Showing papers in "Advances in Mathematics in 1984"

TL;DR: Soit #7B-G la categorie des groupes de Lie G avec une forme bilineaire symetrique non singuliere B sur l'algebre de Lie.

TL;DR: The concept of tight extensions of a metric space was introduced in this article, and the existence of an essentially unique maximal tight extension T x is established for any given metric space X and its properties are studied.

TL;DR: In this article, a generalization in terms of weighted averages is proposed, where there exist at most m points xi and positive weights oi summing to 1 so that \' aifj(Xi) = I”fi dt for j = 1, 2,..., m.

TL;DR: The dual form of the Ramsey's Theorem with colorings of the k-element subsets of ω was shown in this paper, where the coloring of the partitions of the subsets was replaced by the color of the blocks.

TL;DR: In this paper, a des groupes de Coxeter and des groupses a BN-paire sont associes certaines structures combinatoires: les complexes of Coxeter et les constructions de Tits.

TL;DR: In this article, a generalized Toeplitz matrix whose eigenvalue distribution can be found using a theorem of Kac, Murdock, and Szego is presented.

TL;DR: In this paper, a combinatorial method for the construction of free bases for the symmetric polynomials over the subset lattice has been proposed, where the action of a symmetric group on the Stanley-Reisner ring is studied.

TL;DR: In this paper, it was shown that there are many approach regions which are not contained in any nontangential region but for which the conclusions of Fatou's theorem remain true.

TL;DR: In this article, the total hierarchy of the Kadomtsev-Petviashvili (KP) equation is transformed to a system of linear partial differential equations with constant coefficients, and complete integrability of the KP equation is proved by using this linear system.

TL;DR: A finite family of hyperplanes through the origin in C+++' is called an I-arrangement of hyperplane, or simply an l-arrambement as discussed by the authors.

TL;DR: On ecrit le mouvement brownien dans un format complexe [X=a+√1b] and on note son invariance conforme as mentioned in this paper.

TL;DR: On montre que ces deux problems de la theorie de la complexite de calcul, aussi bien, que les autres resolvant la maximisation and l'integration sont equivalents aux problemes de complexite of calcul discret naturel, dont la plupart ont deja beaucoup ete etudies as discussed by the authors.

TL;DR: In this article, the authors proposed the OE(n) partition function, the number of partitions of n in which the parts (arranged in ascending order) alternate in parity starting with the smallest part odd.

TL;DR: In this article, the theory of orthogonal R-separation for the Helmholtz equation on a pseudo-Riemannian manifold was developed, and it was shown that it is the natural analogy of additive separation for the Hamiltonian-Jacobi equation.

TL;DR: In this paper, the authors constructed a compact homogeneous space bH which has a Borel measure μ which knows which sets are homeomorphic and showed that up to a multiplicative constant μ is unique with respect to these properties.

TL;DR: In this article, a recouvrement intermediaire la surface de classe M 1 is defined, and it is shown that M 1 ne porte pas de fonctions harmoniques positives non constantes, signifying that le mouvement brownien sur M 1 a un seul mode d'ecoulement vers l'infini

TL;DR: Morita and Tsuboi as mentioned in this paper proved the vanishing theorem for all closed, foliated n-manifolds in which every leaf has polynomial growth and showed that if every leaf is nonresilient and if no leaf lies at infinite level then gv(sT) = 0.

TL;DR: On produit un nombre infini de treillis non isomorphes partiels finis engendres par 3 elements and montre qu'ils donnent naissance a infinite de 3 types distincts sur la theorie de tout ensemble partiellement ordonne dans lequel ils peuvent etre plonges as mentioned in this paper.

TL;DR: On demontre des theoremes generaux sur la determination des meilleures approximations rationnelles des solutions d'equations differentielles lineaires a coefficients fonction rationnelle as discussed by the authors.

TL;DR: On considere le probleme aux valeurs initiales pour l'equation ∂u/∂t=∂ G m (u)/∂x=K m(u), m≥1

TL;DR: Theorem 7.3 as discussed by the authors shows that the algebraic closure of an infinite field finitely generated over its prime lield can be characterized by the normalized Haar measure, which assigns to the set G(L) the value l/[L: K], if L/K is a finite separable extension.

TL;DR: Locally free selectors as discussed by the authors are a subclass of selectors which are semimodal and can be represented as shelling orders of abstract discs, in the same way that finite distributive lattices are represented by shelling orders (or by linear extensions) of partially ordered sets.

TL;DR: In this paper, it was shown that the invariant polynomials μG(n)q(, Δi, ;, xi,i+1) = γi − δi and xi + 1 + 1 = δI−δi + ǫ−ǫ+ǫǫ + 1, whereǫ denotes the difference of the two sets of variables {γ1, ǔ n} and {δ1,ǫ n}.

TL;DR: In this article, a Lie algebra of infinite dimension was defined, and conjecture that it may be related to the Fischer-Griess Monster group. But this conjecture was later disproved.

TL;DR: Vesentini et al. as discussed by the authors generalize this result to a certain nombre of cases and show that the results of this result do not generalise to other cases.

TL;DR: Courbures principales et energies de Hartree-Fock-Grassmanniens des domaines de forme quadratique. Cycles de Schubert and Fonctions de Morse quadratiques as mentioned in this paper.