The uniqueness of the near hexagon on 729 points

We prove that any regular near hexagon with 729 vertices and lines of size 3 is derived from the ternary Golay code, thus settling the last case in doubt among the regular near hexagons with lines of size 3.     

Résultats négatifs en accélération de la convergence

Summary It is well known that some information is needed for accelerating efficiently the convergence of a sequence. We show in this article that, for several families of sequences, there is no algorithm accelerating the convergence of every sequence of the family.

     

On bounded time-dependent perturbations of operator cosine functions

In this note it is shown that the Cauchy problem associated with the infinitesimal generatorA of a strongly continuous operator cosine function remains uniformly well-posed under bounded time-dependent perturbations ofA.     

Convergence of weighted sums of random elements in D[0, 1]

Convergence in probability for Toeplitz weighted sums is obtained for convex tight random elements in D[0, 1] under pointwise conditions. The almost sure convergence of the weighted sums is proved for independent, convex tight random elements and for independent, identically distributed random elements. Special techniques and concepts are developed in order to obtain these results in the Skorohod topology of D[0, 1].     

Graph factorization,general triple systems,and cyclic triple systems

In this self-contained exposition, results are developed concerning one-factorizations of complete graphs, and incidence matrices are used to turn these factorization results into embedding theorems on Steiner triple systems. The result is a constructive graphical proof that a Steiner triple system exists for any order congruent to 1 or 3 modulo 6. A pairing construction is then introduced to show that one can also obtain triple systems which are cyclically generated.     

Intercalates of α-Sn(HP04)2·H2O with aromatic and heterocyclic bases and some comments on their orientation in the interlayer region

The intercalation of amines into -tin(IV) hydrogen phosphate, -Sn(HP0₄)₂·H₂0, (-SnP) can occur to give mono- or bilayers of the guest molecule. The distribution and orientation of the amines is influenced by geometrical factors, acidity of the guest molecule and moreover, the degree of charge localisation of the guest organic cations. Regarding the monolayer formation, there are two possibilities. The first is that aromatic amines form monolayers with parallel orientation of the amine with respect to the phosphate layer, when the charge is delocalised over the aromatic ring. Monolayer formation with perpendicular orientation occurs when the positive charge is localised in opposite parts of the aromatic ring molecule. Bilayer formation occurs when the positive charge is localised in one part of the molecule and simultaneous interaction with two adjacent layers is not possible.     

The asymptotic number of geometries

A simple proof is given that lim_n?t8(log₂ log₂g_n)/n = 1, where g_n denotes the number of distinct combinatorial geometries on n point