Nearly perfect systems and effective generalizations of Shidlovski's Theorem

An effective proof of Shidlovski's Theorem is presented. The proof utilizes partial differential operators. A number of generalizations of Shidlovski's Theorem are proven, including results about approximation at more than one point. Additionally, partial differential equations are considered. The new methods give a particularly direct proof of Shidlovski's Theorem.     

Monte carlo methods and lattice discontinuities

The choice of the Monte Carlo method for the theoretical study of lattice discontinuities, such as surfaces, grain boundaries and dislocations is justified. A brief, non-rigorous discussion of the basic statistical mechanics required to develop the Monte Carlo method is given. Current work in the theoretical study of interfacial systems in solids is reviewed and problems to which the Monte Carlo method might be applied are suggested.     

The simultaneous diophantine approximation of values of functions satisfying certain n variable q-difference equations

In a previous paper lower bounds were obtained on the simultaneous diophantine approximation of values of certain functions which satisfy linear q-difference equations. In the present paper these results are generalized from n = 1 to n > 1 variables. In order to better see what some of these solutions “look like” the algebraic properties of certain classes of functions are investigated, particularly with regard to a type of multiplication which is analogous to the convolution product. At the end of the paper such algebraic results are also obtained for the case n = 1.     

Quasiconformal extensions to space of Weierstrass-Enneper lifts

The Ahlfors-Weill extension of a conformal mapping of the disk is generalized to the Weierstrass-Enneper lift of a harmonic mapping of the disk to a minimal surface, producing homeomorphic and quasiconformal extensions to space. The extension is defined through the family of best Möbius approximations to the lift applied to a bundle of euclidean circles orthogonal to the disk. Extension of the planar harmonic map is also obtained subject to additional assumptions on the dilatation. The hypotheses involve bounds on a generalized Schwarzian derivative for harmonic mappings in terms of the hyperbolic metric of the disk and the Gaussian curvature of the minimal surface. Hyperbolic convexity plays a crucial role.     

Synthesis of a porphyrin-fullerene pinwheel

We disclose the synthesis of a porphyrin-fullerene pinwheel that was subsequently observed by scanning tunneling microscopy. The molecule was designed to further our understanding of fullerene-surface interactions, directional control, and surface-rolling versus pivoting capabilities of this class of nanomachines. The inner porphyrin provides the square planar configuration that might lead to realization of the pinwheel spiraling motion on surfaces.     

The study of the changes in the thermal properties of <Emphasis Type="Italic">Labeo rohita</Emphasis> bones due to arsenic exposure

The paper presents the changes in the thermal properties of control, arsenic exposed and DMSA treated Labeo rohita bones by using thermo analytical techniques. The result shows that the mass loss due to the thermal decomposition occurs in three distinct steps due to loss of water, organic and inorganic materials. The arsenic exposed bones present a different thermal behaviour compared to the control bones. The residue masses are increased due to arsenic exposure, while the DMSA treatment reduces the residue mass level. These thermal characteristics can be used as a qualitative method to check the metal accumulation in samples.     

Modulation instability in silicon photonic nanowires

We demonstrate that strong modulation instability (MI) of copropagating optical waves can be observed in Si photonic nanowires with a length of only a few millimeters. We consider two distinct cases, namely one in which one wave propagates in the normal group-velocity dispersion (GVD) region and the other one experiences anomalous GVD, and a second case in which both waves propagate in the anomalous GVD region. In both cases we show that, for comparable optical powers, the peak value of the MI gain spectrum is 2 to 3 orders of magnitude larger than that achieved in optical fibers.     

Direct equilibration of soil water for delta(18)O analysis and its application to tracer studies

Current methods for stable oxygen isotopic (delta (18)O) analysis of soil water rely on separation of water from the soil matrix before analysis. These separation procedures are not only time consuming and require relatively large samples of soil, but also have been shown to introduce a large potential source of error. Current research at Queen's University Belfast is focused on using direct equilibration of CO(2) with the pore water to eliminate this extraction step using the automated Multiprep system and a Micromass Prism III isotope ratio mass spectrometer (IRMS). The findings of this research indicate the method is less time consuming, more reliable, and reproducible to within accepted limits (+/-0.1% per thousand delta (18)O). In this study the direct equilibration method is used to analyse delta (18)O tracer profiles in the unsaturated zone of field soils, concurrently with chloride tracer profiles, which can be used to assess infiltration rates and mechanisms through the unsaturated zone. Copyright 1999 John Wiley & Sons, Ltd.     

Secondary ion yields produced by keV atomic and polyatomic ion impacts on a self-assembled monolayer surface

A suite of keV polyatomic or 'cluster' projectiles was used to bombard unoxidized and oxidized self-assembled monolayer surfaces. Negative secondary ion yields, collected at the limit of single ion impacts, were measured and compared for both molecular and fragment ions. In contrast to targets that are orders of magnitude thicker than the penetration range of the primary ions, secondary ion yields from polyatomic projectile impacts on self-assembled monolayers show little to no enhancement when compared with monatomic projectiles at the same velocity. This unusual trend is most likely due to the structural arrangement and bonding characteristics of the monolayer molecules with the Au(111). Copyright 1999 John Wiley & Sons, Ltd.