Sur la congruence des ensembles de points et ses généralisations

Sans résumé Conférence tenue à l'Université de Zurich le 22 Mai 1946.     

Analyse de Fourier,multiplicateurs de Schur sur Sp et ensembles Λ(p)cb non commutatifs

This work deals with various questions concerning Fourier multipliers on L^p, Schur multipliers on the Schatten class S^p as well as their completely bounded versions when L^p and S^p are viewed as operator spaces. We use for this aim subsets ofenjoying the Λ(p)_cb-property which is much stronger than the usual Λ(p)-property. We start by studying the notion of Λ(p)_cb-sets in the general case of an arbitrary discrete group before turning to .     

On the (n − 2)-transversals of n convex subsets of the plane

In this paper we consider families of distinct ovals in the plane, with the property that certain subfamilies have stabbing lines (transversals). Our main result says that if any k member of the family can be stabbed by a line avoiding all the other ovals and k is large enough, then the family consists of at most k+1 ovals. For any n4 we show a family of n ovals, whose n–2 element subfamilies have, but the n–1 element subfamilies do not have, transversals.     

On the Size of a Cap in PG(n,q) with q Even and n ≥ 3

Let m2(n,q), m2(n,q) be, respectively, the maximum value, the second largest value of k for which there exists a complete k-cap in PG(n,q). In this paper, the known upper bound on m2(3,q), q even, q 8, is improved. This new upper bound on m2(3,q) is then used to improve the upper bounds on m2(n,q), q even, q 8 and n 4.     

On the complete integrability and linearization of a Burgers– Korteweg–de Vries-type nonlinear equation

In this work, on the basis of the Bogolyubov–Prykarpats’kyi gradient–holonomic algorithm for the investigation of the integrability of nonlinear dynamical systems on functional manifolds, the exact linearization of a Burgers–Korteweg–de Vries-type nonlinear dynamical system is established. As a result, we describe the linear structure of the space of solutions and show its relation to the convexity of certain functional subsets. The bi-Hamiltonian property of the Burgers–Korteweg–de Vries dynamical system is also established, and the infinite hierarchy of functionally independent invariants is constructed.     

On the chromatic uniqueness of the graphW(n,n − 2, k)

This paper shows that the graphW(n, n – 2, k) is chromatically unique for any even integern 6 and any integerk 1.     

On a Lyapunov-type inequality and the zeros of a certain Mittag–Leffler function

In this work, a Lyapunov-type inequality is obtained for the case when one is dealing with a fractional differential boundary value problem. We then use that result to obtain an interval where a certain Mittag–Leffler function has no real zeros.     

On the generalized Hyers–Ulam stability of module left (m, n)-derivations

We study the generalized Hyers–Ulam stability of functional equations of module left (m, n)-derivations.     

On the existence and the uniqueness of the solution of a fluid–structure interaction scattering problem

The existence and uniqueness of the solution of a fluid–structure interaction problem is investigated. The proposed analysis distinguishes itself from previous studies by employing a weighted Sobolev space framework, the DtN operator properties, and the Fredholm theory. The proposed approach allows to extend the range of validity of the standard existence and uniqueness results to the case where the elastic scatterer is assumed to be only Lipschitz continuous, which is of more practical interest.     

On the invariants of Möbius groupsM(R n )

Suppose that $$\operatorname{Re} (a + d^ * ) \in \left\{ {\begin{array}{*{20}c} {( - 2,2),if g(x) is f.p.f. or elliptic,} \\ {\left[ { - 2,2} \right], if g(x) is parabolic,} \\ {( - \infty ,\infty ), if g(x) is loxodromic.} \\ \end{array} } \right.$$ is a Clifford matrix of dimensionn, g(x)=(ax+b)(cx+d) ^?1. We study the invariant balls and the more careful classifications of the loxodromic and parabolic elements inM(R ⁿ ), prove that the loxodromic elements inM(R ^2k+1 ) certainly have an invariant ball, expound the geometric meaning of Ahlfors' hyperbolic elements, and introduce the uniformly hyperbolic and parabolic elements and give their identifications. We prove that $$\operatorname{Re} (a + d^ * ) \in \left\{ {\begin{array}{*{20}c} {( - 2,2),if g(x) is f.p.f. or elliptic,} \\ {\left[ { - 2,2} \right], if g(x) is parabolic,} \\ {( - \infty ,\infty ), if g(x) is loxodromic.} \\ \end{array} } \right.$$ These results are fundamental in the higher dimensional Möbius groups, especially in Fuchs groups.     

On the (in)finiteness of the image of Reshetikhin–Turaev representations

We state a simple criterion to prove the infiniteness of the image of Reshetikhin–Turaev irreducible representations of the mapping class groups of surfaces. We use it to study some of the Reshetikhin–Turaev representations associated to the tori with one and two punctures and derive an alternative proof of the results of Funar (Pac J Math 188:251–274, 1999).     

On representations of GL(n) distinguished by GL(n − 1) over a p-adic field

For a nonarchimedean local field F, let GL(n):= GL(n, F) and GL(n?1) be embedded in GL(n) via g ? ( _{0 1} ^{g 0} ). Let π be an irreducible admissible representation of GL(n) for n ≥ 3. We prove that π is GL(n ? 1)-distinguished if and only if the Langlands parameter L(π) associated to π by the Local Langlands Correspondence has a subrepresentation L(11 _n?2) of dimension n?2 corresponding to the trivial representation of GL(n?2) such that the two-dimensional quotient L(π)/L(11 _n?2) corresponds either to an infinite-dimensional representation or the one-dimensional representations $\nu ^{ \pm (\tfrac{{n - 2}}{2})} $ of GL(2). We also prove that, for a parabolic subgroup P of GL(n) and an irreducible admissible representation ρ of the Levi subgroup of P, $\dim _\mathbb{C} (Hom_{GL(n - 1)} [ind_P^{GL(n)} (\rho ),\mathbb{I}_{n - 1} ]) \leqslant 2$ . For the standard Borel subgroup B _n of GL(n) and characters x _i of GL(1), we classify all representations ξ of the form $ind_{B_n }^{GL(n)} (\chi _1 \otimes \cdots \otimes \chi _n )$ for which $\dim _\mathbb{C} (Hom_{GL(n - 1)} [\xi ,\mathbb{I}_{n - 1} ]) = 2$ .     

On the value distribution of f a(f')~n

Let f be a transcendental meromorphic function,a a nonzero finite complex number,and n 2 a positive integer.Then f a(f')n assumes every complex value infinitely often.This answers a question of Ye for n = 2.A related normality criterion is also given.     

On Complex-Valued Solutions of the General Loaded Korteweg–de Vries Equation with a Source

Differential Equations - Using the inverse scattering method, we derive the evolution of the scattering data of a nonself-adjoint Sturm–Liouville operator whose potential is a solution of the...