Algebraic theory of optimal filterbanks

We introduce an optimality theory for finite impulse response (FIR) filterbanks using a general algebraic point of view. We consider an admissible set /spl Lscr/ of FIR filterbanks and use scalability as the main notion based on which performance of the elements in /spl Lscr/are compared. We show that quantification of scalability leads naturally to a partial ordering on the set /spl Lscr/. An optimal solution is, therefore, represented by the greatest element in /spl Lscr/. It turns out that a greatest element does not necessarily exist in /spl Lscr/. Hence, one has to settle with one of the maximal elements that exist in /spl Lscr/. We provide a systematic way of finding a maximal element by embedding the partial ordering at hand in a total ordering. This is done by using a special class of order-preserving functions known as Schur-convex. There is, however, a price to pay for achieving a total ordering: there are infinitely many possible choices for Schur-convex functions, and the optimal solution specified in /spl Lscr/ depends on this (subjective) choice. An interesting aspect of the presented algebraic theory is that the connection between several concepts, namely, principal component filterbanks (PCFBs), filterbanks with maximum coding gain, and filterbanks with good scalability, is clearly revealed. We show that these are simply associated with different extremal elements of the partial ordering induced on /spl Lscr/ by scalability.     

Thin microwire with negative magnetostriction in a zero magnetic field

The effect of residual mechanical stresses on the distribution of magnetization in thin metal microwires with negative magnetostriction has been studied in a zero magnetic field. It is established that the microwire has a nonzero residual magnetization in the absence of twisting and bulging rotational modes.     

Analysis of spontaneous electrochemical oscillations by energy distribution technique

Analysis of non-stationary electrochemical oscillations emerges utilization of the techniques allowing an observation of time evolution of their parameters such as instantaneous frequency, amplitude or frequency band. An algorithm of extraction of these parameters can be based on one of linear or quadratic time-frequency representations of oscillations record. In this paper, the authors present representatives of such transformations (Choi-Williams and Cone-shaped) originating from one of the most popular joint time-frequency energy distribution—Wigner-Ville distribution. Short introduction to the mathematics of the topic discussed is provided, then the authors present an example of application in the analysis of current oscillations of copper dissolution process.     

Problems of Wastewater Treatment and Methods of Solving Them

The studies show that in the combined use of biological and chemisorption stages of treatment, a deeper degree of removal of industrial pollutants from wastewaters is attained. The chemisorption stage allows stabilizing the treatment process in different concentration-temperature drops and increasing the degree of removal of synthetic surfactants (SSF), petroleum products, and nitrogen compounds. The possibility of regulating the selectivity of the treatment process by varying the composition of the chemisorption material is demonstrated.     

Reactions Between Ingredients in Binary Silicate Glasses

It is demonstrated that the density of binary glasses upon variation of the molar content of the modifier in their compositions obeys a parabolic dependence, whose parameters can be used to estimate the extent and type of reactions between the components. The reaction parameters in glasses that are prone to liquation are lower by an order of magnitude and have the negative sign.     

Orthorhombic Materials and Perfect Lenses

The potential of orthorhombic materials for perfect lenses is theoretically examined.     

X-Ray Study of the Effect of Heat on the Structural Parameters of Armos Fibres

In studying a series of fibre samples spun in steady-state conditions, the following was found: as a function of the conditions of processing Armos fibre, two structural modifications of the polymer can form; intensive crystallization of the modification corresponding to the 28.7° reflection begins in heat treatment above 220°C; above 320°C, intensive crystallization of the modification corresponding to the 14.25° reflection is observed; at 360°C, symbatic enhancement of the intensities of both reflections with a weak change in the other structural parameters of the fibre is observed.     

The measurement of the diffusion coefficient and the sorption isotherm of water in paint films

An experimental technique together with a numerical model is proposed with which the diffusion coefficient and the sorption isotherm of water in paint can be measured. Inside a closed vessel, paint films are on stainless-steel plates. Water is present as water vapour in the air and in the paint. After blowing dry or wet air through the vessel for some time, the situation moves to a new equilibrium. The relative humidity of the air inside the vessel is measured as a function of time. From fitting the theoretical/numerical model against the experimental values, follow the diffusion coefficient and the sorption isotherm of water in the paint. The results show large scattering. When the independently measured sorption isotherm is used as an input parameter in the model, the fitting procedure gives much smaller scattering for the diffusion coefficient.