A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit Circle

We prove a general Borg-type result for reflectionless unitaryCMV operators U associated with orthogonal polynomials on theunit circle. The spectrum of U is assumed to be a connectedarc on the unit circle. This extends a recent result of Simonin connection with a periodic CMV operator with spectrum thewhole unit circle. In the course of deriving the Borg-type result we also use exponentialHerglotz representations of Caratheodory functions to provean infinite sequence of trace formulas connected with the CMVoperator U.     

Thermodynamic and stress analysis of laser-induced forward transfer of metals

On the basis of a two-temperature model taking into account the laser-generated stress waves, we have performed an analysis of heating and melting dynamics in different metallic films (Au, Zn, Cr) irradiated by femtosecond laser pulses for the experimental conditions on laser-induced forward transfer. The modeling results have allowed puzzling out why, even within the same family of materials, substances can be transferred in the different phase states under rather similar laser-irradiation conditions.     

Blow-up for Joseph–Egri equation: Theoretical approach and numerical analysis

This work develops the theory of the blow-up phenomena for Joseph–Egri equation. The existence of the nonextendable solution of two initial-boundary value problems (on a segment and a half-line) is demonstrated. Sufficient conditions of the finite-time blow-up of these solutions, as well as the analytical estimates of the blow-up time, are obtained. A numerical method that allows to precise the blow-up moment for specified initial data is proposed.     

Everywhere regularity of certain nonlinear diffusion systems

In this paper I discuss nonlinear parabolic systems that are generalizations of scalar diffusion equations. More precisely, I consider systems of the form $$\mathbf{u}_t -\Delta\left[ \mathbf{\nabla}\Phi(\mathbf{u})\right] = 0,$$ where ${\Phi(z)}$ is a strictly convex function. I show that when ${\Phi}$ is a function only of the norm of u, then bounded weak solutions of these parabolic systems are everywhere Hölder continuous and thus everywhere smooth. I also show that the method used to prove this result can be easily adopted to simplify the proof of the result due to Wiegner (Math Ann 292(4):711–727, 1992) on everywhere regularity of bounded weak solutions of strongly coupled parabolic systems.     

Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection

Light scattered from biological tissues can exhibit an inverse power law spectral component. We develop a model based on the Born approximation and von Karman (self-affine) spatial correlation of submicron tissue refractive index to account for this. The model is applied to light scattering spectra obtained from excised esophagi of normal and carcinogen-treated rats. Power law exponents used to fit dysplastic tissue site spectra are significantly smaller than those from normal sites, indicating that changes in tissue self-affinity can serve as a potential biomarker for precancer.     

On generalized shock models for deteriorating systems

Standard assumptions in shock models are that failures of items are related either to the cumulative effect of shocks (cumulative models) or that they are caused by shocks that exceed a certain critical level (extreme shocks models). In this paper, we present useful generalizations of this setting to the case when an item is deteriorating itself, for example, when the boundary for the fatal shock magnitude is decreasing with time. Three stochastic failure models describing different impacts of shocks on items are considered. The cumulative effect of shocks is modeled in a way similar to the proportional hazards model. Explicit formulas for the corresponding survival functions are derived and several simple examples are considered. Copyright © 2012 John Wiley & Sons, Ltd.     

Mixed algebras and quivers related to cell complexes

In this paper we study finite dimensional algebras arising from categories of perverse sheaves on finite regular cell complexes (cellular perverse algebras). We prove that such algebras are quasi-hereditary and have finite global dimension. We discuss some restrictions, under which cellular perverse algebras are Koszul. We also study the relationship between Koszul duality functors in the derived categories of categories of graded and non-graded modules over an algebra and its quadratic dual.     

Thermal and physical properties of sodium niobate ceramics over a wide temperature range

The temperature dependences of the heat capacity C _p (T) and thermal expansion coefficient α(T) of NaNbO₃ ceramic samples have been investigated in the temperature range from 2 to 800 K. In addition to the anomalies associated with the known phase transitions at temperatures T ₆ ≈ 265 K, T ₅ ≈ 638 K, T ₄ ≈ 760 K, and T ₃ ≈ 793 K, anomalies in the behavior of C _p (T) and α(T) have been observed near T _5″ ≈ 500 K and T _5′ ≈ 600 K. It has been found that all the observed structural transformations, according to the values of the entropy change, are not related to the ordering of structural elements. It has been shown that, with an increase in the temperature, the unit cell volume during the phase transitions near 265, 515, 604, and 638 K decreases. The specific features of the transition to the phase R3c have been examined. Two possible scenarios of the sequence of phase transformations in the temperature range between T ₅ and T ₆ have been analyzed.