Preliminary characterization of anhydrous ethanol used in Brazil as automotive fuel

This work reports preliminary studies on the characterisation of anhydrous ethanol (AEA) used as an automotive fuel mixed with gasoline in Porto Alegre (South Brazil). Pre-concentration of the impurities contained in 1000 ml of AEA was carried on through solid-phase extraction using XAD4 resin. The main compounds in the extract were identified by means of spectral data from the library of the equipment. The concentrate was then fractionated using a preparative liquid chromatographic column filled with activated silica gel and the elution procedure was carried out with, n-hexane, n-hexane-benzene (1:1, v/v) and dichloromethane. Prior to analysis by GC-MS, each fraction was reduced to 1 ml with a gentle stream of nitrogen. Saturated linear hydrocarbons and aromatic hydrocarbons eluted in the first fraction and oxygenated compounds such as aldehydes. ketones and alcohols, eluted in the second one. were the main compounds detected in the sample.     

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.     

Chaotic scattering in the gravitational three-body problem

We summarize some results of an ongoing study of the chaotic scattering interaction between a bound pair of stars (a binary) and an incoming field star. The stars are modeled as point masses and their equations of motion are numerically integrated for a large number of initial conditions. The global features of the resulting initial-value space maps are presented, and their evolution as a function of system parameters is discussed. We find that the maps contain regular regions separated by rivers of chaotic behavior. The probability of escape within the chaotic regions is discussed, and a straightforward explanation of the scaling present in these regions is reviewed. We investigate a statistical quantity of interest, namely the cross section for temporarily bound interactions, as a function of the third star's incoming velocity and mass. Finally, a new way of considering long-lived trajectories is presented, allowing long data sets to be qualitatively analyzed at a glance.     

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.