Vibrational spectra and ab initio computations of sarcosinium oxalate monohydrate

Single crystals of sarcosinium oxalate monohydrate (SOM) are grown by the slow-evaporation technique at ambient temperature, and vibrational spectroscopic analysis is carried out using NIR-FT Raman, FT-IR, and SERS spectra. The normal mode frequencies and corresponding vibrational analysis of SOM are examined theoretically using the Gaussian’98 set of quantum chemical codes. The two bands present in the SOM ν C=O region, clearly observed in the Raman spectrum, are assigned to “free” and “bonded” carbonyl groups with the hydrogen atom. Vibrational analysis indicates the presence of C-H—O hydrogen bonding interaction producing a blueshift of the C-H stretching frequency.     

Enlightened sonochemistry

Sonochemistry and photochemistry are initiated by high-energy transient species, which may be prone to mutual interaction. Electronic excitation of solutes by energy transfer from high energy species generated in collapsing bubbles is already supported by experimental evidence. The rates of photochemical reactions can be affected by ultrasound-induced mixing of liquids caused by microstreaming near pulsating cavitation bubbles and shockwaves due to bubble collapse. This may not only improve light absorption but also modify the pathway of reaction by increasing the contact between reagents. Finally, one may speculate about a potentially new chemistry of photoexcited solutes under the extreme conditions inside cavitation microreactors. This work reviews research on the excitation of solutes by sonoluminescence, the combined effects of ultrasound and light on liquid systems and the effect of ultrasound on photocatalytic reactions.     

Barycentric coordinates for convex sets

In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation in higher dimensions. Moreover, there has been no attempt to extend these functions into the continuous domain, where barycentric coordinates are related to Green’s functions and construct functions that satisfy a boundary value problem. First, we review the properties and construction of barycentric coordinates in the discrete domain for convex polytopes. Next, we show how these concepts extend into the continuous domain to yield barycentric coordinates for continuous functions. We then provide a proof that our functions satisfy all the desirable properties of barycentric coordinates in arbitrary dimensions. Finally, we provide an example of constructing such barycentric functions over regions bounded by parametric curves and show how they can be used to perform freeform deformations.      

Optimality relationships forp-cyclic SOR

Summary The optimality question for blockp-cyclic SOR iterations discussed in Young and Varga is answered under natural conditions on the spectrum of the block Jacobi matrix. In particular, it is shown that repartitioning a blockp-cyclic matrix into a blockq-cyclic form,q, results in asymptotically faster SOR convergence for the same amount of work per iteration. As a consequence block 2-cyclic SOR is optimal under these conditions.Research supported in part by the US Air Force under Grant no. AFOSR-88-0285 and the National Science Foundation under grant no. DMS-85-21154 Present address: Boeing Computer Services, P.O. Box 24346, MS 7L-21, Seattle, WA 98124-0346, USA     

A Framework for Monitoring Progress and Planning Teaching Towards the Effective Use of Computer Algebra Systems

This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS technology and how these may be used to monitor students' developing use of CAS; from this, the framework may be used to plan teaching in order to gain greater benefit from the availability of CAS. Four case studies describing students' development over a semester are reported. These demonstrate a variety of combinations of technical competencies and personal attributes. They indicate the importance of both the technical and personal aspects but suggest that negative attitudes rather than technical difficulties can limit the effective use of CAS. Finally practical suggestions are given for teaching strategies which may promote effective use of CAS.This revised version was published online in September 2005 with corrections to the Cover Date.     

Co-doped In2O3 thin films: Room temperature ferromagnets

Laser-ablated Co-doped In₂O₃ thin films were fabricated under various growth conditions on R-cut Al₂O₃ and MgO substrates. All Co:In₂O₃ films are well-crystallized, single phase, and room temperature ferromagnetic. Co atoms were well substituted for In atoms, and their distribution is greatly uniform over the whole thickness of the films. Films grown at 550 °C showed the largest magnetic moment of about 0.5 μ_B/Co, while films grown at higher temperatures have magnetic moments of one order smaller. The observed ferromagnetism above room temperature in Co:In₂O₃ thin films has confirmed that doping few percent of magnetic elements such as Co into In₂O₃ could result in a promising magnetic material.