On Computation of Scattering Matrices and on Surface Waves for Diffraction Gratings

Summary.  A method for the numerical computation of the so-called augmented scattering matrices (ASM) is suggested for diffraction gratings. To construct such (unitary) matrices one has to take into account not only the oscillating modes but also those which exponentially grow (attenuate) in amplitude away from the grating. The method uses an optimization procedure to identify the coefficients in the asymptotics of such modes. A justification of the approach is given and its numerical implementation is discussed. Reliable numerical results allow us to study the occurrences of surface waves by means of a general existence criterion based on the properties of ASM. To illustrate the method we give some examples of surface waves in gratings. Received October 25, 2001 / Revised version received May 23, 2002 / Published online October 29, 2002 Mathematics Subject Classification (1991): 78M10, 78M50, 78A45     

On permutative grammars generating context-free languages

A grammar is said to be permutative if it has permutation productions of the formAB BA in addition to context-free productions. Szilard languages and label languages are studied as examples of languages generable by permutative grammars. Particularly, sufficient conditions for a permutative grammar to generate a context-free language are studied.This work was supported by the Academy of Finland.     

New practical synthesis of prazosin

A new four step synthesis of prazosin, 2-[4-(2-furoyl)piperazin-l-yl]-4-amino-6,7-dimethoxyquinazoline, has been described. The method is also adaptable for the preparation of other substituted 4-aminoquinazolines. The yields are good in every step and the reactions are performed with ease. Prazosin hydrochloride of high purity is obtained directly in the last step.     

Some aspects of approach to equilibrium in classical and quantum systems

Investigations of general properties of time evolution of both classical and quantum systems show that the evolution (on a microscopic level) is reversible, and, if there is an approach to equilibrium, it exists only in the sense of weak convergence and necessarily in both directions of time. In this connection attempts to derive irreversibility and the approach to equilibrium in the sense of strong convergence and without any loss of information (using the so-called Lyapunov converters) are discussed. After demonstrating their drawbacks, an alternative approach is proposed based on the spectral properties of the generator of the group. The relevant spectral criteria for the approach of both classical and quantum ensembles to equilibrium are given, and the decisive role of loss of information in obtaining stronger variants of convergence is emphasized. The asymmetry between initial and any other state —consisting of different levels of information needed to prepare the states—is proposed as an adequate explanation of irreversibility. The importance of the method of complex scaling in this context is discussed, and its application in proving some spectral properties in the quantal Hamiltonian formulation is stressed.     

Optical coherence tomography as a method of quality inspection for printed electronics products

Application of time domain, ultra high resolution optical coherence tomography (UHR-OCT) in printed electronics products’ quality inspection is demonstrated. Presented study was done using experimental UHR-OCT device based on a Kerr-lens mode locked Ti:sapphire femtosecond laser, photonic crystal fibre and modified, free-space Michelson interferometer. Possibilities of the technique are demonstrated by analysis of an RF antenna—example of printed electronics products. Measurements were done with submicron axial resolution, offered by UHR-OCT system developed in our laboratory. Such high resolution is necessary due to the thickness of material layers used in printed electronics. In addition to tomography imaging, numerical results were compared with data provided by two commercially available measurement devices: Wyko NT3300 optical profiler and Dektak 8 stylus profiler (both Veeco). Comparison of profile heights and their spatial correlation is presented. Ability for full volumetric reconstruction and accuracy justified with reference measurements prove OCT to be a reliable tool in printed electronics product testing.