QR factoring to compute the GCD of univariate approximate polynomials

We present a stable and practical algorithm that uses QR factors of the Sylvester matrix to compute the greatest common divisor (GCD) of univariate approximate polynomials over /spl Ropf/[x] or /spl Copf/[x]. An approximate polynomial is a polynomial with coefficients that are not known with certainty. The algorithm of this paper improves over previously published algorithms by handling the case when common roots are near to or outside the unit circle, by splitting and reversal if necessary. The algorithm has been tested on thousands of examples, including pairs of polynomials of up to degree 1000, and is now distributed as the program QRGCD in the SNAP package of Maple 9.     

Nonstationary Simulation Model of Absorber with Falling Film of Suspension

A nonstationary model of SO₂ absorption from a gas phase to a countercurrent falling film of absorbing slurry was developed. Laminar, wavy and turbulent film structures were considered based on published information. Resistances to the mass transfer on the gas and the liquid sides of the interphase were considered, together with chemical reactions in the liquid phase. Relevant chemical equilibria in the liquid phase were modeled. Original experimental data on the neutralization reagent dissolution rate presented as a polydispersed two‐phase system of solids and on the rate of dissolved sulfite oxidation were used. The model was verified with experimental data from a laboratory‐scale falling‐film absorber using a single vertical tube under various geometrical and operating conditions, and a very good agreement was found with the experiment. Parametric sensitivity analysis showed the critical parts of the model.     

An improved statistical analysis of the least mean fourth (LMF) adaptive algorithm

The paper presents an improved statistical analysis of the least mean fourth (LMF) adaptive algorithm behavior for a stationary Gaussian input. The analysis improves previous results in that higher order moments of the weight error vector are not neglected and that it is not restricted to a specific noise distribution. The analysis is based on the independence theory and assumes reasonably slow learning and a large number of adaptive filter coefficients. A new analytical model is derived, which is able to predict the algorithm behavior accurately, both during transient and in steady-state, for small step sizes and long impulse responses. The new model is valid for any zero-mean symmetric noise density function and for any signal-to-noise ratio (SNR). Computer simulations illustrate the accuracy of the new model in predicting the algorithm behavior in several different situations.     

2-D symmetry: theory and filter design applications

In this comprehensive review article, we present the theory of symmetry in two-dimensional (2-D) filter functions and in 2-D Fourier transforms. It is shown that when a filter frequency response possesses symmetry, the realization problem becomes relatively simple. Further, when the frequency response has no symmetry, there is a technique to decompose that frequency response into components each of which has the desired symmetry. This again reduces the complexity of two-dimensional filter design. A number of filter design examples are illustrated.     

The effects of nonlocal impact ionization on the speed of avalanche photodiodes

The nonlocal enhancement in the velocities of charge carriers to ionization is shown to outweigh the opposing effects of dead space, increasing the avalanche speed of short avalanche photodiodes (APDs) over the predictions of a conventional local model which ignores both of these effects. The trends in the measured gain-bandwidth product of two short InAlAs APDs reported in the literature support this result. Relatively large speed benefits are predicted to result from further small reductions in the lengths of short multiplication regions.     

Optimised anaerobic treatment of house-sorted biodegradable waste and slaughterhouse waste in a high loaded half technical scale digester.

Anaerobic co-digestion of organic wastes from households, slaughterhouses and meat processing industries was optimised in a half technical scale plant. The plant was operated for 130 days using two different substrates under organic loading rates of 10 and 12 kgCOD.m(-3).d(-1). Since the substrates were rich in fat and protein components (TKN: 12 g.kg(-1) the treatment was challenging. The process was monitored on-line and in the laboratory. It was demonstrated that an intensive and stable co-digestion of partly hydrolysed organic waste and protein rich slaughterhouse waste can be achieved in the balance of inconsistent pH and buffering NH4-N. In the first experimental period the reduction of the substrate COD was almost complete in an overall stable process (COD reduction >82%). In the second period methane productivity increased, but certain intermediate products accumulated constantly. Process design options for a second digestion phase for advanced degradation were investigated. Potential causes for slow and reduced propionic and valeric acid degradation were assessed. Recommendations for full-scale process implementation can be made from the experimental results reported. The highly loaded and stable codigestion of these substrates may be a good technical and economic treatment alternative.     

Analysis of feedback for higher order polarization-mode dispersion mitigation of NRZ 40-Gb/s optical transmission

First-order polarization-mode dispersion (PMD) compensation by means of a polarization controller and a differential delay line is not sufficient to guarantee error-free transmission for 40-Gb/s channels when higher order effects severely increase signal distortion. Higher order mitigation is possible by cascading more than one first-order block. However, only two-stage or three-stage devices remain simple enough to be actually controlled. The performance of such higher order PMD compensators is evaluated by means of numerical simulations. Two different feedback signals have been used, demonstrating that first-order and higher order PMD distortion of nonreturn-to-zero (NRZ) pulses at 40 Gb/s can be strongly mitigated for instantaneous values of the differential group delay (DGD) up to the bit slot, when the compensator is properly controlled.