Une axiomatisation de la substitution

We investigate the notion of substitution in an abstract way, without defining it explicitly. We single out the essential features of the operation of performing a substitution in order to define a concept of substitutive structure, called logos. We then prove a completeness theorem making precise and justifying the intuition that formulas true for the usual substitution can be proved from the logos axioms only. To cite this article: M. Crabbé, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Equivariant fixed-point indices of iterated maps

We describe an equivariant version (for actions of a finite group G) of Dold’s index theory, [10], for iterated maps. Equivariant Dold indices are defined, in general, for a G-map U → X defined on an open G-subset of a G-ANR X (and satisfying a suitable compactness condition). A local index for isolated fixed-points is introduced, and the theorem of Shub and Sullivan on the vanishing of all but finitely many Dold indices for a continuously differentiable map is extended to the equivariant case. Homotopy Dold indices, arising from the equivariant Reidemeister trace, are also considered.      

Thermal analysis of vinyl siding

Vinyl siding is typically produced by co-extruding a capstock (surface layer) over a PVC substrate formulation. The capstock is often non-PVC, these systems can result in warpage during or after production. In our study we will show that this warpage can result from an interfacial induced stress related to the mismatch between the glass transition of the substrate and the capstock. Additionally, both TMA and TMDSC were used to probe the stress release. Capstock formulations which better match the glass transition of the PVC substrate result in superior performance.     

Propagating fronts,chaos and multistability in a cell replication model

Numerical solutions to a model equation that describes cell population dynamics are presented and analyzed. A distinctive feature of the model equation (a hyperbolic partial differential equation) is the presence of delayed arguments in the time (t) and maturation (x) variables due to the nonzero length of the cell cycle. This transport like equation balances a linear convection with a nonlinear, nonlocal, and delayed reaction term. The linear convection term acts to impress the value of u(t,x=0) on the entire population while the death term acts to drive the population to extinction. The rich phenomenology of solution behaviour presented here arises from the nonlinear, nonlocal birth term. The existence of this kinetic nonlinearity accounts for the existence and propagation of soliton-like or front solutions, while the increasing effect of nonlocality and temporal delays acts to produce a fine periodic structure on the trailing part of the front. This nonlinear, nonlocal, and delayed kinetic term is also shown to be responsible for the existence of a Hopf bifurcation and subsequent period doublings to apparent "chaos" along the characteristics of this hyperbolic partial differential equation. In the time maturation plane, the combined effects of nonlinearity, nonlocality, and delays leads to solution behaviour exhibiting spatial chaos for certain parameter values. Although analytic results are not available for the system we have studied, consistency and validation of the numerical results was achieved by using different numerical methods. A general conclusion of this work, of interest for the understanding of any biological system modeled by a hyperbolic delayed partial differential equation, is that increasing the spatio-temporal delays will often lead to spatial complexity and irregular wave propagation. (c) 1996 American Institute of Physics.     

Proton magnetic resonance studies of compounds with bridgehead nitrogen atoms—XXVI : Configurational studies with derivatives of perhydro-oxazolo[3,4-c]oxazole and the conformational analysis of perhydro-imidazo[1,5-c]thiazole

A series of 3-monosubstituted, 3,3′-disubstituted, and 3,5-disubstitted perhydro-7a-methyloxazolo[3,4-c]oxazoles has been synthesised. Some indication of the predominant conformations of these systems and of the related perhydro-imidazo[1,5-c]thiazoles is obtainable from the magnitude of the geminal coupling constants of the methylene group protons situated between the heteroatoms.     

Oxidatively truncated docosahexaenoate phospholipids: total synthesis,generation, and Peptide adduction chemistry

The recent immunological detection of extraordinarily high levels of carboxyethylpyrrole (CEP) modifications of proteins from the retinas of individuals with age-related macular degeneration provided presumptive evidence for the involvement of docosahexaenoate-derived oxidatively truncated phospholipids in retinal pathology. To facilitate the in vivo detection and characterization of the chemistry and biological activities of these postulated naturally occurring molecules, a family of oxidatively truncated phospholipids was prepared by total syntheses. Their formation in oxidation reactions of a docosahexaenoate ester of 2-lysophosphatidylcholine (DHA-PC) was also demonstrated. Free radical-induced oxidative cleavage of DHA-PC promoted by myeloperoxidase or copper ions generates similar mixtures of these phospholipids. The most abundant products were 1-palmitoyl-2-succinoyl-sn-glycero-3-phosphatidylcholine (4.7%) and 2-(6-carboxy-4-oxohex-5-enoyl)-1-palmitoyl-sn-glycero-3-phosphatidylcholine (1.7%). Both of these oxidatively truncated phospholipids are homologues of biologically active arachidonate-derived phospholipids. A minor product from DHA-PC, 2-(4-hydroxy-7-oxohept-5-enoyl)-1-palmitoyl-sn-glycero-3-phosphatidylcholine (0.4% yield), reacted with the epsilon-amino group of a peptide lysyl residue to produce a CEP derivative in 0.7% yield. These observations support the previous conclusion, based on immunological evidence, that CEPs are generated by the reaction of an oxidatively truncated phospholipid with proteins in the retina and further indicate that CEP protein modifications probably represent only a tiny fraction of the products generated upon oxidative damage of DHA-PC in photoreceptor disk membranes.