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.     

Measuring the similarity between trajectories using clustering techniques

A clustering method has been developed to group signals that display similar dynamic behavior. The procedure involves using the method of time delay embedding to construct a trajectory in state space from a time series. Certain features that characterize the geometry of the trajectory have been defined. These features were subjected to a series of statistical tests to determine their usefulness in a hierarchical clustering analysis. The latter is aimed at finding groups of similar trajectories. The trajectory-based clustering algorithm has been applied to simulated data, which included both stochastic data generated by a linear AR model, and nonlinear data generated by a Duffing oscillator. The results show that the algorithm works reliably in both cases.     

Synthesis and Photochromic Properties of Azido Analogues ofSpiropyran and Spirooxazine as Nucleic Acid Labeling Reagent

A series of photo active azido analogues have been synthesized and their photochromic properties have also been investigated by UV-Vis spectrum. It will be used for the rapid and reliable preparation of large amounts of stable, non-radioactive labeled DNA and RNA hybridization probes. And it is supposed to be easily detected for its photochromic properties.     

Light-driven molecular motors: stepwise thermal helix inversion during unidirectional rotation of sterically overcrowded biphenanthrylidenes

To investigate the unidirectional rotation of chiral overcrowded biphenanthrylidenes in more detail, the size of the substituent next to the double bond responsible for the unidirectionality of rotation was varied. The thermal and photochemical isomerization of three sterically overcrowded alkenes is described. The behavior of the biphenanthrylidenes with methyl and ethyl substituents is rather similar, and these compounds undergo a unidirectional 360 degrees rotation around the central double bond in a four-step sequence involving two photochemical cis-trans isomerizations and two thermal helix inversions. The only difference between these two true molecular motors was a small entropic effect, which causes the ethyl substituted molecular motor to rotate slightly faster. The behavior of the i-propyl substituted compound differs significantly from that of the other two. Although not all different isomers of the i-propyl substituted molecular motor were detected spectroscopically, experimental data led to the conclusion that this compound can also be considered as a molecular motor and is capable of performing a 360 degrees unidirectional rotation. (1)H NMR and X-ray analysis show a meso-like form as an intermediate in the unidirectional rotation, which proves that the thermal helix inversion is a stepwise process.