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- CONTENTS 1987 - VOLUME 305 - SECTION I - N° 8
- .......... Page(s) .......... 319
- .......... Page(s) .......... 319
- Let d>0 be an integer, Vd the vector space of homogeneous polynomials in x and y, of degree d, with complex coefficients, C[Vd] the algebra of polynomial functions
. The group G=SL(2, C) operates in a natural way in Vd' and so in C; let Ad be the subalgebra of G-invariant elements in C; let be the number of elements in any minimal generating system of the algebra Ad (number of fundamental invariants for binary forms of degree d). We improve some minorations of obtained by V. G. Kac and V. L. Popov.
- .......... Page(s) .......... 323
- .......... Page(s) .......... 323
- This Note takes place in the frame of the study of Differential Geometry on the unitary dual of a Lie group G in the neighbourhood of a point in particular of the deformations of ; we consider here the case where G is a motion group (see also [4]); a similar study in the case of a semi-simple group G has been made in [3].
- .......... Page(s) .......... 331
- The coexistence of two stable periodic solutions for a two-dimensional autonomous ordinary differential system including the cubic term xy2 as the only nonlinearity is studied by mean of the theoretical approach of singularities proposed by M. Golubitsky and W. Langford. The unfolding obtained by a perturbation of a-codimension 2 organizing centre yields a topological description of this system's multiple periodic trajectories that bifurcate from the equilibrium solution.
- .......... Page(s) .......... 337
- .......... Page(s) .......... 337
- Let us consider a semi linear equation and a subvariety by which there are exactly two characteristic hypersurfaces with standard hypothesis of transversality. If u is a sufficiently regular solution, conormal with respect to we define its two principal symbols on the conormal bundles to and to ; these symbols coïncide outside with the ordinary symbols, and each of them satisfies a transport equation; in the case of a second order equation, we can study complete symbols in the same way, and we deduce the propagation on (for instance) of properties of the kind "u is classical conormal in the neighborhood of a point .
- .......... Page(s) .......... 341
- .......... Page(s) .......... 341
- The bisecants to a space curve with coplanar tangents at the intersection points form a curve whose singularities are studied by the method of principal parts.
- .......... Page(s) .......... 345
- We give the number of rational points of some algebraic curves over finite fields associated with special cyclic codes. We deduce examples where the Weil bounds are reached.
- .......... Page(s) .......... 349
- .......... Page(s) .......... 349
- In this Note, we introduce the cobordism group Dn of links of n intervals. This group both generalizes the classical knot cobordism group and braid group. Actually, Bn injects in and is isomorphic to the knot cobordism group. To conclude, we construct an invariant for . This construction uses the localization of a wedge of n circles. Some examples are computed.
- Dynamical Systems
- (see Tome 305, Series I, 1897, p. 331)
- .......... Page(s) .......... 353
- On a rectangular domain divided in two squares, we solve a Poisson equation by a spectral method on the first square and a finite element method on the second one. Error estimates are given for two kinds of matching conditions on the interface.
- MATHEMATIQUE 1987 - Tome 305 - Série I - n° 8