAPM model. Reductions are given in the form of different second order ordinary differential equations. In all cases we provide solutions to these equations in an exact or parametric form. We discuss the properties of these reductions and the corresponding invariant solutions.Comment: larger version with exact solutions, corrected typos, 13 pages, Symposium on Optimal Stopping in Abo/Turku 200

Factorization and Lie point symmetries of general Lienard-type equation in the complex plane

We present a variational approach to a general Lienard-type equation in order to linearize it and, as an example, the Van der Pol oscillator is discussed. The new equation which is almost linear is factorized. The point symmetries of the deformed equation are also discussed and the two-dimensional Lie algebraic generators are obtained

Investigation of mechanical properties of thermal coatings obtained during plasma spraying of powder zirconium dioxide

© Published under licence by IOP Publishing Ltd.Thermal coatings of zirconia partially stabilized with yttrium, deposited by low-temperature plasma, are the basis for the thermal protection of aircraft engine. At the same time there is an actual problem of selection of coating systems "ceramic layer - underlayer" of great thickness, providing better thermal protection, but having low strength characteristics due to the accumulation of internal stresses. To determine the optimal thickness of the test method used in the 4-point bending to allow the surface coating to explore in the elastic-plastic behavior of the field of coatings and strength. Based on the experimental results established the role of underlayer in the formation of the complex mechanical properties of thermal barrier coatings. With a well formed underlayer (PVNH16U6) system becomes sensitive to a change in thickness of the coating, to optimize the response on the strength and deformation criteria. According to the results the optimum ratio of the thickness of the ceramic layer and the underlayer should be regarded as the ratio of 3-5 for which the highest strength values were obtained for all the test coating systems