1,1,3-Trimethyl-3-phenylindan as a Luminescent Additive to a Plastic Scintillator Based on Poly(methyl Methacrylate)

The luminescence and scintillation properties of poly(methyl methacrylate) containing 1,1,3-trimethyl-3-phenylindan were studied.     

Reaction of Methylmalonyl Dichloride with Unsaturated Carboxamides

Methylmalonyl dichloride reacts with (2E)-3-phenylacrylamides and (2E)-3-(2-furyl)acrylamide to give the corresponding E-isomeric 2-substituted 4-hydroxy-5-methyl-6H-1,3-oxazin-6-ones. The reaction of methylmalonyl dichloride with acrylamide afforded N-(3-chloropropionyl)-2-methylmalonamic acid. The structure of the products was confirmed by the ¹H and ¹³C NMR, IR, and UV spectra.     

NMR excitation by an electric field as a dynamic manifestation of magnetoelectric and antiferroelectric interactions

The possibility of excitation of NMR signals by an ac electric field in magnetically ordered crystals is discussed. Such signals can be recorded using the time-dependent component of the electric polarization vector. It is assumed that the electric and magnetic characteristics are coupled to each other through magnetoelectric and antiferroelectric interactions. Several types of magnetic structures are analyzed in which these interactions are not forbidden by symmetry. Such structures include two-sublattice single-position ferro-and antiferromagnetic phases in centrosymmetrical crystals, two-sublattice magnetic crystals without a center of symmetry (such as KNiPO₄), and four-sublattice antiferromagnetic crystals with three types of antiferromagnetism vectors (such as Cr₂O₃ and α-Fe₂O₃).     

Multilayer optics for XUV spectral region: technology fabrication and applications

We present research investigations in the field of multilayer optics in X-ray and extreme ultra-violet ranges (XUV), aimed at the development of optical elements for applications in experiments in physics and in scientific instrumentation. We discuss normal incidence multilayer optics in the spectral region of “water window”, multilayer optics for collimation and focusing of hard X-ray, multilayer dispersing elements for X-ray spectroscopy of high-temperature plasma, multilayer dispersing elements for analysis of low Z-elements. Our research pays special attention to optimization of multilayer optics for projection EUV-lithography (ψ-13nm) and short period multilayer optics.     

Lattice parameter and luminescence properties of europium activated yttrium oxide

Samples of yttrium oxide doped with trivalent europium have been prepared by ceramic techniques, under different synthesis conditions; barium chloride (BaCl₂) and sodium tetraborate (Na₂B₄O₇) were tested as flux. The improvement of luminescence properties in dependence on substitution of Eu³⁺ for Y³⁺ in the host lattice, under electron and UV excitations is demonstrated. The lattice parameter as a quantitative assessment of activator incorporation degree is proposed. The obtained results are discussed with respect to the employed processing method.     

Finite-Dimensional Approximations for Scattering Theory Operators in the Wave-Packet Representation

We consider some types of packet discretization for continuous spectra in quantum scattering problems. As we previously showed, this discretization leads to a convenient finite-dimensional (i.e., matrix) approximation for integral operators in the scattering theory and allows reducing the solution of singular integral equations connected with the scattering theory to some suitable purely algebraic equations on an analytic basis. All singularities are explicitly singled out. Our primary emphasis is on realizing the method practically.     

Toda Chains in the Jacobi Method

We use the Jacobi method to construct various integrable systems, such as the Stäckel systems and Toda chains, related to various root systems. We find canonical transformations that relate integrals of motion for the generalized open Toda chains of types B _n, C _n, and D _n.     

Solving of second order nonlinear PDE problems by using artificial controls with controlled error

In this paper, we find the approximate solution of a second order nonlinear partial differential equation on a simple connected region inR ². We transfer this problem to a new problem of second order nonlinear partial differential equation on a rectangle. Then, we transformed the later one to an equivalent optimization problem. Then we consider the optimization problem as a distributed parameter system with artificial controls. Finally, by using the theory of measure, we obtain the approximate solution of the original problem. In this paper also the global error inL ₁ is controlled.     

Solving Linear Systems Whose Elements Are Nonlinear Functions of Intervals

The paper addresses the problem of solving linear algebraic systems the elements of which are, in the general case, nonlinear functions of a given set of independent parameters taking on their values within prescribed intervals. Three kinds of solutions are considered: (i) outer solution, (ii) interval hull solution, and (iii) inner solution. A simple direct method for computing a tight outer solution to such systems is suggested. It reduces, essentially, to inverting a real matrix and solving a system of real linear equations whose size n is the size of the original system. The interval hull solution (which is a NP-hard problem) can be easily determined if certain monotonicity conditions are fulfilled. The resulting method involves solving n+1 interval outer solution problems as well as 2n real linear systems of size n. A simple iterative method for computing an inner solution is also given. A numerical example illustrating the applicability of the methods suggested is solved.     

On p-Extensions of Fields of Characteristic p

It is proved that a Galois extension of a field of characteristic p is completely determined by its Galois group and the endomorphism of the additive group of the group algebra that corresponds to the raising to the power p.