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.     

Interaction between p-tetraphenyl tetrahomodioxacalix[4]arene amide derivatives and alkali and alkaline-earth metal cations

The binding properties of four amido derivatives of p-tetraphenyl tetrahomodioxacalix[4]arene towards alkali and alkaline-earth metal cations using UV-absorption spectrophotometry, ¹H NMR and ESI-mass spectrometry techniques are reported.     

Synthesis of mono-, di-, and trinitro tricarboxymethyl calix[6]arenes for the complexation of uranium(VI)

Mono-, di-, and trinitro tricarboxymethyl calix[6]arenes 3(a-c) have been synthesised and their acid-base behaviour determined by potentiometric investigations. It was shown that the nitro groups do not play a major role on the acid-base properties. Preliminary complexation of uranyl is presented.     

Complexation and DFT studies of lower rim hexahomotrioxacalix[3]arene derivatives bearing pyridyl groups with transition and heavy metal cations. Cone versus partial cone conformation

The binding of representative alkali, alkaline earth, transition and heavy metal cations by 2‐pyridylmethoxy derivatives (1b, in cone and partial cone conformations) of p‐tert‐butylhexahomotrioxacalix[3]arene was studied. Binding was assessed by extraction studies of the metal picrates from water into dichloromethane and by stability constant measurements in acetonitrile and methanol, using spectrophotometric and potentiometric techniques. Microcalorimetric studies of some selected complexes in acetonitrile were performed, as well as proton NMR titrations. Computational methods (density functional theory calculations) were also employed to complement the NMR data. The results are compared with those obtained with the dihomooxacalix[4]arene 2b and the calix[4]arene 3b derivative analogues. Partial cone‐1b is the best extractant for transition and heavy metal cations. Both conformers of 1b exhibit very high stability constants for soft and intermediate cations Pb²⁺, Cd²⁺, Hg²⁺, Zn²⁺ and Ni²⁺, with cone‐1b the strongest binder (ML, log β ≥ 7) and partial cone‐1b the most selective. Both derivatives show a slight preference for Na⁺. Besides the formation of ML complexes, ML₂ and M₂L species were also observed. The former complexes were, in general, formed with the transition and heavy metal cations, whereas the latter were obtained with Ag⁺ and Hg²⁺ and partial cone‐1b. In most cases, these species were corroborated by the proton NMR and density functional theory studies. Copyright © 2013 John Wiley & Sons, Ltd.     

A Mean-Square Stability Analysis of the Least Mean Fourth Adaptive Algorithm

This paper presents a new convergence analysis of the least mean fourth (LMF) adaptive algorithm, in the mean square sense. The analysis improves previous results, in that it is valid for non-Gaussian noise distributions and explicitly shows the dependence of algorithm stability on the initial conditions of the weights. Analytical expressions are derived presenting the relationship between the step size, the initial weight error vector, and mean-square stability. The analysis assumes a white zero-mean Gaussian reference signal and an independent, identically distributed (i.i.d.) measurement noise with any even probability density function (pdf). It has been shown by Nascimento and Bermudez ["Probability of Divergence for the Least-Mean Fourth (LMF) Algorithm," IEEE Transactions on Signal Processing, vol 54, no. 4, pp. 1376-1385, Apr. 2006] that the LMF algorithm is not mean-square stable for reference signals whose pdfs have infinite support. However, the probability of divergence as a function of the step size value tends to rise abruptly only when it moves past a given threshold. Our analysis provides a simple (and yet precise) estimate of the region of quick rise in the probability of divergence. Hence, the present analysis is useful for predicting algorithm instability in most practical applications.     

Fluorimetric determination of pantothenic acid in foods by liquid chromatography with post-column derivatization

A method to determine the content of free pantothenic acid in various foods by reverse phase liquid chromatography-fluorimetry is reported. It includes a purification of the samples by successive passages through anion and cation exchange cartridges and a post-column derivatization of pantothenic acid as the fluorescent 1-alkylthio-2-alkylisoindole (reaction of beta-alanin, formed by hot alkaline hydrolysis of pantothenic acid, with orthophthaldialdehyde in the presence of 3-mercaptopropionic acid). An enzymatic hydrolysis prior to the purification step (pepsin at 50 degrees C for 3 h, then pantetheinase and alkaline phosphatase at 20 degrees C for 18 h) made it possible to release the bound pantothenic acid and thus to obtain the total Vitamin B5 content of these foodstuffs. The method proposed for the determination of free and bound pantothenic acid gives a good recovery rate (96-101%) and a satisfactory repeatability (R.S.D.r less than 8%). Owing to its low detection limit (0.65 microg g(-1)) and the good resolution of the pantothenic acid peak, it could most probably be applied to the determination of this vitamin in any foodstuff.