Numerical blow‐up for the porous medium equation with a source

We study numerical approximations of positive solutions of the porous medium equation with a nonlinear source, where m > 1, p > 0 and L > 0 are parameters. We describe in terms of p, m, and L when solutions of a semidiscretization in space exist globally in time and when they blow up in a finite time. We also find the blow‐up rates and the blow‐up sets, proving that there is no regional blow‐up for the numerical scheme. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004     

Domination by Positive Narrow Operators

We prove that each positive operator from a Köthe function-space E() to a Banach lattice F with a narrow majorant is itself narrow provided the norm on F is order continuous. We also prove that every l ²-strictly singular regular operator from L ^p[0,1], 1p < , to a Banach lattice F is narrow, provided F has an order continuous norm.     

Acoustic Analysis of Pathological Voices Compressedwith MPEG System

The MPEG-1 Layer 3 compression schema of audio signal, commonly known as mp3, has caused a great impact in recent years as it has reached high compression rates while conserving a high sound quality. Music and speech samples compressed at high bitrates are perceptually indistinguishable from the original samples, but very little was known about how compression acoustically affects the voice signal. A previous work with normal voices showed a high fidelity at high-bitrate compressions both in voice parameters and the amplitude-frequency spectrum. In the present work, dysphonic voices were tested through two studies. In the first study, spectrograms, long-term average spectra (LTAS), and fast Fourier transform (FFT) spectra of compressed and original samples of running speech were compared. In the second study, intensities, formant frequencies, formant bandwidths, and a multidimensional set of voice parameters were tested in a set of sustained phonations. Results showed that compression at high bitrates (96 and 128 kbps) preserved the relevant acoustic properties of the pathological voices. With compressions at lower bitrates, fidelity decreases, introducing some important alterations. Results from both works, Gonzalez and Cervera and this paper, open up the possibility of using MPEG-compression at high bitrates to store or transmit high-quality speech recordings, without altering their acoustic properties.     

Stereo‐ and Regioselective Alkyne Hydrometallation with Gold(III) Hydrides

The hydroauration of internal and terminal alkynes by gold(III) hydride complexes [(C^N^C)AuH] was found to be mediated by radicals and proceeds by an unexpected binuclear outer‐sphere mechanism to cleanly form trans‐insertion products. Radical precursors such as azobisisobutyronitrile lead to a drastic rate enhancement. DFT calculations support the proposed radical mechanism, with very low activation barriers, and rule out mononuclear mechanistic alternatives. These alkyne hydroaurations are highly regio‐ and stereospecific for the formation of Z‐vinyl isomers, with Z/E ratios of >99:1 in most cases.     

An improved synthesis of alpha-carbolines under microwave irradiation

[reaction: see text]. Alpha-carbolines are interesting core structures for designing DNA-interacting small molecules. However, these compounds are not commercially available and their synthetic methods are low yielding or time consuming. The shortest synthetic route, the modified Graebe-Ullmann reaction, has been optimized by using microwave heating in four different types of apparatus to give shorter reaction times and enhanced yields. Optimized conditions enabled the preparation of a small library of alpha-carbolines.     

An integrative approach for analyzing metal–polyelectrolyte interactions

An integrative approach based on the combined use of both experiments and modelling is discussed here aimed at investigating metal–polyelectrolyte interactions in solution. Electrochemical techniques are applied because of their potential to measure the actual speciation without disturbing the solution physico–chemical equilibrium. The experimental methodologies are complementary since the ranges of applicability depend on the solution composition itself. To complement and interpret the results of these experimental techniques, a physico–chemical association model, based on the so-called ‘chemical model’ of counterion condensation theory, is used. The model considers that, in addition to the usual electrostatic interactions and entropic effects, territorial affinity and chemical bonding interactions take place between the small counterions in solution and the polyelectrolyte. A number of particular cases of metal/polyelectrolyte systems are discussed aimed at showing that the integrative approach leads to additional information about the solution system which can not be deduced from experimental results solely. Future challenges with respect to the applications in the study of natural aquatic systems are pointed out.     

Building C(sp3) Molecular Complexity on 2,2′-Bipyridine and 1,10-Phenanthroline in Rhenium Tricarbonyl Complexes

The reactions of [Re(N-N)(CO)₃(PMe₃)]OTf (N-N=2,2′-bipyridine, bipy; 1,10-phenanthroline, phen) compounds with tBuLi and with LiHBEt₃ have been explored. Addition to the N-N chelate took place with different site-selectivity depending on both chelate and nucleophile. Thus, with tBuLi, an unprecedented addition to C5 of bipy, a regiochemistry not accessible for free bipy, was obtained, whereas coordinated phen underwent tBuLi addition to C2 and C4. Remarkably, when LiHBEt₃ reacted with [Re(bipy)(CO)₃(PMe₃)]OTf, hydride addition to the 4 and 6 positions of bipy triggered an intermolecular cyclodimerization of two dearomatized pyridyl rings. In contrast, hydride addition to the phen analog resulted in partial reduction of one pyridine ring. The resulting neutral Re^I products showed a varied reactivity with HOTf and with MeOTf to yield cationic complexes. These strategies rendered access to Re^I complexes containing bipy- and phen-derived chelates with several C(sp³) centers.     

Novel generation of an o-quinone methide from 2-(2'-cyclohexenyl)phenol by excited state intramolecular proton transfer and subsequent C-C fragmentation

Formation of an o-quinone methide via C-C fragmentation of a zwitterion formed by intramolecular excited state proton transfer from an o-allylphenol derivative is reported for the first time.     

Electrochemical sensing in microfluidic systems using electrogenerated chemiluminescence as a photonic reporter of redox reactions

This paper describes a microfluidics-based sensing system that relies on electrochemical detection and electrogenerated chemiluminescent (ECL) reporting. The important result is that the ECL reporting reaction is chemically decoupled from the electrochemical sensing reaction. That is, the electrochemical sensing reaction does not participate directly in the ECL process, but because electrochemical cells require charge balance, the sensing and ECL reactions are electrically coupled. This provides a convenient and sensitive means for direct photonic readout of electrochemical reactions that do not directly participate in an ECL reaction and thus broadens the spectrum of redox compounds that can be detected by ECL. The approach can be implemented in either a two-electrode or bipolar (single-electrode) configuration. By manipulating the placement and dimensions of the conductors, the photonic response can be enhanced. The system is used to electrochemically detect benzyl viologen present in solution and report its presence via Ru(bpy)(3)(2+) (bpy = 2,2'-bipyridine) luminescence.