High performance liquid chromatographic separation of polar and non-polar chlorophyll pigments from algae using a wide pore polymeric octadecylsilica column

A method employing a wide pore polymeric reversed phase column has been developed for the separation of most of the chlorophylls and related compounds previously described as occurring in marine microalgae. The high selectivity toward molecular shape of this kind of stationary phase has enabled compounds of very similar structure, such as chlorophylls c₁, c₂ and Mg-divinylpheoporphyrin a₅ monomethyl ester, and chlorophyll a and the phytol-substituted chlorophyll c-like pigments, which commonly coelute on monomeric bonded phases, to be resolved in a single run. Some of these pigments, formerly thought to be a single compound, have, in fact, been demonstrated to be groups of two or more. The method has been successfully applied to both algal cultures and natural sea water samples. When visible light absorbance detection was used, the method proved suitable for separation of various carotenoids.     

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.     

Classification of the space spanned by theta series and applications

We determine a class of functions spanned by theta series of higher degree. We give two applications: A simple proof of the inversion formula of such theta series and a classification of skew-holomorphic Jacobi forms.

     

Zeros of functions with finite Dirichlet integral

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.

     

Heuristic Algorithms and Scatter Search for the Cardinality Constrained P||Cmax Problem

We consider the generalization of the classical P||C_max problem (assign n jobs to m identical parallel processors by minimizing the makespan) arising when the number of jobs that can be assigned to each processor cannot exceed a given integer k. The problem is strongly NP-hard for any fixed k > 2. We briefly survey lower and upper bounds from the literature. We introduce greedy heuristics, local search and a scatter search approach. The effectiveness of these approaches is evaluated through extensive computational comparison with a depth-first branch-and-bound algorithm that includes new lower bounds and dominance criteria.     

Letter: Models of Relativistic Particle with Curvature and Torsion Revisited

Models, describing relativistic particles, where Lagrangian densities depend linearly on both the curvature and the torsion of the trajectories, are revisited in D=3 space forms. The moduli spaces of trajectories are completely and explicitly determined using the Lancret program. The moduli subspaces of closed solitons in the three sphere are also determined.     

Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some criteria ensuring existence of isoperimetric regions: for instance, local convexity of the cone at some boundary point.

We also characterize which are the stable regions in a convex cone, i.e., second order minima of perimeter under a volume constraint. From this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone.

     

A risk model driven by Lévy processes

We present a general risk model where the aggregate claims, as well as the premium function, evolve by jumps. This is achieved by incorporating a Lévy process into the model. This seeks to account for the discrete nature of claims and asset prices. We give several explicit examples of Lévy processes that can be used to drive a risk model. This allows us to incorporate aggregate claims and premium fluctuations in the same process. We discuss important features of such processes and their relevance to risk modeling. We also extend classical results on ruin probabilities to this model. Copyright © 2003 John Wiley & Sons, Ltd.     

Partitioning Balls into Topologically Equivalent Pieces

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Partitioning Balls into Topologically Equivalent Pieces

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