Weak Covering at Large Cardinals

We show that weakly compact cardinals are the smallest large cardinals k where k⁺ < k⁺ is impossible provided 0^# does not exist. We also show that if k^+Kc < k⁺ for some k being weakly compact (where K^c is the countably complete core model below one strong cardinal), then there is a transitive set M with M ? ZFC + “there is a strong cardinal”.     

Apparent viscosity of a mixture of a Newtonian fluid and interacting particles

We investigate the behavior of fluid–particle mixtures subject to shear stress, by mean of direct simulation. This approach is meant to give some hints to explain the influence of interacting red cells on the global behavior of the blood. We concentrate on the apparent viscosity, which we define as a macroscopic quantity which characterizes the resistance of a mixture against externally imposed shear motion. Our main purpose is to explain the non-monotonous variations of this apparent viscosity when a mixture of fluid and interacting particles is submitted to shear stress during a certain time interval. Our analysis of these variations is based on preliminary theoretical remarks, and some computations for some well-chosen static configurations. To cite this article: A. Lefebvre, B. Maury, C. R. Mecanique 333 (2005).     

Multiple fractures produced by the bending of brittle beams

This paper describes experiments where the bending of beams results in two or more fractures being formed, apparently simultaneously. This is explained in terms of the stress waves emitted by the initial fracture process. It is shown that three separate types of secondary fracture may occur as a result of the interaction between the stress pulses produced by the initial fracture and the loading stresses already present in the beam. In treating these problems it has been found helpful to use an analytical solution for the bending wave propagated when a semi-infinite beam, which is subjected to a constant bending moment, is suddenly unloaded at the free end. In modelling the longitudinal stress pulse produced by the fracture we have used a simplified model which assumes that the forcing function on the fracture plane is a force field equal to the resultant force acting on the unbroken portion of the fracture surface prior to the onset of fracture.     

Photophysics of a Ruthenium 4H‐Imidazole Panchromatic Dye in Interaction with Titanium Dioxide

The photophysics of bis(4,4′‐di‐tert‐butyl‐2,2′‐bipyridine‐κ²N,N′)[2‐(4‐carboxyphenyl)‐4,5‐bis(p‐tolylimino‐κN)imidazolato]ruthenium(II) hexafluorophosphate is investigated, both in solution and attached to a nanocrystalline TiO₂ film. The studied substitution pattern of the 4H‐imidazole ligand is observed to block a photoinduced structural reorganization pathway within the 4H‐imidazole ligand that has been previously investigated. Protonation at the 4H‐imidazole ring decreases the excited‐state lifetime in solution. When the unprotonated dye is anchored to TiO₂, photoinduced electron injection occurs from thermally nonrelaxed triplet metal‐to‐ligand charge transfer (³MLCT) states with a characteristic time constant of 0.5 ps and an injection efficiency of roughly 25 %. Electron injection from the subsequently populated thermalized ³MLCT state of the dye does not take place. The energy of this state seems to be lower than the conduction band edge of TiO₂.     

Aminoglycoside analysis in food of animal origin with a zwitterionic stationary phase and liquid chromatography–tandem mass spectrometry

In this study, fourteen highly polar aminoglycoside (AGs) antibiotics were selected. Various stationary phases were tested, including Obelisc R, ZIC-HILIC, BEH amide and aminopropyl. The nature of the stationary phase, mobile phase (water or buffer solutions and acetonitrile), pH (percentage of formic acid), gradient conditions and injection solvents were systematically studied as relevant parameters for tuning retention selectivity and detectability of AGs in liquid chromatography electrospray tandem mass spectrometry (LC–(ESI)–MS/MS). Only the two zwitterionic phases (Obelisc R and ZIC-HILIC) achieved a proper chromatographic separation considering interferences due to the crosstalk effect in low resolution mass spectrometers. The water/acetonitrile mobile phase containing 1% formic acid used with Obelisc R provided more sensitivity than the highly concentrated buffered mobile phases required for ZIC-HILIC. A solid phase extraction (SPE) clean-up procedure with polymeric weak cation exchange (WCX) cartridges was optimized for honey, milk and liver samples. Different brands of cartridges and elution solvents were tested, and the Taurus WCX offered the best recovery rate with a buffer elution at pH 3. The final optimized method was validated in these matrices according to Decision 2002/657/EC. A monitoring campaign for sixty honey, milk and liver samples was carried out at the Food Authority Control in Geneva. The concentration of dihydrostreptomycin (DSTP) found in one ovine liver exceeded the established maximum residue levels (MRLs) within the European and Swiss legislations but it was compliant taking into account the validation data.     

Approximations in Sobolev spaces by prolate spheroidal wave functions

Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) ${\psi }_{n,c},c>0$. This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space $H^s([?1,1])$. The quality of the spectral approximation and the choice of the parameter c when approximating a function in $H^s([?1,1])$ by its truncated PSWFs series expansion, are the main issues. By considering a function $f\in H^s([?1,1])$ as the restriction to $[?1,1]$ of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples.     

DOSY-NMR analysis of ring-closing metathesis (RCM) products from β-lactam precursors

The discrimination between cyclomonomers and various oligomers formed during a ring-closing metathesis (RCM) process is not an easy task. Their (1)H NMR patterns are often very similar, and the use of mass spectrometry techniques is usually recommended. Here, we show that the DOSY-NMR method is a reliable tool to help in the identification of cyclomonomers versus cyclodimers by comparing the translational diffusion coefficient of the compounds issued from RCM reactions with the diffusion coefficient of their respective precursors.     

Degradation kinetics of poly(lactic-co-glycolic) acid block copolymer cast films in phosphate buffer solution as revealed by infrared and Raman spectroscopies

Poly(lactic-co-glycolic) acid (PLGA) is an important copolymer used in drug delivery platforms where controlled release is required. In this work we investigated the in vitro degradation of four PLGA copolymers with L/G molar compositions of 50/50, 65/35, 75/25 and 95/5. ATR-IR and Raman spectroscopies were used to differentiate and quantify the degradation rates of glycolic and lactic units. Both techniques were used to determine the polymer composition as a function of degradation time and the degradation rate constants for the hydrolysis of glycolic and lactic units were calculated using a 1st order kinetics approach. Our results revealed a two stage process for the degradation of PLGA cast films in PBS in agreement with our previous work. The degradation rate constant for glycolic unit was found to be 1.3 times higher than for lactic units. In addition the degradation rate constants for L and G units were shown to decrease proportionally with increasing initial lactic content of the copolymer used to prepare the films.