RESTRICTION RESPECTUEUSE ET RECONSTRUCTION DES CHAINES ET DES RELATIONS INFINITES

We show a faithful restriction theorem among infinite chains which implies a reconstructibility conjecture of Halin. This incite us to study the reconstructibility in the sense of Fraïssé and to prove it for orders of cardinality infinite or ≥ 3 and for multirelations of cardinality infinite or ≥ 7, what improves the theory obtained by G. Lopez in the finite case. For this work we had to study the infinite classes of difference which have to be a linear order of type ω, ω* or ω* + ω; this complete the theory made by G. Lopez for the finite case ([13]). We show also Ulam-reconstructibility for linear orders which have a fixed point.     

111In–L–LDL and 153Gd–L–LDL as radiotracers for detection of AR4‐2J rat pancreatic tumors

Pancreatic cancer has an extremely poor prognosis, due, in part, to lack of methods for early diagnosis. The present study was designed to evaluate the potential of labeling low‐density lipoprotein (LDL) with a radionuclide using a lipid chelating agent, bis(stearylamide) of diethylenetriaminepentaacetic acid (L), to detect pancreatic tumors by gamma‐scintigraphy. Previous studies indicated that the difficulty of visualization of pancreatic tumors was due to their poor vascularization. This study compares the ability of two radiotracers, ¹¹¹In–L–LDL and ¹⁵³Gd–L–LDL to target highly vascularized rat pancreatic tumors (AR4‐2J) implanted in nude mice. Biodistribution studies showed that the tumor uptake of ¹¹¹In–L–LDL and ¹⁵³Gd–L–LDL tracers was twofold and fivefold higher respectively than with the controls (¹¹¹In citrate and ¹⁵³Gd citrate respectively). These tracers would thus be suitable for scintigraphic imaging. We show here that LDL could be employed as a delivery system for tracers such as ¹¹¹In or ¹⁵³Gd when these two radionuclides are complexed by a lipid‐chelating anchor, and that ¹¹¹In–L–LDL and ¹⁵³Gd–L–LDL enabled better visualization of the pancreatic tumor tissues, with a better result with ¹⁵³Gd–L–LDL. Copyright © 2004 John Wiley & Sons, Ltd.     

An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.     

Analysis of a Poisson system with boundary conditions

We consider a class of problems originating from a Raman laser amplification model, for which the equations can be written as a Poisson system with boundary conditions. Once reformulated, this system becomes an integro-differential equation that we study here in some detail. In particular, we show the existence of a smooth solution under general assumptions, and prove its uniqueness for boundary values that are not too far apart. Eventually, we completely solve the question of uniqueness for systems of dimensions one and two. To cite this article: F. Castella et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

New estimates for the Laplacian,the div–curl,and related Hodge systems

We establish new estimates for the Laplacian, the div–curl system, and more general Hodge systems in arbitrary dimension, with an application to minimizers of the Ginzburg–Landau energy. To cite this article: J. Bourgain, H. Brezis, C. R. Acad. Sci. Paris, Ser. I 338 (2004).