The prediction of coal properties using compressed infrared data from osculating polynomials

Reduction of the representation of infrared spectra from coal samples by osculating polynomials of degree nine is discussed. The reduced representation contains polynomial coefficients of order zero to four. Mathematical models of the original spectra are obtained by linear combination of the coefficients. These compressed models are statistically correlated to coal properties, namely, volatile matter, fixed carbon, ash content, heating value, hydrogen, carbon, sulphur, nitrogen, and maximum vitrinite reflectance, and the results are compared with those previously obtained from second derivatives of the same spectra. The use of compressed data, while giving slightly better correlations for some of the properties, has the advantage of requiring less computational time.     

Some characterisations of supported algebras

We give several equivalent characterisations of left (and hence, by duality, also of right) supported algebras. These characterisations are in terms of properties of the left and the right parts of the module category, or in terms of the classes L₀ and R₀ which consist respectively of the predecessors of the projective modules, and of the successors of the injective modules.     

In‐situ synthesis of transparent and conductive carbon nanotube networks

A method for the production of transparent carbon nanotube networks (CNTNs) over transparent substrates was developed. In this method, CNTNs were grown directly in the target surface by applying the catalyst in specific zones of the substrate through lithographic techniques. The networks can be also transferred from the original substrate to other surfaces. The newly grown carbon nanotubes have a very high aspect ratio (>50000). Thus far, networks with an optical transmittance of 94% at 550 nm and a surface resistivity of 3.6 kΩ/sq have been produced. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elastic instability of the nano-structured state as an intrinsic probe to study the early formation stages of sol–gel derived (Pb<Subscript>1-x</Subscript>Ca<Subscript>x</Subscript>)TiO<Subscript>3</Subscript> thin films

A novel method to investigate the early formation stages of polycrystalline (Pb_1-xCa_x)TiO₃ (PCT) perovskite films by means of traditional Brillouin and micro-Brillouin spectroscopy (BS, mBS) is described in the present work. The films were prepared by chemical solution deposition (CSD) onto oxidized (100)Si substrates and treated at temperatures between 350–650 °C by rapid thermal processing (RTP). The elastic instability observed by Brillouin spectroscopy at the nano-structured state of the PCT films was used here to determine their crystallization temperatures. Coexistence of different nanocrystalline phases (e.g., pyrochlore, perovskite) in the films could also be detected by this technique. The reliability of these results is demonstrated by complementary information obtained by X-ray diffraction (XRD) and scanning force microscopy (SFM). The effects of the annealing temperature and of the Ca²⁺ content on the crystallization process of these films are also discussed. PACS 78.35.+c; 77.84.-s; 61.82.Rx     

关于离散HJB方程的下解与上解

本文讨论HJB方程上、下解的几个性质,并讨论了从上解出发的一个迭代法的收敛性.     

Adjugates in Banach algebras

A simple formula for the adjugate of a block triangle offers an alternative route to the determinant theory for Banach algebras.

     

Fractal strings as an alternative justification for El Naschie''s cantorian spacetime and the fine structure constant

Beginning with the most general fractal strings/sprays construction recently expounded in the book by Lapidus and Frankenhuysen, it is shown how the complexified extension of El Naschie's cantorian-fractal spacetime model belongs to a very special class of families of fractal strings/sprays whose scaling ratios are given by suitable pinary (pinary, p prime) powers of the Golden Mean. We then proceed to show why the logarithmic periodicity laws in Nature are direct physical consequences of the complex dimensions associated with these fractal strings/sprays. We proceed with a discussion on quasi-crystals with p-adic internal symmetries, von Neumann's Continuous Geometry, the role of wild topology in fractal strings/sprays, the Banach-Tarski paradox, tesselations of the hyperbolic plane, quark confinement and the Mersenne-prime hierarchy of bit-string physics in determining the fundamental physical constants in Nature.