Countably compact extensions of topological spaces

We study the question whether a topological space X with a property $\text{P}$ can be embedded in a countably compact space X? with the same property $\text{P}$.     

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.     

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