Synthesis, nuclear, and magnetic structures and magnetic properties of [Mn3(OH)2(SO4)2(H2O)2

[Mn(3)(OH)(2)(SO(4))(2)(H(2)O)(2)] and its deuterated analogue were synthesized by a hydrothermal technique and characterized by differential thermal analysis, thermogravimetric analysis, and IR spectroscopy. Its nuclear structure, determined by single-crystal X-ray analysis and Rietveld analysis of neutron powder-diffraction data, consists of a 3D network of chains of edge-sharing Mn(1)O(6), running along the c axis, connected by the apices of Mn(2)O(6) and SO(4) units. It is isostructural to the nickel analogue. Determination of the magnetic structure and measurements of magnetization and heat capacity indicate the coexistence of both magnetic long-range ordering (LRO) and short-range ordering (SRO) below a Néel temperature of 26 K, while the SRO is retained at higher temperatures. The moments of the two independent Mn atoms lie in the bc plane, and that of Mn(1) rotates continuously by 54 degrees towards the c axis on decreasing the temperature from 25 to 1.4 K. While the SRO may be associated with frustration of the moments within a Mn(3) trimer, the LRO is achieved by antiparallel alignment of the four symmetry-related trimers within the magnetic unit cell. A spin-flop field, measured by dc and ac magnetization on a SQUID, is observed at 15 kOe.     

Effects of Added Surfactant on the Dynamic Interfacial Tension Behavior of Acidic Oil/Alkaline Systems

The effects of a ready-made surfactant (sodium dodecyl sulfate) on the dynamic interfacial tension between a model acidic oil (linoleic acid dissolved in paraffin oil) and various aqueous alkaline (NaOH) systems have been studied using pendant drop tensiometry at surfactant concentrations both below and above the critical micelle concentration (CMC). Below the CMC the added surfactant contributes significantly to a further reduction of interfacial tension of the reacting acid/alkaline system, whereas above the CMC the added surfactant plays an important role in damping the dynamic trends observed for the reactive system alone. Copyright 2001 Academic Press.     

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.