For n ≥ 2 let ∆ be a Dynkin diagram of rank n and let I = {1, . . . , n} be the set of labels of ∆. A group G admits a weak Phan system of type ∆ over C if G is generated by subgroups Ui, i ∈ I , which are central quotients of simply connected compact semisimple Lie groups of rank one, and contains subgroups Ui,j = 〈Ui, Uj〉, i 6= j ∈ I , which are central quotients of simply connected compact s...

a normed space $mathfrak{x}$ is said to have the fixed point property, if for each nonexpansive mapping $t : e longrightarrow e $ on a nonempty bounded closed convex subset $ e $ of $ mathfrak{x} $ has a fixed point. in this paper, we first show that if $ x $ is a locally compact hausdorff space then the following are equivalent: (i) $x$ is infinite set, (ii) $c_0(x)$ is infinite dimensional, (...

I review the Marseille GRAPE systems and the N-body simulations done with them. First I briefly describe the available hardware and software, their possibilities and their limitations. I then describe work done on interacting galaxies and groups of galaxies. This includes simulations of the formation of ring galaxies, simulations of bar destruction by a massive compact satellite, of merging in ...

Fifty years ago, at the International Congress in Bologna, Hermann Weyl gave a report on representations of compact groups and, in particular, of compact Lie groups. Most of the important results had just been proved by him and by others, and at the time of his lecture, in 1928, the representation theory of compact Lie groups had become a very appealing subject. To a large extent, Weyl's theory...

Theorem. If fo is a continuous function on a compact set C without interior and with connected complement of the complex plane, and if fi, • • ■ i fn are continuous functions on a compact totally disconnected subset E of C, then there exists a sequence {pi} of polynomials such that pi-^fo uniformly on C as i—* , and pim—*fk uniformly on E as i—>», for lslk^n, where pi[k] is the kth derivativ...

I discuss the nature of the compact X-ray source inside the supernova remnant RCW 103. Several models, based on the accretion onto a compact object such as a neutron star or a black hole (isolated or binary), are analyzed. I show that it is more likely that the X-ray source is an accreting neutron star than an accreting black hole. I also argue that models of a binary system with an old accreti...