Broadening the scope of 1,2,4-triazine synthesis by the application of microwave technology

By the application of microwave technology, a general protocol has been developed for the rapid synthesis of diverse 3,5,6-trisubstituted 1,2,4-triazines in excellent yield and purity, including many previously unknown 3-heterocyclic-1,2,4-triazines.     

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.     

Precision of a dual energy X-ray absorptiometry device

The standard method to diagnose and follow-up osteoporosis is the measurement of bone mineral density (BMD) using dual X-ray absorptiometry (DEXA). Manufacturers' manuals of DEXA devices state the intrascanner coefficient of variance is less than 0.01 g/cm². The aim of this study was to evaluate the in vivo coefficient of variance of a Lunar DPX scanner in male and female healthy adult subjects. Average BMD for females and males were 1.170±0.091 g/cm² and 1.272±0.115 g/cm², respectively. Monthly phantom measurements provided and controlled by the manufacturer were 1.243±0.008 g/cm² (range 1.222 to 1.257) and the coefficient of variance was 0.006. It is concluded that the in vivo coefficient of variance of DEXA devices can slightly be higher than that proposed by the manufacturer. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Shape Optimization and Fictitious Domain Approach for Solving Free Boundary Problems of Bernoulli Type

This contribution deals with an efficient method for the numerical realization of the exterior and interior Bernoulli free boundary problems. It is based on a shape optimization approach. The state problems are solved by a fictitious domain solver using boundary Lagrange multipliers.     

On separation of gradient Young measures

Let be a linear subspace of real matrices without rank-one matrices and let be a finite set. Suppose is a bounded arcwise connected Lipschitz domain and is a sequence of bounded vector-valued mappings in such that in as , where is the closed -neighbourhood and the distance function to . We give estimates for such that up to a subsequence, in for some fixed . In other words, we give estimates on such that separates gradient Young measure. The two point set with is a special case of such sets up to a translation. Received: 20 July 2001 / Accepted: 23 January 2002 / Published online: 5 September 2002     

Approximate symmetries and conservation laws for Itô and Stratonovich dynamical systems

A new definition for the approximate symmetries of Itô dynamical system is given. Determining systems of approximate symmetries for Itô and Stratonovich dynamical systems have been obtained. It has been shown that approximate conservation laws can be found from the approximate symmetries of stochastic dynamical systems which do not arise from a Hamiltonian. The results have been applied to an example.