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     

Two new diterpene polyesters from Euphorbia decipiens

Two new myrsinol-type diterpene polyesters 3,5,13,17-tetra-O-acetyl-7-O-benzoyl-15-hydroxymyrsinol (1) and 3,5,13,17-tetra-O-acetyl-7-O-butanoyl-13-hydroxymyrsinol (2), with a tricyclic carbon skeleton have been isolated from Euphorbia decipiens Boiss. & Buhse. The structure elucidation of the isolated compounds was based primarily on HREIMS, EIMS, IR, UV, ID-, and 2D-NMR analyses, including COSY, HMQC, HMBC, and NOESY correlations. Compounds 1 and 2 also showed activity against urease enzyme.     

Local behaviour of polynomials

In this paper we study the local behaviour of a trigonometric polynomial around any of its zeros in terms of its estimated values at an adequate number of freely chosen points in . The freedom in the choice of sample points makes our results particularly convenient for numerical calculations. Analogous results for polynomials of the form are also proved.

     

Certain extremal problems for polynomials

Extensions of two classical results about polynomials, one due to W. Markov and the other due to Duffin and Schaeffer, are obtained in this paper. An interesting result of S. Bernstein, which went unnoticed until it was rediscovered by P. Erdos, years later, is also generalized. Our results are especially amenable to numerical calculations, and may, therefore, be of some practical importance.

     

Alkali-induced effects on metal substrates and coadsorbed molecules

We present results of ab initio electronic structure calculations based on density functional theory which show in detail several effects of alkali adsorption on metal substrates and on molecules coadsorbed on the substrate. First, calculations of the isoelectronic reactivity index demonstrate a dramatic enhancement of the electronic polarizability of the metal substrate extending it several angstroms into the vacuum. This phenomenon is traceable to an unusual feature induced in the surface potential on alkali adsorption. The effect appears to be general and helps explain the observed substantial decrease in the vibrational frequency of molecules such as CO and O₂ when co-adsorbed with alkalis on metal surfaces. Next, for the oxidation of CO on Pd(111), we illustrate the changes in the reaction pathway and activation energy barriers induced in the presence of coadsorbed K. PACS 73.20.-r; 71.15.-m     

Spatial-dependent probe transmission based high-precision two-dimensional atomic localization

Herein, we propose a scheme for the realization of two-dimensional atomic localization in aλ-type three-level atomic medium such that the atom interacts with the two orthogonal standing-wave fields and a probe field. Because of the spatially dependent atom-field interaction, the information about the position of the atom can be obtained by monitoring the probe transmission spectra of the weak probe field for the first time. A single and double sharp localized peaks are observed in the one-wavelength domain. We have theoretically archived high-resolution and high-precision atomic localization within a region smaller thanλ/25×λ/25. The results may have potential applications in the field of nano-lithography and advance laser cooling technology.