Existence and uniqueness of viscosity solution for Hamilton-Jacobi equation with discontinuous coefficients dependent on time

The main result is a proof of the existence of a unique viscosity solution for Hamilton-Jacobi equation, where the hamiltonian is discontinuous with respect to variable, usually interpreted as the spatial one. Obtained generalized solution is continuous, but not necessarily differentiable.

An approximate solution method for boundary layer flow of a power law fluid over a flat plate

The work in this paper deals with the development of momentum and thermal boundary layers when a power law fluid flows over a flat plate. At the plate we impose either constant temperature, constant flux or a Newton cooling condition. The problem is analysed using similarity solutions, integral momentum and energy equations and an approximation technique which is a form of the Heat Balance Integral Method. The fluid properties are assumed to be independent of temperature, hence the momentum equation uncouples from the thermal problem. We first derive the similarity equations for the velocity and present exact solutions for the case where the power law index n = 2. The similarity solutions are used to validate the new approximation method. This new technique is then applied to the thermal boundary layer, where a similarity solution can only be obtained for the case n = 1.

Use of quantum dots in aqueous solution to detect blood fingermarks on non-porous surfaces.

A new and original reagent based on the use of highly fluorescent cadmium telluride (CdTe) quantum dots (QDs) in aqueous solution is proposed to detect weak fingermarks in blood on non-porous surfaces. To assess the efficiency of this approach, comparisons were performed with one of the most efficient blood reagents on non-porous surfaces, Acid Yellow 7 (AY7). To this end, four non-porous surfaces were studied, i.e. glass, transparent polypropylene, black polyethylene, and aluminium foil. To evaluate the sensitivity of both reagents, sets of depleted fingermarks were prepared, using the same finger, initially soaked with blood, which was then successively applied on the same surface without recharging it with blood or latent secretions. The successive marks were then cut in halves and the halves treated separately with each reagent. The results showed that QDs were equally efficient to AY7 on glass, polyethylene and polypropylene surfaces, and were superior to AY7 on aluminium. The use of QDs in new, sensitive and highly efficient latent and blood mark detection techniques appears highly promising. Health and safety issues related to the use of cadmium are also discussed. It is suggested that applying QDs in aqueous solution (and not as a dry dusting powder) considerably lowers the toxicity risks.

An iterative Multiscale Finite-Volume algorithm converging to the exact solution

The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).

Pregnancy malaria: cryptic disease, apparent solution

Malaria during pregnancy can be severe in non-immune women, but in areas of stable transmission, where women are semi-immune and often asymptomatic during infection, malaria is an insidious cause of disease and death for mothers and their offspring. Sequelae, such as severe anaemia and hypertension in the mother and low birth weight and infant mortality in the offspring, are often not recognised as consequences of infection. Pregnancy malaria, caused by Plasmodium falciparum, is mediated by infected erythrocytes (IEs) that bind to chondroitin sulphate A and are sequestered in the placenta. These parasites have a unique adhesion phenotype and distinct antigenicity, which indicates that novel targets may be required for development of an effective vaccine. Women become resistant to malaria as they acquire antibodies against placental IE, which leads to higher haemoglobin levels and heavier babies. Proteins exported from the placental parasites have been identified, including both variant and conserved antigens, and some of these are in preclinical development for vaccines. A vaccine that prevents P. falciparum malaria in pregnant mothers is feasible and would potentially save hundreds of thousands of lives each year.

Bis-sulfonamides quirals amb simetria C2 com a possibles organocatalitzadors per a l'addició estereoselectiva de nucleòfils a cations N-acilimini

En aquest treball s’ha plantejat estudiar la capacitat de diferents bissulfonamides per promoure, actuant com a àcids Brønsted, l’addició estereoselectiva d’un grup al·lil o un indole a un catió acilimini. Per això, s’han sintetitzat diversos tipus de bis-sulfonamides amb simetria C2, en forma enantiopura, i preparat precursors genèrics de cations N-acilimini. S’han dut a terme reaccions d’al·lilació i d’addició d’indole en diferents condicions i amb les diferents sulfonamides. Es va estudiar la possible estereoselectivitat dels productes d’addició, però en cap cas la presència de les bis-sulfonamides sintetitzades en la reacció ha afectat a l’estereoselectivitat de les addicions.

An axiomatic characterization of the strong constrained egalitarian solution

In this paper we axiomatize the strong constrained egalitarian solution (Dutta and Ray, 1991) over the class of weak superadditive games using constrained egalitarianism, order-consistency, and converse order-consistency. JEL classification: C71, C78. Keywords: Cooperative TU-game, strong constrained egalitarian solution, axiomatization.

Accidental cross-clamping of the superior vena cava: management and BIS evolution.

The case of a 38-year old man with recurrent adenocarcinoma of the right lung and infiltration of the thoracic wall, who underwent a right pneumonectomy with thoracic wall resection, is described. Dissection of the right pulmonary hilous was extremely difficult due to the previous operations. The superior vena cava (SVC) was accidentally ligated, resulting in profound hypotension and increased venous pressure in the internal jugular vein. Immediate blood aspiration through a 8.5-French introducer sheath lowered the venous congestion. After the SVC was cross-clamped, the Bispectral Index (BIS) acutely decreased to 0 and remained low during the resuscitation. Over the next 5 hours, BIS was directly affected by mean arterial pressure. Four days postoperatively, the patient was neurologically intact.

[ Phot. de la "demoiselle de Fontenaille", rocher du Calvados, don Gabriel Desclozières en 1880. Voir le Bulletin de la S.G., 6e s., 20 (1880), p. 92, et les ouvrages cotés D4/532 et 532 bis]

Donateur : Desclozières, Gabriel (18..-18..?)