Diffusion-induced Spatio-temporal Oscillations in an Epidemic Model with Two Delays

We investigate a diffusive, stage-structured epidemic model with the maturation delay and freelymoving delay. Choosing delays and diffusive rates as bifurcation parameters, the only possible way to destabilize the endemic equilibrium is through Hopf bifurcation. The normal forms of Hopf bifurcations on the center manifold are calculated, and explicit formulae determining the criticality of bifurcations are derived. There are two different kinds of stable oscillations near the first bifurcation: ...     

Constructing banking networks under decreasing costs of link formation

The structure of networks plays a central role in the behavior of financial systems and their response to policy. Real-world networks, however, are rarely directly observable: banks’ assets and liabilities are typically known, but not who is lending how much and to whom. This paper adds to the existing literature in two ways. First, it shows how to simulate realistic networks that are based on balance-sheet information. To do so, we introduce a model where links cause fixed-costs, independent of contract size; but the costs per link decrease the more connected a bank is (scale economies). Second, to approach the optimization problem, we develop a new algorithm inspired by the transportation planning literature and research in stochastic search heuristics. Computational experiments find that the resulting networks are not only consistent with the balance sheets, but also resemble real-world financial networks in their density (which is sparse but not minimally dense) and in their core-periphery and disassortative structure.

     

Convolution semigroups and central limit theorem associated with a dual convolution structure

We consider hypergroups associated with Jacobi functions ⁽⁾ (x), (–1/2). We prove the existence of a dual convolution structure on [0,+[i(]0,s ₀]{{) =++1,s ₀=min(,–+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem.     

An energy-transport model for semiconductors derived from the Boltzmann equation

An energy-transport model is rigorously derived from the Boltzmann transport equation of semiconductors under the hypothesis that the energy gain or loss of the electrons by the phonon collisions is weak. Retaining at leading order electron-electron collisions and elastic collisions (i.e., impurity scattering and the elastic part of phonon collisions), a rigorous diffusion limit of the Boltzmann equation can be carried over, which leads to a set of diffusion equations for the electron density and temperature. The derivation is given in both the degenerate and nondegenerate cases.     

Subordination des résolvantes

Résumé Soit (V ₎₀ une résolvante définie sur un espace mesurable telle que le noyau initial est borné; on trouve une condition nécéssaire et suffisante pour qu'un noyau borné U possède une résolvante (U ₎₀ telle que U V pour tout 0. On donne plusieurs applications de ce résultat.     

Macroscopic expression of the chirality of amino alcohols by a double amplification mechanism in liquid crystalline media

The central chirality of simple amino alcohols was amplified by binding to a dynamically axially chiral biphenol receptor and expressed as supramolecular chirality by effecting a change from a nematic to a cholesteric liquid crystalline phase.     

Inaccessible hydroxyl groups on silica are accessible in supercritical CO2

The three main types of hydroxyl groups on a silica surface are classified as isolated, hydrogen bonded, and inaccessible. The isolated and hydrogen bonded groups are the most important as these readily exchange with D(2)O and thus are exposed to reactant molecules. However, it has generally been accepted that the inaccessible groups do not participate in surface reactions as only a small fraction of these groups exchange with D(2)O. It is shown that the inaccessible hydroxyl groups on nonporous fumed silica and mesoporous MCM-48 silica powders and films fully exchange with D(2)O and are reactive with octadecylydimethylchlorosilane when supercritical CO(2) is used as the solvent. Furthermore, it is found that the CO(2) penetrating the regions containing the inaccessible groups is not removed by simple evacuation but rather slowly diffuses from the silica over periods of months.