Finite automata based algorithms on subsequences and supersequences of degenerate strings

In this paper, we present linear-time algorithms for the construction two novel types of finite automata and show how they can be used to efficiently solve the Longest Common Subsequence (LCS), Shortest Common Supersequence (SCS) and Constrained Longest Common Subsequence (CLCS) problems for degenerate strings.     

Douglas algebras which are invariant under the Bourgain map

Part of this work was done while the second author was visiting the University of Georgia, Athens/Georgia, USA.     

Optically-active bis(methyl-1-naphthylphenylsilyl)mercury

(+)-Bis(methyl-1-naphthylphenylsilyl)mercury has been prepared, though probably in an optically impure state. Racemization without decomposition takes place at about 150°, and stereospecific cleavages of the Si—Hg bonds are possible.     

Low frequency surface resonance modes in electron energy loss spectroscopy

Electron energy loss spectroscopy has proved a powerful probe of vibrational modes of a wide variety of adsorbed species. Here the primary focus has been on modes with frequency well above the maximum phonon frequency of the substrate. Examples are internal vibration modes of adsorbed molecules, possibly shifted significantly in frequency from their gas phase analogues, and high frequency vibrations of an adsorbed molecule or atom against the substrate. Recent experiments explore features in the energy loss spectrum with frequency below the maximum phonon frequency of the substrate, for ordered overlayers of atoms adsorbed on low index metal surfaces. We shall summarize our theoretical studies of such spectra for several adsorbate/substrate combinations, with emphasis oh the physical origin of the features which appear in the calculations. We obtain a good account of the existing data, within the framework of a rather simple lattice dynamical model, and the calculations show that the features which appear are quite sensitive to the symmetry of the adsorption sits, and other details of the surface geometry. We shall illustrate this with several specific examples.     

Numerical response of an arbitrarily shaped harbour

The numerical development of resonance of a harbour of arbitrary shape and depth is studied. The harbour is subdivided into subregions according to the variations of bottom topography such that each subregion is of uniform depth. The Helmholtz wave equation is formulated in each subregion as an integral equation of the Green's theorem. The solution to the entire harbour basin is obtained by a matching procedure at the subregion boundaries. Here, we consider a harbour with basins of constant depths connected in series successively to accommodate a more complicated harbour geometry. An application of this study is made to Kincardine harbour with five basins connected in series successively.     

Extension results in the Hardy space associated with a logmodular algebra

An interpolation result related to the Hardy space H^∞(m) associated with a logmodular algebra A is presented, where m is the representing measure for some γ?M (A). The above result is used to answer a question rasied in [6].     

Absorption spectra for a model double resonance system involving continuum: Effects of gaussian distribution of levels

The theory of double resonance through the continuum is considered in view of incorporating statistical effects. After resolving the relevant Schrödi