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.     

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.     

On the Behavior of Some Second Order Nonlinear Differential Equations

Qualitative behavior of second order nonlinear differential equations of type y″+p(t)y+q(t)f(y)=0, is studied. It includes properties such as positivity, number of zeros, oscillating nature, boundedness and monotonicity of the solutions.     

关于不含k-C-圈的n阶r-一致超图的若干结果

主要讨论了不含k-C-圈的n阶r-一致超图,对不同的k,分别得出了它的极大边数的一个下界,并且得出在有些情况下它的下界是最大的.另外,我们得到了Krn含k-C-圈的一个充分必要条件.     

Measurement of surface topography by RGB Shadow-Moiré with direct phase demodulation

In this paper we present the application of a direct demodulation method for the measurement of surface topography by means of Shadow-Moiré. In our set-up, we use three LEDs (with green, red and blue peak wavelengths) to illuminate the grating. Due to the different position of these light sources, a polychromatic Shadow-Moiré fringe pattern is produced, which can be described as the superposition of three monochromatic (red, green and blue) fringe patterns. Taking the image of this polychromatic fringe pattern with a RGB CCD camera, we get a monochromatic fringe pattern stored at each RGB channel of the CCD. The direct demodulation algorithm employed uses these fringe patterns to calculate the wrapped phase map. After unwrapping the phase map using a standard multi-grid technique, we implemented an automatic procedure to detect the area of interest of the phase map by removing low modulation zones and to calculate the absolute value of the phase. In this way it is possible to determine the topography of a surface with a single RGB snapshot maintaining a simple experimental set-up, which is an important feature, especially for the study of dynamic phenomena such as deformations. We present the experimental results obtained after measuring different objects with both smooth and rough surface textures.     

The electrochemical reduction of perezone in the presence of benzoic acid in acetonitrile

An electrochemical study using transient techniques of a quinone-type natural product, perezone, has been performed in acetonitrile and in the presence of benzoic acid. Using linear sweep voltametry and single potential step chronoamperometry, it was possible to establish that the reduction mechanism of perezone involves a monoelectronic charge-transfer step, followed by a protonation step and homogeneous charge transfer due to disproportionation of the protonated intermediate. The mechanism for the homogeneous charge-transfer step was found to be of the type DISP1 (disproportionation order one) from the results of double potential step chronoamperometry experiments. The occurrence of the DISP1 mechanism was provoked by the mildly acidic medium used in this study.