Dependence of the closed-shell repulsive interaction on the overlap of the electron densities

The relationship between the closed-shell repulsive interactions and overlap of the electron densities is investigated. It is found that the repulsive interactions vary in almost direct proportion to the absolute size of the density overlaps.     

Crystal Structures of Analogs of threo-Methylphenidate

The crystal structures of the chloride salts of five analogs of threo-methylphenidate have been obtained. Four of these have different substituents on the phenyl ring while the fifth is the ethyl ester of methylphenidate. All five structures have similar three-dimensional conformations and these are compared with the global minimum obtained by MM2-87 calculations. There is good agreement between the crystal structures and the computed global minimum with the major difference being the presence of a chloride counterion in the crystal structures that prevents the carbonyl oxygen from approaching the equatorial ammonium hydrogen as closely as in the computed global minimum.     

Minimization of wafer bowing in GaN-based vertical light-emitting diodes by selective area growth using metal-organic chemical vapor deposition

The effect of selective area growth (SAG) on wafer bowing of GaN-based light-emitting diodes (LEDs) is investigated. The SAG of LED structures was carried out on a silicon dioxide (SiO₂) mask pattern with periodic 1000×1000 μm openings, along the sapphire 〈1?1 0 0〉 and 〈?1?1 2 0〉 directions. The morphology of a selectively-grown n-GaN epilayer was examined in relation to various growth parameters such as temperature, pressure, and V/III ratio. Under optimized growth conditions, formation of a ridge-shaped epilayer with a v-pit free smooth surface was realized. Furthermore, the ridge-shaped vertical LED structure, after the removal of the sapphire substrate by laser lift-off (LLO) showed less wafer bowing compared with conventional vertical LED structures. This is attributed to the suppression of lateral strain and dislocations during the site-selective growth process, due to a reduction in the lateral dimensions.     

Effect of particle size on the photochromic response of PWA/SiO2 nanocomposite

A series of photochromic phosphotungstic acid (PWA)/SiO₂ composites were synthesized using the sol-gel method. Depending on the feeding schedule of PWA during synthesis, the size of the formed PWA/SiO₂ particles varied considerably from as small as 1.2 nm to ca. 10 nm. With decreasing silica particle size, the total contact area/interaction between SiO₂ and PWA increases, as revealed by FT-IR and solid-state ²⁹Si-NMR analyses. Particularly, when the size of PWA/SiO₂ is ~1 nm, crystallization of PWA is inhibited, and PWA presents as amorphous molecular entities distributing uniformly in the SiO₂ host, which is in evidence in the XRD spectroscopy and HR-TEM imaging. In contrast, substantial crystallization of PWA takes place when PWA/SiO₂ particles are as large as 10 nm, in which case less amount of surface free Si-OH is available for PWA to make bonds with. Photochromism occurs activated by ultraviolet light irradiation. The rate of coloration/bleaching is found to depend strongly on the particle size of PWA/SiO₂; specifically, the rate increases twice when the particle size is reduced from 10 nm to 1.2 nm.     

Testing set proportionality and the Ádám isomorphism of circulant graphs

Given two k element subsets , we give a quasi-linear algorithm to either find such that S=λT or prove that no such λ exists.This question is closely related to isomorphism testing of circulant graphs and has recently been studied in the literature.     

Binary inorganic salt mixtures as high conductivity liquid electrolytes for >100 degrees C fuel cells

We report the successful application of low-melting inorganic salts with protonated cations (e.g. ammonium) as electrolytes in fuel cells operating in the temperature range 100-200 degrees C, where even with unoptimized electrodes, cell performance is comparable to that of the phosphoric acid fuel cell operating with optimized electrodes in the same temperature range, while open circuit voltages, and efficiencies at low current densities, can be much better--and there is no need for humidification or pressure to sustain performance.     

Correlated Fractal Percolation and the Palis Conjecture

Let F ₁ and F ₂ be independent copies of one-dimensional correlated fractal percolation, with almost sure Hausdorff dimensions dim?_H(F ₁) and dim?_H(F ₂). Consider the following question: does dim?_H(F ₁)+dim?_H(F ₂)>1 imply that their algebraic difference F ₁?F ₂ will contain an interval? The well known Palis conjecture states that ‘generically’ this should be true. Recent work by Kuijvenhoven and the first author (Dekking and Kuijvenhoven in J. Eur. Math. Soc., to appear) on random Cantor sets cannot answer this question as their condition on the joint survival distributions of the generating process is not satisfied by correlated fractal percolation. We develop a new condition which permits us to solve the problem, and we prove that the condition of Dekking and Kuijvenhoven (J. Eur. Math. Soc., to appear) implies our condition. Independently of this we give a solution to the critical case, yielding that a strong version of the Palis conjecture holds for fractal percolation and correlated fractal percolation: the algebraic difference contains an interval almost surely if and only if the sum of the Hausdorff dimensions of the random Cantor sets exceeds one.     

Mathematics learning support and engagement in first year engineering

This paper considers the effects of both free optional mathematics learning support and engagement on the mathematics performance in a foundation mathematics subject of a cohort of engineering students entering university with poor mathematical skills. New engineering students were directed to either a foundation or standard mathematics subject based on the results of a placement test. For students in the foundation subject, it was found that high levels of learning support were associated with greater improvement over the semester. Some form of learning support was used by 57.9% of the students, a reasonably high proportion of the cohort. Some factors for this high level of use of learning support are considered. One possible factor, the placement test, appears to have had a positive effect. Engagement in the subject activities as measured by tutorial attendance and learning management system use was found to have a positive association with final mark. Students who utilized a high level of learning support were more likely to be more engaged with the subject, making it impossible to draw conclusions about improvements being solely due to the use of learning support.     

Radial kernels and their reproducing kernel Hilbert spaces

We describe how to use Schoenberg’s theorem for a radial kernel combined with existing bounds on the approximation error functions for Gaussian kernels to obtain a bound on the approximation error function for the radial kernel. The result is applied to the exponential kernel and Student’s kernel. To establish these results we develop a general theory regarding mixtures of kernels. We analyze the reproducing kernel Hilbert space (RKHS) of the mixture in terms of the RKHS’s of the mixture components and prove a type of Jensen inequality between the approximation error function for the mixture and the approximation error functions of the mixture components.