Comparison characterization of copper selenide thin layers prepared on polyamide 6 films by sorption-diffusion method

Some earlier synthesized copper selenide (Cu _x Se) layers formed on the surface of polyamide 6 by sorption-diffusion method using potassium selenotrithionate (K₂SeS₂O₆) as precursor of selenium were characterized by the XRD, XPS and SEM methods. According to the results of the SEM studies, the most uniform Cu _x Se layers form at the 2.5 h polyamide seleniumized duration at the temperature of 60°C. The thickness of layers, which dependeds on the duration of seleniumization, changed in the range of 0.8–3.2 µm. The XRD patterns of not previously studied Cu _x Se layers showed their phase composition of six copper selenides: Cu₂Se, two phases of CuSe₂, Cu₃Se₂, berzellianite, Cu_2-x Se, and bellidoite Cu₂Se. Analysis of the XRD and XPS data shows that the macrostructure and composition of the Cu_xSe layers depend on the conditions of formation of these layers.      

Some decidable classes of formulas of pure hybrid logic

We consider the formulas of pure hybrid logic without occurrences of a satisfaction operator. We describe a couple of formula derivation tactics in sequent calculus and prove the decidability of two classes of formulas. Decidable classes are obtained by setting restrictions on nominal occurrences in the formulas. Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 563–572, October–December, 2007.     

The Discounted Limit Theorems

The large deviation theorems, exponential inequalities and a non-uniform estimate of the Berry–Esséen theorem in a discounted version are proved.Dedicated to Professor Vytautas Statulevičius on the occasion of his 75th birthday.     

Discrete Universality in the Selberg Class

The Selberg class S consists of functions L(s) that are defined by Dirichlet series and satisfy four axioms (Ramanujan conjecture, analytic continuation, functional equation, and Euler product). It has been known that functions in S that satisfy the mean value condition on primes are universal in the sense of Voronin, i.e., every function in a sufficiently wide class of analytic functions can be approximated by the shifts L(s + iτ ), τ ∈ R. In this paper we show that every function in the same class of analytic functions can be approximated by the discrete shifts L(s + ikh), k = 0, 1,..., where h > 0 is an arbitrary fixed number.     

A numerical algorithm for simulation of the Q-switched fiber laser using the travelling wave model

We develop a finite-difference scheme for approximation of a system of nonlinear PDEs describing the Q-switching process. We construct it by using staggered grids. The transport equations are approximated along characteristics, and quadratic nonlinear functions are linearized using a special selection of staggered grids. The stability analysis proves that a connection between time and space steps arises only due to approximation requirements in order to follow exactly the directions of characteristics. The convergence analysis of this scheme is done in two steps. First, some estimates of the uniform boundedness of the discrete solution are proved. This part of the analysis is done locally, in some neighborhood of the exact solution. Second, on the basis of the obtained estimates, the main stability inequality is proved. The second-order convergence rate with respect to the space and time coordinates follows from this stability estimate. Using the obtained convergence result, we prove that the local stability analysis in the selected neighborhood of the exact solution is sufficient.     

Solvability of a mathematical model of dissociative adsorption and associative desorption type

A mathematical model of dissociative adsorption and associative desorption for diatomic molecules is generalized. The model is described by a coupled system of parabolic and ordinary differential equations. The existence and uniqueness theorem of the classical solution is proved.