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.     

Preparation and characterization of the antibacterial Cu nanoparticle formed on the surface of SiO2 nanoparticles

Cu deposition on the surface of spherical SiO2 nanoparticles was studied to achieve the hybrid structure of Cu-SiO2 nanocomposite. SiO2 nanoparticles served as seeds for continuous Cu metal deposition. The chemical structure and morphology were studied with X-ray photoelectron spectroscopy (XPS), scanning electron microscope energy dispersive X-ray (SEM-EDX), and a transmission electron microscope (TEM). The antibacterial properties of the Cu-SiO2 nanocomposite were examined with disk diffusion assays. The homogeneously formed Cu nanoparticles on the surface of SiO2 nanoparticles without aggregation of Cu nanoparticles showed excellent antibacterial ability.     

Science at the Hard X-ray Diffraction Limit (XDL2011), Part 1

There is growing excitement in the synchrotron materials science community about the potential of nearly diffraction-limited, high-repetition rate, hard X-ray sources, such as an Energy Recovery Linac (ERL) or an Ultimate Storage Ring (USR), and that these sources will pave the way to scientific insights and discoveries not possible with existing facilities. These future sources will deliver highly coherent, nearly diffraction-limited X-ray beams that will power ultra-intense, nanometer-scale X-ray probes and imaging capabilities approaching atomic resolution. They will produce X-ray pulses at MHz to GHz repetition rates and span pulse durations from below 50 femtoseconds to tens of picoseconds, enabling new classes of experiments in hard X-ray science.     

On the linear dependence of 13C spin polarization parameters

The Jahn-Teller (J-T) effect in systems of four-fold symmetry is well known to differ from that in all other point groups with respect to the nature of the J-T active normal modes of vibration. The present report addresses some previously unnoticed features which are of intrinsic importance in recognizing and understanding the unique manifestations of quadrate symmetry in both the static and dynamic Jahn-Teller effects. We first consider the nature of the static J-T potential surfaces when coupling to and strains in two modes, b ₁ and b ₂, are included in the hamiltonian.

The second part of this paper is devoted to an examination of the dynamic J-T effect in four-fold systems. Utilizing both perturbation theory and numerical solution to the Schrödinger equation, we examine the spin-hamiltonian parameters for a metalloporphyrin ³ E_u triplet state and discuss some dynamical processes, including reorientation of the system between minima, spin-lattice relaxation, and the dependences of these phenomena on the nature and magnitude of the off-diagonal terms in the hamiltonian. There emerge from this analysis several signal differences between the Jahn-Teller effect for a doubly degenerate state in four-fold systems and in the more usual cubic or tetrahedral situation.     

Piecewise linear prewavelets over type-2 triangulations

In this article, we study the construction of piecewise linear prewavelets over type-2 triangulations. Different from a so-called semi-prewavelet approach, we investigate the orthogonal conditions directly and obtain parameterized prewavelets with a smaller support. The conditions for parameterized prewavelet basis on the parameters are also given.     

New type of eigenoscillations and total-transmission resonance through an iris with below-cutoff hole in a rectangular waveguide

The total-transmission phenomenon of the main mode of a rectangular waveguide through a below-cutoff hole in the waveguide shorting before the point of occurrence of the higher-order waveguide modes is found. The effect is due to generation of high-Q eigenoscillations at the evanescent E₁₁ mode and is originated from a specific oscillation formed near a step junction of two waveguides, namely a larger single-mode waveguide and a smaller below-cutoff one. The iris composed of such two junctions is longitudinally symmetric. Thus, a pair of resonances occurs in accordance with the existence of a pair of symmetric and antisymmetric field distributions at the iris. Analogy with the recently found effects in double-periodic gratings with small holes is revealed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 2, pp. 111–121, February 2008.