A fractional porous medium equation

We develop a theory of existence, uniqueness and regularity for the following porous medium equation with fractional diffusion, with m>m_?=(N−1)/N, N?1 and f∈L¹(RN). An L¹-contraction semigroup is constructed and the continuous dependence on data and exponent is established. Nonnegative solutions are proved to be continuous and strictly positive for all x∈RN, t>0.     

Combination of radon and stable isotope analysis as a tool for decision support concerning the remediation of NAPL-contaminated sites

The non-aqueous phase-liquid (NAPL)-contaminated aquifer at a major refinery site in Mexico was investigated. Owing to the depth of the contaminated aquifer section (NAPL source zone) of over 100 m below the surface, the actual aquifer material was not accessible for sampling. Information on the residual NAPL contamination of the aquifer could only be obtained indirectly by analysing groundwater samples from a few wells available at the site. To tackle the problem, an approach alternative to conventional groundwater analysis for dissolved NAPL was chosen. For evaluating the recent contamination and estimating its probable future development, the radioisotope radon-222 and the stable isotopes 13C, 34S and 18O were used as naturally occurring contamination tracers and process indicators. Radon was used as partitioning tracer for the approximate localization and semi-quantitative assessment of the NAPL source zone. The stable isotopes were used as indicators for naturally occurring biodegradation processes, which might potentially be implemented into future remediation schemes.     

Aldimines generated from aza-Wittig reaction between bis(iminophosphoranes) derived from 1,1'-diazidoferrocene and aromatic or heteroaromatic aldehydes: electrochemical and optical behaviour towards metal cations

Aldimine 4 bearing a 2-quinolyl group was prepared by aza-Wittig reaction between the triphenyliminophosphorane derived from the 1,1'-diazidoferrocene and 2-formylquinoline. However, aldimine 5, bearing a pyrene ring, was prepared using the most reactive tributyliminophosphorane derivative and the corresponding 1-formylpyrene. On the other hand, formation of aldimine 8 involves a tandem process, Staudinger reaction/intramolecular aza-Wittig reaction, by using directly 1,1'-diazidoferrocene and 2-(diphenylphosphonyl)benzaldehyde. Aldimine 4 behaves as chemosensor molecule for Ni(2+), Zn(2+), Cd(2+), Hg(2+) and Pb(2+) cations through two different channels: electrochemical (ΔE(1/2) = 222-361 mV) and chromogenic (Δλ = 122-153 nm), which can be used for the "naked eye" detection of these metal cations. Aldimine 5 behaves as a highly selective redox (in CH(3)CN) and fluorescent (in CH(3)Cl-DMF) probe for Hg(2+) metal cations even in the presence of a large excess of the other metal cations tested. Aldimine 8 displays electrochemical affinity (ΔE(1/2) = 60-288 mV) to Li(+), Ca(2+), Mg(2+), Zn(2+) and Pb(2+) metal cations, with the phosphorus oxide functionality as a binding site. From the (1)H NMR titration data as well as DFT calculations, different tentative binding modes have been established, for these structurally related ferrocenyl derivatives.     

Le serie lineari speciali sulle curve trigonali

Sunto Introdotto, per le curve trigonali di dato genere. un altro carattere invariante per trasformazioni birazionali della curva (carattere che qui vien chiamatola specie della curva stessa), si procede alla determinazione delle serie lineari speciali complete su ogni curva trigonale di generep e di speciem, precisandone la dimensione. In fine. come applicazione. si determinano le curve trigonali. di dato genere e di data specie, appartenenti ad unS _r e aventi il minimo ordine. Ricevuta in Redazione nel gennaio del 1945.     

Densities of One-Dimensional Backward SDEs

This work is devoted to the study of the existence and smoothness of the marginal densities of the solution of one-dimensional backward stochastic differential equations. Under monotonicity conditions of a function of the coefficients, we obtain that the smoothness properties of the forward process influencing the backward equation, transfer to the densities of the solution. Once established these conditions, we apply the result to study the tail behavior of the solution process. Mathematics Subject Classification (2000) 60H10.Fabio Antonelli: The first author was partially supported by the MIUR COFIN grant 2000.Arturo Kohatsu-Higa: The second author was partially supported by grants BFM2003-03324 and BFM 2003-04294. The authors wish to thank the referee for his/her comments.     

Non-simultaneous quenching in a system of heat equations coupled at the boundary

We study the solutions of a parabolic system of heat equations coupled at the boundary through a nonlinear flux. We characterize in terms of the parameters involved when non-simultaneous quenching may appear. Moreover, if quenching is non-simultaneous we find the quenching rate, which surprisingly depends on the flux associated to the other component. Partially supported by project BFM2002-04572 (Spain). Partially supported by UBA grant EX046, CONICET and Fundación Antorchas (Argentina). Received: February 17, 2004; revised: July 5, 2004     

Implementation of an algorithm for detecting patterns in defocused scenes using binary joint transform correlation

An original method to detect images in defocused scenes by means of a binary joint transform correlation is presented. Defocused images are described in frequency domain as the product between the Fourier transform of the in-focus scene by the optical transfer function of the imaging lens. This function, which presents positive and negative values, introduces sign errors in the joint power spectrum. The goal of this study is to detect the sign of the optical transfer function starting from the defocused image by means of a digital algorithm. Information provided by the algorithm allows to compensate the sign errors in the binary joint power spectrum and to obtain invariant correlations with respect to defocusing. Theoretical analysis and digital experiments to test the procedure are provided.     

Solution of the Navier-Stokes equations by the spectral-difference method

The Jacobi polynomial collocation method is extended to two and three dimensions by superimposing the individual one-dimensional expansions. Two innovative ideas are introduced in this article. The first is the cornerless/edgeless computational grid, and the second is the modified compressibility method, which is an iterative pressure solver. To evaluate the new method's applicability in solving the Navier-Stokes equation, the lid-driven cavity flow problem was solved. Two configurations were considered, the square cavity and the rectangular cavity with an aspect ratio of 2. A comparison of the center-line velocity profiles from two- and three-dimensional simulations at a Reynolds number of 1000 is provided for each of the configurations. The center-line velocity comparisons showed good quantitative agreement with previous studies. © 1994 John Wiley & Sons, Inc.