On Fourier integral transforms for qq-Fibonacci and qq-Lucas polynomials

We study in detail two families of $q$-Fibonacci polynomials and $q$-Lucas polynomials, which are defined by non-conventional three-term recurrences. They were recently introduced by Cigler and have been then employed by Cigler and Zeng to construct novel $q$-extensions of classical Hermite polynomials. We show that both of these $q$-polynomial families exhibit simple transformation properties with respect to the classical Fourier integral transform

Lie discrete symmetries of lattice equations

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the discrete symmetries of the discrete Painlev\'e I equation and of the Toda lattice equation

On a discrete Davey-Stewartson system

We propose a differential difference equation in ${\mathcal R}^1\times {\mathcal Z}^2$ and study it by Hirota's bilinear method. This equation has a singular continuum limit into a system which admits the reduction to the Davey-Stewartson equation. The solutions of this discrete DS system are characterized by Casorati and Grammian determinants. Based on the bilinear form of this discrete DS system, we construct the bilinear B\"{a}cklund transformation which enables us to obtain its Lax pair.Comment: 12 pages, 2 figure

The Kundu--Eckhaus equation and its discretizations

In this article we show that the complex Burgers and the Kundu--Eckhaus equations are related by a Miura transformation. We use this relation to discretize the Kundu--Eckhaus equation.Comment: 10 page

The Jacobi last multiplier for difference equations

We present a discretization of the Jacobi last multiplier, with some applications to the computation of solutions of difference equations.Comment: 9 page

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

The eggshell membrane : A potential biomaterial for corneal wound healing

The eggshell membrane (ESM) is an abundant resource with innate complex structure and composition provided by nature. With at least 60 million tonnes of hen eggs produced globally per annum, utilisation of this waste resource is highly attractive in positively impacting sustainability worldwide. Given the morphology and mechanical properties of this membrane, it has great potential as a biomaterials for wound dressing. However, to date, no studies have demonstrated nor reported this application. As such, the objective of this investigation was to identify and optimise a reproducible extraction protocol of the ESM and to assess the physical, chemical, mechanical and biological properties of the substrate with a view to use as a wound dressing. ESM samples were isolated by either manual peeling (ESM-strip) or via extraction using acetic acid [ESM-A0.5] or ethylenediaminetetraacetic acid, EDTA [ESM-E0.9]. Energy dispersive X-ray spectroscopy (EDS) confirmed that there were no traces of calcium residues from the extraction process. Fourier transform infrared (FTIR) spectroscopy revealed that the extraction method (acetic acid and EDTA) did not alter the chemical structures of the ESM and also clarified the composition of the fibrous proteins of the ESM. Scanning electron microscopy (SEM) analyses revealed a three-layer composite structure of the ESM: an inner layer as continuous, dense and non-fibrous (limiting membrane), a middle layer with a network of fibres (inner shell membrane) and the outer layer (outer shell membrane) of larger fibres. Material properties including optical transparency, porosity, fluid absorption/uptake, thermal stability, mechanical profiling of the ESM samples were performed and demonstrated suitable profiles for translational applications. Biological in vitro studies using SV40 immortalised corneal epithelial cells (ihCEC) and corneal mesenchymal stromal cells (C-MSC) demonstrated excellent biocompatibility. Taken together, these results document the development of a novel sustainable biomaterial that may be used for ophthalmic wounds and/or other biomedical therapies.Peer reviewe

Prime Focus Spectrograph (PFS) for the Subaru Telescope: Overview, recent progress, and future perspectives

PFS (Prime Focus Spectrograph), a next generation facility instrument on the 8.2-meter Subaru Telescope, is a very wide-field, massively multiplexed, optical and near-infrared spectrograph. Exploiting the Subaru prime focus, 2394 reconfigurable fibers will be distributed over the 1.3 deg field of view. The spectrograph has been designed with 3 arms of blue, red, and near-infrared cameras to simultaneously observe spectra from 380nm to 1260nm in one exposure at a resolution of ~1.6-2.7A. An international collaboration is developing this instrument under the initiative of Kavli IPMU. The project is now going into the construction phase aiming at undertaking system integration in 2017-2018 and subsequently carrying out engineering operations in 2018-2019. This article gives an overview of the instrument, current project status and future paths forward.Comment: 17 pages, 10 figures. Proceeding of SPIE Astronomical Telescopes and Instrumentation 201

T1DBase: integration and presentation of complex data for type 1 diabetes research

T1DBase () [Smink et al. (2005) Nucleic Acids Res., 33, D544–D549; Burren et al. (2004) Hum. Genomics, 1, 98–109] is a public website and database that supports the type 1 diabetes (T1D) research community. T1DBase provides a consolidated T1D-oriented view of the complex data world that now confronts medical researchers and enables scientists to navigate from information they know to information that is new to them. Overview pages for genes and markers summarize information for these elements. The Gene Dossier summarizes information for a list of genes. GBrowse [Stein et al. (2002) Genome Res., 10, 1599–1610] displays genes and other features in their genomic context, and Cytoscape [Shannon et al. (2003) Genome Res., 13, 2498–2504] shows genes in the context of interacting proteins and genes. The Beta Cell Gene Atlas shows gene expression in β cells, islets, and related cell types and lines, and the Tissue Expression Viewer shows expression across other tissues. The Microarray Viewer shows expression from more than 20 array experiments. The Beta Cell Gene Expression Bank contains manually curated gene and pathway annotations for genes expressed in β cells. T1DMart is a query tool for markers and genotypes. PosterPages are ‘home pages’ about specific topics or datasets. The key challenge, now and in the future, is to provide powerful informatics capabilities to T1D scientists in a form they can use to enhance their research