Random and stochastic disturbances on the input flow in chemostat models with wall growth

In this paper, we analyze a chemostat model with wall growth where the input flow is perturbed by two different stochastic processes: the well-known standard Wiener process, which leads into several drawbacks from the biological point of view, and a suitable Ornstein-Uhlenbeck process depending on some parameters which allow us to control the noise to be bounded inside some interval that can be fixed previously by practitioners. Thanks to this last approach, which has already proved to be very realistic when modeling other simplest chemostat models, it will be possible to prove the persistence and coexistence of the species in the model without needing the theory of random dynamical systems and pullback attractors needed when dealing with the Wiener process. This is an advantage since the theoretical framework in this paper is much less complicated and provides us much more information than the other.     

A compact rational Krylov method for large‐scale rational eigenvalue problems

In this work, we propose a new method, termed as R‐CORK, for the numerical solution of large‐scale rational eigenvalue problems, which is based on a linearization and on a compact decomposition of the rational Krylov subspaces corresponding to this linearization. R‐CORK is an extension of the compact rational Krylov method (CORK) introduced very recently in the literature to solve a family of nonlinear eigenvalue problems that can be expressed and linearized in certain particular ways and which include arbitrary polynomial eigenvalue problems, but not arbitrary rational eigenvalue problems. The R‐CORK method exploits the structure of the linearized problem by representing the Krylov vectors in a compact form in order to reduce the cost of storage, resulting in a method with two levels of orthogonalization. The first level of orthogonalization works with vectors of the same size as the original problem, and the second level works with vectors of size much smaller than the original problem. Since vectors of the size of the linearization are never stored or orthogonalized, R‐CORK is more efficient from the point of view of memory and orthogonalization than the classical rational Krylov method applied directly to the linearization. Taking into account that the R‐CORK method is based on a classical rational Krylov method, to implement implicit restarting is also possible, and we show how to do it in a memory‐efficient way. Finally, some numerical examples are included in order to show that the R‐CORK method performs satisfactorily in practice.     

Design alternatives for a thin lens spatial integrator array

In this paper we analyze different alternatives in the design of optimized optical arrays having spatial integration feature in a plane arrangement. More specifically, we focus our attention in the evaluation of the number of useful individual units, and its contribution to the synthetic image characteristics. The analysis has been made by using matrix optics relations. Two examples of planar thin lens spatial integrator arrays are designed and compared.     

Inter-channel de-correlation for perceptual audio coding

Sound reproduction is evolving towards multi-channel systems with a growing number of channels. Consequently, high quality multi-channel codecs are required. Last generation perceptual audio codecs, represented by MPEG advanced audio coder (AAC), can efficiently code typical surround multi-channel material but may benefit from a previous block of inter-channel de-correlation, for certain audio recordings. These recordings present high correlation between non-symmetric channels, or correspond to loudspeaker arrangements different from surround, such as linear loudspeaker arrays. In order to valuate the advantages of this new coding approach, a multi-channel perceptual quality measure is developed.     

Best approach regions for potential spaces

We characterize the approach regions so that the non-tangential maximal function is of weak-type on potential spaces, for which we use a simple argument involving Carleson measure estimates.

     

New biimidazole and bibenzimidazole derivatives: mono and binuclear palladium(II) or platinum(II) complexes and heterobinuclear palladium(II)-rhodium(I) or platinum(II)-rhodium(I) complexes

Novel neutral biimidazolate or bibenzimidazolate palladium(II) and platinum(II) complexes of the type M(NN)₂(dpe) [M = Pd, Pt; (NN)₂^2? = BiIm^2?, BiBzIm^2?. dpe = 1,2-bis(diphenylphosphino) ethane] have been obtained by reacting MCl₂(dpe) with TI₂(NN)₂. Complexes M(NN)₂(dpe) which are Lewis bases react with HClO₄ or [M(dpe)(Me₂CO)₂](ClO₄)₂ to yield, respectively, mononuclear cationic complexes of general formula [M{H₂(NN)₂](dpe) (M = Pd, Pt; H₂(NN)₂ = H₂BiIm, H₂BiBzIm) and homobinuclear palladium(II) or platinum(II) cationic complexes of the type [M₂{μ - (NN)₂}(dpe)₂](ClO₄)₂. Reactions of M(BiBzIm)(dpe) with [Rh(COD) (Me₂CO)_X](ClO₄) render similar heterobinuclear palladium(II)-rhodium(I) and platinum(II)-rhodium(I) cationic complexes, of general formula [(dpe)M(μ-BiBzIm)Rh(COD)](ClO₄) (M = Pd, Pt; COD = 1,5-cyclooctadiene). Di- and mono-carbonyl derivatives [(dpe)M(μ-BiBzIm)Rh(CO)L](ClO₄) (M = Pd, Pt; L = CO, PPh₃) have also been prepared. The structures of the resulting complexes have been elucidated by conductance studies and IR spectroscopy.