The eigenvalue problem for solitary waves of a boussinesq equation,via a generalization of the rouché theorem

We consider the study of an eigenvalue problem obtained by linearizing about solitary wave solutions of a Boussinesq equation. Instead of using the technique of Evans functions as done by Pego and Weinstein in [R. Pego and M. Weinstein, Convective Linear Stability of Solitary Waves for Boussinesq equation. AMS, 99, 311–375] for this particular problem, we perform Fourier analysis to characterize solutions of the eigenvalue problem in terms of a multiplier operator and use the strong relationship between the eigenvalue problem for the linearized Boussinesq equation and the eigenvalue problem associated with the linearization about solitary wave solutions of a special form of the KdV equation. By using a generalization of the Rouché Theorem and the asymptotic behavior of the Fourier symbol corresponding to the eigenvalues problem for the Boussinesq equation and the Fourier symbol corresponding to the eigenvalues problem for the KdV equation, we show nonexistence of eigenvalues with respect to weighted space in a planar region containing the right-half plane.     

Two-time-scale Jump-Diffusion Models with Markovian Switching Regimes

This work is concerned with two-time-scale jump diffusion models modulated by continuous-time Markov chains. One of our motivations stems from generalization of insurance risk models. The models are hybrid in the sense that they involve both continuous dynamics and discrete events. Two cases are considered. One of them has a fast-varying switching process, and the other contains a rapidly fluctuating diffusion. Two-time scale is used for complexity reduction. Using weak convergence methods, we derive their limit processes. The insight and implication provided by the analysis are: to reduce the complexity, one can ignore the detailed variations and concentrate on the limit or the reduced models.     

Fast‐scanning high‐flux microprobe for biological X‐ray fluorescence microscopy and microXAS

There is a growing interest in the biomedical community in obtaining information concerning the distribution and local chemical environment of metals in tissues and cells. Recently, biological X‐ray fluorescence microscopy (XFM) has emerged as the tool of choice to address these questions. A fast‐scanning high‐flux X‐ray microprobe, built around a recently commissioned pair of 200 mm‐long Rh‐coated silicon Kirkpatrick–Baez mirrors, has been constructed at BioCAT beamline 18ID at the Advanced Photon Source. The new optical system delivers a flux of 1.3 × 10¹² photons s^?1 into a minimum focal spot size of ～3–5 µm FWHM. A set of Si drift detectors and bent Laue crystal analyzers may be used in combination with standard ionization chambers for X‐ray fluorescence measurements. BioCAT's scanning software allows fast continuous scans to be performed while acquiring and storing full multichannel analyzer spectra per pixel on‐the‐fly with minimal overhead time (<20 ms per pixel). Together, the high‐flux X‐ray microbeam and the rapid‐scanning capabilities of the BioCAT beamline allow the collection of XFM and micro X‐ray absorption spectroscopy (microXAS) measurements from as many as 48 tissue sections per day. This paper reports the commissioning results of the new instrument with representative XFM and microXAS results from tissue samples.     

Vibrational Spectroscopic Analysis of L,D-Dipeptides

Raman and infrared spectra of Boc-D-Leu-L-Leu-OMe, Boc-L-Ile-D-aIle-OMe and its N-deuterated derivative have been obtained. Normal mode frequencies on the models of these dipeptides have been calculated and the conformationally sensitive amide I, II, III and V modes are compared with the experimentally observed frequencies. The calculated frequencies are in good agreement with the observed frequencies. It is observed that the amide frequencies in these dipeptides are not very sensitive to their backbone conformation. This is in contrast to the well established conformational dependence of the amide modes in peptides, polypeptides and proteins. The normal mode calculations on these peptides also show absence of mixing in amide I and II modes, and hence lack of appreciable splitting in these modes due to transition dipole coupling.

     

Nucleation of the Al6(Fe,Mn)-to-α-Al–(Fe,Mn)–Si transformation in 3XXX aluminium alloys. II. Transformation in cast aluminium alloys

The nucleation behaviour of the homogenization-induced Al₆(Fe,?Mn)-to-α-Al–(Fe,?Mn)–Si transformation is investigated in a companion paper to part I (a study with roll-bonded diffusion couples). Diffusion experiments using silicon-coated Al–0.53?wt%?Fe–1.02?wt%?Mn alloy blocks allow control of the thermodynamic driving force for transformation within a microstructure typical of a cast ingot. As expected, this microstructure appears to give ready and yet stochastic nucleation as silicon diffuses into the alloy sections. In addition, transmission electron microscopy is used to analyse partially transformed particles in heat-treated alloy samples of fixed silicon content. This confirms the suggestion made in part I that the transformation preferentially nucleates at matrix grain/cell boundaries. Nucleation theory suggests this results from the ability of the boundaries to relieve volume changes associated with the nucleation event.     

Contact mechanisms and design principles for alloyed Ohmic contacts to p-type GaN

Contact mechanisms and design principles of alloyed Ohmic contacts to p-type GaN (p-GaN) are studied. Illustrative studies include bilayer, trilayer and quadrilayer Ohmic contacts. Almost all contacts appear to follow the proposed design principles. The removal of the surface insulating layer, preferably by plasma etching, leads to metal/semiconductor barrier lowering. This, together with thermionic emission, plays a crucial role for yielding low-resistance metal/p-GaN contacts. Band-gap narrowing and/or image force lowering due to heavy doping also contribute to the low contact resistivity. A judicious choice of the layer thicknesses of appropriate metal combination, rapid thermal annealing (RTA) time, RTA temperature and RTA ambient can produce large-work-function alloy(s) in contact with the p-GaN epitaxial layer, creating a robust low-resistivity thermionic-emission-induced Ohmic contact. The fundamental physics of contact mechanisms and design principles proposed in the study is useful for making other contacts. These are general enough to be extended to other III–V nitride materials, at the least.     

Neighbourhood-Perfect Line Graphs

We show that the line graph of any balanced hypergraph is neighbourhood-perfect. This result is a hypergraphic extension of a recent theorem in [GKLM] saying that the line graphs of bipartite graphs are neighbourhood-perfect. The note contains also a graphical extension of the same theorem: the characterization of all graphs with neighbourhood-perfect line graph. The proof relies on a characterization of neighbourhood-perfect graphs among line graphs in terms of forbidden induced subgraphs.