The periodic solutions of the second order nonlinear difference equation

Periodic and asymptotically periodic solutions of the nonlinear equation OZX~ +- a f(xn) = 0, n E N, are studied

On the hyperbolic partial difference equations and their oscillatory properties

For the solutions of hyperbolic partial difference equation D2/1,2 y(m,n) = a(m,n) y(m,n) satisfying some boundary conditions an analytical formula is presented. The solutions are then studied in relation to their oscillatory properties

Color-octet scalars at the LHC

Elements of the phenomenology of color-octet scalars (sgluons), as predicted in the hybrid N=1/N=2 supersymmetric model, are discussed in the light of forthcoming experiments at the CERN Large Hadron Collider.Comment: LaTeX, 10 pages, 4 figures. Talk at the Epiphany Conference on Hadron Interactions at the Dawn of the LHC, 5-7 January 2009, Cracow, Polan

NASSAM: a server to search for and annotate tertiary interactions and motifs in three-dimensional structures of complex RNA molecules

Similarities in the 3D patterns of RNA base interactions or arrangements can provide insights into their functions and roles in stabilization of the RNA 3D structure. Nucleic Acids Search for Substructures and Motifs (NASSAM) is a graph theoretical program that can search for 3D patterns of base arrangements by representing the bases as pseudo-atoms. The geometric relationship of the pseudo-atoms to each other as a pattern can be represented as a labeled graph where the pseudo-atoms are the graph's nodes while the edges are the inter-pseudo-atomic distances. The input files for NASSAM are PDB formatted 3D coordinates. This web server can be used to identify matches of base arrangement patterns in a query structure to annotated patterns that have been reported in the literature or that have possible functional and structural stabilization implications. The NASSAM program is freely accessible without any login requirement at http://mfrlab.org/grafss/nassam/

UV cross-linked polyvinylpyrrolidone electrospun fibres as antibacterial surfaces

Many bacteria become progressively more resistant to antibiotics and it remains a challenging task to control their overall levels. Polymers combined with active biomolecules come to the forefront for the design of antibacterial materials that can address this encounter. In this work, we investigated the photo-crosslinking approach of UV-sensitive benzophenone molecule (BP) with polyvinylpyrrolidone (PVP) polymer within electrospun fibres. The BP and PVP solutions allowed fabricating polymer mats that were subsequently functionalised with antibacterial lysozyme. The physical properties of the crosslinked electrospun fibres were investigated by scanning electron microscopy and atomic force microscopy. The average diameter of the obtained fibres decreased from 290 ± 50 nm to 270 ± 70 nm upon the addition of the crosslinking molecules and then to 240 ± 80 nm and 180 ± 90 nm after subsequent crosslinking reaction at an increasing time: 3 and 5 h, respectively. The peak force quantitative nanomechanical mapping (PF-QNM) indicated the increase of DMT modulus of obtained cross-linked fibres from 4.1 ± 0.8 GPa to 7.2 ± 0.5 GPa. Furthermore, the successful crosslinking reaction of PVP and BP solution into hydrogels was investigated in terms of examining photo-crosslinking mechanism and was confirmed by rheology, Raman, Fourier transform infrared and nuclear magnetic resonance. Finally, lysozyme was successfully encapsulated within cross-linked PVP-BP hydrogels and these were successfully electrospun into mats which were found to be as effective antibacterial agents as pure lysozyme molecules. The dissolution rate of photo cross-linked PVP mats was observed to increase in comparison to pure PVP electrospun mats which opened a potential route for their use as antibacterial, on-demand, dissolvable coatings for various biomedical applications

R3D-BLAST: a search tool for similar RNA 3D substructures

R3D-BLAST is a BLAST-like search tool that allows the user to quickly and accurately search against the PDB for RNA structures sharing similar substructures with a specified query RNA structure. The basic idea behind R3D-BLAST is that all the RNA 3D structures deposited in the PDB are first encoded as 1D structural sequences using a structural alphabet of 23 distinct nucleotide conformations, and BLAST is then applied to these 1D structural sequences to search for those RNA substructures whose 1D structural sequences are similar to that of the query RNA substructure. R3D-BLAST takes as input an RNA 3D structure in the PDB format and outputs all substructures of the hits similar to that of the query with a graphical display to show their structural superposition. In addition, each RNA substructure hit found by R3D-BLAST has an associated E-value to measure its statistical significance. R3D-BLAST is now available online at http://genome.cs.nthu.edu.tw/R3D-BLAST/ for public access

Color-Octet Scalars of N=2 Supersymmetry at the LHC

The color gauge hyper-multiplet in N=2 supersymmetry consists of the usual N=1 gauge vector/gaugino super-multiplet, joined with a novel gaugino/scalar super-multiplet. Large cross sections are predicted for the production of pairs of the color-octet scalars $\sigma$ [sgluons] at the LHC: $gg, q\bar{q} \to \sigma\sigma^{\ast}$. Single $\sigma$ production is possible at one-loop level, but the $g g\to \sigma$ amplitude vanishes in the limit of degenerate $L$ and $R$ squarks. When kinematically allowed, $\sigma$ decays predominantly into two gluinos, whose cascade decays give rise to a burst of eight or more jets together with four LSP's as signature for $\sigma$ pair events at the LHC. $\sigma$ can also decay into a squark-antisquark pair at tree level. At one-loop level $\sigma$ decays into gluons or a $t \bar t$ pair are predicted, generating exciting resonance signatures in the final states. The corresponding partial widths are very roughly comparable to that for three body final states mediated by one virtual squark at tree level.Comment: LaTeX, 12 pages, 5 embedded figures. Added a couple of references; version to appear in Phys. Lett.