Optimal Investment in a Levy Market

In this paper we consider the optimal investment problem in a market where the stock price process is modeled by a geometric Levy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the resulting models are incomplete and there are many equivalent martingale measures. However, the model can be completed by the so-called power-jump assets. By doing this we allow investment in these new assets and we can try to maximize the expected utility of these portfolios. As particular cases we obtain the optimal portfolios based in stocks and bonds, showing that the new assets are superfluous for certain martingale measures that depend on the utility function we use.     

Embedded eigenvalues of Sturm Liouville operators

In this work we study the behavior of embedded eigenvalues of Sturm-Liouville problems in the half axis under local perturbations. When the derivative of the spectral function is strictly positive, we prove that the embedded eigenvalues either disappear or remain fixed. In this case we show that local perturbations cannot add eigenvalues in the continuous spectrum. If the condition on the spectral function is removed then a local perturbation can add infinitely many eigenvalues.     

Boundary conditions of Sturm-Liouville operators with mixed spectra

We study bounds on averages of spectral functions corresponding to Sturm-Liouville operators on the half line for different boundary conditions. As a consequence constraints are obtained which imply existence of singular spectrum embedded in a.c. spectrum for sets of boundary conditions with positive measure and potentials vanishing in an interval [0,N]. These constraints are related to estimates on the measure of sets where the spectral density is positive.     

Dispersion Characteristics of Waveguide Arrays in Optical Spectrum Analyzers

Formulas for calculating the spectral characteristics of waveguide arrays, which are incorporated into waveguide spectrum analyzers based on planar waveguides, channel waveguides, and fiber optical waveguides, are derived taking into account the contribution of both the waveguide dispersion and the material dispersion to the dispersion factor. These formulas are used to study the dependence of the dispersion factor on the waveguide-system parameters for specific models of waveguide arrays. It is shown that consideration of contributions of the waveguide dispersion and material dispersion can affect profoundly the spectral characteristics of waveguide arrays.     

Effects of alcohols on micellization and on the reaction methyl 4‐nitrobenzenesulfonate + Br− in cetyltrimethylammonium bromide aqueous micellar solutions

The effects of n‐hexanol, n‐pentanol, and n‐butanol on the critical micelle concentration (cmc), on the micellar ionization degree (α), and on the rate of the reaction methyl 4‐nitrobenzenesulfonate + Br^? have been investigated in cetyltrimethylammonium bromide (CTAB) aqueous solutions. An increase in the alcohol concentration present in the solution produces a decrease in the cmc and an increase in the micellar ionization degree. Kinetic data show that the observed rate constant decreases as alcohol concentration increases. This result was rationalized by considering variations in the equilibrium binding constant of the methyl 4‐nitrobenzenesulfonate molecules to the micelles, variations in the interfacial bromide ion concentration, and variations in the characteristics of the water–alcohol bulk phase provoked by the presence of alcohols. When these operative factors are considered, kinetic data in this and other works show that the second‐order rate constants in the micellar pseudophases of water–alcohol micellar solutions are quite similar to those estimated in the absence of alcohols. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 634–641, 2004     

Incubation period in the 2,2,4,4‐tetramethyl‐1‐piperidinyloxy‐mediated thermal autopolymerization of styrene: Kinetics and simulations

Mechanisms and simulations of the induction period and the initial polymerization stages in the nitroxide‐mediated autopolymerization of styrene are discussed. At 120–125 °C and moderate 2,2,4,4‐tetramethyl‐1‐piperidinyloxy (TEMPO) concentrations (0.02–0.08 M), the main source of radicals is the hydrogen abstraction of the Mayo dimer by TEMPO [with the kinetic constant of hydrogen abstraction (k_h)]. At higher TEMPO concentrations ([N?] > 0.1 M), this reaction is still dominant, but radical generation by the direct attack against styrene by TEMPO, with kinetic constant of addition k_ad, also becomes relevant. From previous experimental data and simulations, initial estimates of k_h ≈ 1 and k_ad ≈ 6 × 10^?7 L mol^?1 s^?1 are obtained at 125 °C. From the induction period to the polymerization regime, there is an abrupt change in the dominant mechanism generating radicals because of the sudden decrease in the nitroxide radicals. Under induction‐period conditions, the simulations confirm the validity of the quasi‐steady‐state assumption (QSSA) for the Mayo dimer in this regime; however, after the induction period, the QSSA for the dimer is not valid, and this brings into question the scientific basis of the well‐known expression k_th[M]³ (where [M] is the monomer concentration and k_th is the kinetic constant of autoinitiation) for the autoinitiation rate in styrene polymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6962‐6979, 2006     

Gold ultra-microelectrode arrays: application to the steady-state voltammetry of hydroxide ion in aqueous solution.

Gold ultra-microelectrode arrays are used to explore the electrochemical oxidation of hydroxide ions and are shown to be analytical useful. Two types of ultra-microelectrode arrays are used; the first consist of 256 individual electrodes of 5 microm in radius, 170 of which are electrochemically active in a cubic arrangement which are separated from their nearest neighbour by a distance of 100 microm. The second array compromises 2597 electrodes of 2.5 microm in radius and of which 1550 of which are electrochemically active in a hexagonal arrangement separated by the nearest neighbour by 55 microm. Well defined voltammetric waves are found with peak currents proportional to the concentration of hydroxide ions in the range 50 microM to 1 mM. Detection limits of 20 microM using the 170 ultra-microelectrode and 10 microM with the 1550 ultra-microelectrode array are shown to be possible but with a higher sensitivity of 4 mA M(-1) observed using the 1550 ultra-microelectrode array compared to 1.2 mA M(-1) with the 170 ultra-microelectrode array.