Metal-chelating nanoparticles as selective fluorescent sensor for Cu2+

A fluorescent sensor for Cu(2+) at the nanomolar level in water has been designed by associating a BODIPY fluorophore and a selective ligand (cyclam) in ultrafine polymer nanoparticles.     

Tetrahedral onsager crosses for solubility improvement and crystallization bypass

Pure organic molecules exhibiting a suitable concave rigid shape are expected to give porous glasses in the solid state. Such a feature opens new opportunities to avoid crystallization and to improve molecular solubility in relation to the high internal energy of these solid phases. To quantitatively explore the latter strategy, a series of rigid tetrahedral conjugated molecules nC and the corresponding models nR have been synthesized. Related to the present purpose, several properties have been investigated using UV absorption, steady-state fluorescence emission, differential scanning calorimetry, (1)H NMR translational self-diffusion, magic angle spinning (13)C NMR, and multiple-beam interferometry experiments. The present tetrahedral crosses are up to 8 orders of magnitude more soluble than the corresponding model compounds after normalization to the same molecular length. In addition, they give concentrated monomeric solutions that can be used to cover surfaces with homogeneous films whose thickness goes down to the nanometer range. Such attractive features make cross-like molecular architectures promising for many applications.     

For Which Densities are Random Triangle-Free Graphs Almost Surely Bipartite?

Denote by the class of all triangle-free graphs on n vertices and m edges. Our main result is the following sharp threshold, which answers the question for which densities a typical triangle-free graph is bipartite. Fix > 0 and let . If n/2 m (1 – ) t ₃, then almost all graphs in are not bipartite, whereas if m (1 + )t ₃, then almost all of them are bipartite. For m (1 + )t ₃, this allows us to determine asymptotically the number of graphs in . We also obtain corresponding results for C -free graphs, for any cycle C of fixed odd length. Forschergruppe Algorithmen, Struktur, Zufall supported by Deutsche Forschungsgemeinschaft grant FOR 413/1-1     

On a Construction of Fast Direct Solvers

Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped and a fast direct solver is used there. All extendable domains are found. Eigenproblems are also considered.     

Approximation and Prediction of the Numerical Solution of Some Burgers Problems

The Aitken's ²-prediction of Brezinski has already been used by Morandi Cecchi et al. in order to compute a numerical approximation of the solution of a parabolic initial-boundary value problem. This method consists in two consecutive steps: the first one is the approximation with a finite elements method, where the solution of the involved nonlinear system is computed by Gauss–Seidel method; the second one is a prediction of further terms with Aitken's ²-process. By comparison with this method, we use other methods of prediction in another way. First, we consider a generalization of ²-prediction, the so-called -prediction. In this paper, we only use vector prediction which is more stable than the scalar one. Then, the methods of prediction presented can be used in order to predict the starting vector of the Gauss–Seidel method.     

Asymptotic behaviour of linear evolutionary integral equations

The asymptotic behaviour of bounded solutions of evolutionary integral equations in a Banach spaceX

Vorwort

Ohne Zusammenfassung     

On totally monotonic families of sequences

Summary. Total positivity is an important concept which has been studied by Gantmacher, Karlin and Schoenberg. In section 1, new properties of totally positive functions are given. The concept of totally monotonic families of sequences (TMFS), by mean of positivity of some determinant, is defined and studied. Applications to extrapolation algorithms are given. Received October 22, 1997 / Revised version received April 14, 1998 / Published online August 19, 1999