Building Giant Carbocycles by Reversible C−C Bond Formation

We describe a simple way to build giant macrocyclic hydrocarbons by the reversible formation of carbon–carbon bonds. Specifically, extended spirobifluorene‐substituted derivatives of Wittig's hydrocarbon were synthesized and found to undergo oligomerization, giving the largest hydrocarbon that has been crystallized and characterized by X‐ray diffraction to date.     

Nucleophilic addition to 3-substituted pyridinium salts: expedient syntheses of (-)-L-733,061 and (-)-CP-99,994

[reaction: see text] The addition of nucleophiles to 3-substituted pyridinium salts prepared from N-methylbenzamide and various pyridines has been investigated. Good to excellent regioselectivities favoring the 2,3-disubstituted 1,2-dihydropyridines were observed. The resulting 1,2-dihydropyridines led to the corresponding 2,3-disubstituted pyridines upon treatment with Mn(OAc)3/NaIO4. This methodology was also successfully applied to the enantioselective syntheses of (-)-L-733,061 and (-)-CP-99,994, two members of a new class of highly potent, nonpeptide, Substance P antagonists.     

Existence results for some quasilinear parabolic problems

We first give an existence theorem, for some equations associated with Leray-Lions operators, assuming the existence of a subsolution smaller than a supersolution. Then we prove, with an additional hypothesis on the operator, that in the previous theorem, we can replace the subsolution by two subsolutions and the supersolution by two supersolutions. Finally, we deduce the existence of a smallest and a greatest solution.     

Mild method for the conversion of amides to thioamides

Aqueous ammonium sulfide was found to be an ideal substitute for hydrogen sulfide for the thiolysis of activated amides. High yields of the corresponding thioamides were obtained for a broad range of substrates, using two different procedures that are both operationally simple and inexpensive, as well as amenable to large-scale preparation. Preliminary results indicate that aqueous ammonium sulfide may also replace hydrogen sulfide in the synthesis of thionoesters from amides.     

L r Estimates for Degenerate Elliptic Problems

We prove L ^r estimates for the Dirichlet problem –div(a(x,u,Du))=f with f in L ^q for 1q+, where the operator satisfies (|s|)|| ^p a(x,s,), with p>1. These estimates are obtained without symmetrization and are sharp in some cases.     

Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms

In this Note we prove an a priori estimate and the existence of a solution for a class of nonlinear elliptic problems whose model is $?\mathrm{div}A(x)Du+{\alpha }_{0}u=\gamma {|Du|}^q+f(x)$, when $1<q<2$ and $f\in L^m(\Omega )$ for some suitable m. The main interest of the result lies in the a priori estimate, the complete proof of which is given in the Note. To cite this article: N. Grenon et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Parabolic Differential Equations in Ordered Banach Spaces of Bounded Functions

Let A be a set, and let E be the Banach space of bounded functions : A R, equipped with its natural order. With a rectangle R = (a,b) × (0,T] let F(x,t,) : R × E E be a bounded, continuous function satisfying a local Hölder condition and being quasimonotone increasing with respect to . Then there exists a solution u: [a,b] × [0,T] E of the problem ut(x,t) – uxx(x,t) = F(x,t,u(x,t)) ((x,t) R), u(x,t) = 0 ((x,t) R R).