An introduction to preconvexity spaces

Axioms are given for a preconvexity space and certain consequences obtained. In particular, it is shown that in a very natural way, a preconvexity on a space yields an abstract convexity space in much the same manner as a proximity yields a topological space. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cascade polycyclization: exploration of a convergent route to access various tricyclic and tetracyclic products related to sterols

The expedient synthesis of tricyclic and tetracyclic compounds via a cascade polycyclization methodology is described. Nazarov substrates (II) containing two Michael acceptors and a cyclohexenone ester (I) underwent cycloaddition followed by intramolecular 1,4-addition to furnish, in a highly stereoselective manner, tricyclic and tetracyclic products (III). Such compounds are interesting intermediates for the synthesis of polycyclic natural and unnatural products.     

A study of biodegradation of polyethylene and biodesulfurization of rubber

Applied Biochemistry and Biotechnology - The present study provides preliminary data on the involvement of such microorganisms asAspergillus niger in the biodegradation of commercially available...     

Hydrogen electrosorption in nanocrystalline Ti-based alloys

The electrochemical behavior in alkaline solution (1 M NaOH) of nanocrystalline Ti:Ru:Fe:O (2:1:1:2) prepared by high-energy ball milling was studied over its whole electroactivity domain, with a particular emphasis on the hydrogen evolution reaction (her). Comparison has also been made with nanocrystalline Ti:Ru:Fe (2:1:1) and a mixture of Ti:TiO:Ru:Fe₂O₃ (3/2:1/2:1:1/2). It was shown by cyclic voltammetry, open circuit potential decay and chronopotentiometry measurements that hydrogen absorption in the electrode material occurs during hydrogen discharge. The electrochemical behavior of nanocrystalline Ti:Ru:Fe:O (2:1:1:2) closely follows that of Ti:Ru:Fe (2:1:1), but differs radically from that of Ti:TiO:Ru:Fe₂O₃ (3/2:1/2:1:1/2). This is due to the fact that the former two compounds contain a significant fraction of B2 phase (59 and 97 wt.%, respectively), while the latter does not. In steady state conditions, the ratio H/B2 phase in nanocrystalline Ti:Ru:Fe:O (2:1:1:2) is 0.15, about 1.6 times less than that for the O-free nanocrystalline compound. The coefficient of diffusion of hydrogen in nanocrystalline Ti:Ru:Fe:O (2:1:1:2) is 2.6×10⁻¹³ cm² s⁻¹, more than three times less than that in nanocrystalline Ti:Ru:Fe (2:1:1). The difference between the hydrogen absorption characteristics of both nanocrystalline compounds are tracked down to the fact that their B2 phases have different stoichiometries.     

Convexity and a certain propertyP m

The propertyP _m (directly analogous to Valentine’s propertyP ₃) is used to prove several curious results concerning subsets of a topological linear space, among them the following: (a) If a closed setS has propertyP _m and containsk points of local nonconvexity no distinct pair of which can see each other viaS, thenS is the union ofm − k − 1 or fewer starshaped sets. (b) Any closed connected set with propertyP _m is polygonally connected. (c) A closed connected setS with propertyP _m is anL _m−1 set (each pair of points may be joined by a polygonal arc ofm − 1 of fewer sides inS). (d) A finite-dimensional set with propertyP _m is anL _{2m − 3} set. A new proof of Tietze’s theorem on locally convex sets is given, and various examples refute certain plausible conjectures.     

Fabrication of buried waveguides in planar silica films using a direct CW laser writing technique

A CW CO₂ laser ablation technique is used to form buried waveguides in planar silica films. It is shown that the refractive index of a silica thin film is reduced sufficiently adjacent to the laser processed region to allow the fabrication of low loss waveguides. The refractive index distribution of these structures is measured using the reflectance of a focussed spot from the surface of the films. The change in refractive index is measured to be of the order of the core cladding refractive index difference of typical single mode waveguides. The spatial resolution of the reflectance technique is 1.3 μm with a refractive index resolution of ±5 × 10^?4. Devices such as 1 × 2 and 1 × 4 multi-mode interference (MMI) splitters have also been demonstrated and shown to exhibit low transmission losses.     

Enhanced stability and activity of PtRu nanotubes for methanol electrooxidation

PtRu 1D nanostructures on titanium are prepared and analysed as electrocatalysts for methanol electrooxidation. The morphology and composition of the 1D nanostructure are characterized by scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). The electrocatalytic properties of such catalysts for methanol oxidation are investigated by cyclic voltammetry (CV) and chronoamperometry (CA) in 1.0 M CH₃OH + 0.5 M H₂SO₄ aqueous solution. The results show that Pt₄₆Ru₅₄ nanotubes yields to a five-fold improvement of the mass specific activity and to a three-fold improvement of the long-term poisoning rate as compared to PtRu black of similar composition.     

Identification of switched linear systems using subspace and integer programming techniques

We consider the identification of a switched linear system which consists of linear sub-models, with a rule that orchestrates the switching mechanism between the sub-models. Taking a set of switched linear systems and using a state space framework, we show that it is possible to combine subspace methods with mixed integer programming for system identification. The states of the system are first extracted from input–output data using sub-space methods. Once the state variables are known, the switched system is re-written as a mixed logical dynamical (MLD) system and the model parameters are calculated for via mixed integer programming. We report an example at the end of this paper together with simulation results in the presence of noise.