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- CONTENTS
- 1987 - VOLUME 305 - SECTION I - N° 2
- Number Theory
- .......... Page(s) .......... 39
- We prove that the minimal (for the component-wise order on Nk) positive integer solutions of the homogeneous equation with and satisfy and This improves a result of G. Huet [1].
- Mathematical Analysis
- .......... Page(s) .......... 41
- We show that the classic Choquet theorem on "contingent and paratingent" has several applications to nonsmooth analysis.
- Functional Analysis
- .......... Page(s) .......... 45
- Let X, Y be two real Banach spaces;
a sequence of continuous linear operators from X onto Y converging, in (X, Y), to a surjective operator ; a sequence of lipschitzian operators from X into Y pointwise converging to a lipschitzian operator . In this Note, for y given in Y, we study the set of solutions of the equation . In particular, under a suitable hypothesis, we prove that if is a sequence in Y converging to y, then, for every , there exists a sequence in X converging to x and such that for all .
- Probability Theory
- .......... Page(s) .......... 49
- In a previous Note (I), we stated three theorems, and proved only the two first ones. We prove the third one here, and we extend the three theorems to the case where the vector spaces E, F, G, are replaced by manifolds U, V, W.
- Mathematical Problems in Mechanics
- We consider a problem in three-dimensional linearized elasticity, posed over a domain consisting of a plate with thickness 2, clamped into a solid whose Lamé constants are independent of . If the Lamé constants of the material constituting the plate vary as , we show that the solution of the three-dimensional problem converges, as approaches 0, to the solution of a variational problem of a new type, posed simultaneously over a three-dimensional open set with a slot and a two-dimensional open set.
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