Voronoi cells via linear inequality systems

The theory and methods of linear algebra are a useful alternative to those of convex geometry in the framework of Voronoi cells and diagrams, which constitute basic tools of computational geometry. As shown by Voigt and Weis in 2010, the Voronoi cells of a given set of sites T, which provide a tesselation of the space called Voronoi diagram when T is finite, are solution sets of linear inequality systems indexed by T. This paper exploits systematically this fact in order to obtain geometrical information on Voronoi cells from sets associated with T (convex and conical hulls, tangent cones and the characteristic cones of their linear representations). The particular cases of T being a curve, a closed convex set and a discrete set are analyzed in detail. We also include conclusions on Voronoi diagrams of arbitrary sets.     

Functional micropatterned surfaces prepared by simultaneous UV‐lithography and surface segregation of fluorinated copolymers

A new procedure focused on the design and preparation of structured and functional polymer surfaces by combination of two approaches acting simultaneously is developed. The elaboration of micrometer size patterned surfaces by UV‐light lithography is reported where, in addition, the surface chemical composition can be controlled by surface segregation of a fluorinated copolymer incorporated in the photopolymerizable mixture. As evidenced by contact angle and XPS measurements, the surface composition can be modified depending on such factors as with the environmental conditions or the concentration of copolymer in the blend. Moreover, the functionality of the copolymer is enhanced by the surface pattern created. As a consequence, the wettability of the films can be modified depending on the pattern and composition of the blend. By using this methodology, functional adaptive sensitive surfaces with a well‐defined topography will be obtained in one single step and without the use of tedious and time‐consuming multistep procedures. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Behavioral,electrophysiological and histopathological consequences of systemic manganese administration in MEMRI

Manganese (Mn²⁺)-enhanced magnetic resonance imaging (MEMRI) offers the possibility to generate longitudinal maps of brain activity in unrestrained and behaving animals. However, Mn²⁺ is a metabolic toxin and a competitive inhibitor for Ca²⁺, and therefore, a yet unsolved question in MEMRI studies is whether the concentrations of metal ion used may alter brain physiology. In the present work we have investigated the behavioral, electrophysiological and histopathological consequences of MnCl₂ administration at concentrations and dosage protocols regularly used in MEMRI. Three groups of animals were sc injected with saline, 0.1 and 0.5 mmol/kg MnCl₂, respectively. In vivo electrophysiological recordings in the hippocampal formation revealed a mild but detectable decrease in both excitatory postsynaptic potentials (EPSP) and population spike (PS) amplitude under the highest MnCl₂ dose. The EPSP to PS ratio was preserved at control levels, indicating that neuronal excitability was not affected. Experiments of pair pulse facilitation demonstrated a dose dependent increase in the potentiation of the second pulse, suggesting presynaptic Ca²⁺ competition as the mechanism for the decreased neuronal response. Tetanization of the perforant path induced a long-term potentiation of synaptic transmission that was comparable in all groups, regardless of treatment. Accordingly, the choice accuracy tested on a hippocampal-dependent learning task was not affected. However, the response latency in the same task was largely increased in the group receiving 0.5 mmol/kg of MnCl₂. Immunohistological examination of the hippocampus at the end of the experiments revealed no sign of neuronal toxicity or glial reaction. Although we show that MEMRI at 0.1 mmol/Kg MnCl₂ may be safely applied to the study of cognitive networks, a detailed assessment of toxicity is strongly recommended for each particular study and Mn²⁺ administration protocol.     

A note on the universal consistency of the kernel distribution function estimator

The problem of universal consistency of data driven bandwidth selectors for the kernel distribution estimator is analyzed. We provide a uniform in bandwidth result for the kernel estimate of a continuous distribution function. Our smoothness assumption is minimal in the sense that if the true distribution function has some discontinuity then the kernel estimate is no longer consistent.     

A corrector for the sverdrup solution for a domain with islands

In this paper we look at the influence of the Coriolis force on the quasi-geostrophic equations on a domain with islands. We prove that asymptotically we obtain the solution of the Sverdrup equation with homogeneous Dirichlet conditions on the inward boundary plus a corrector function which takes into account the presence of the islands. This work is motivated by the fact that in oceanography most of the surfaces are not simply connected. This is the case for example for the North Pacific with the Japanese islands. At our knowledge, in all the previous mathematical works, just simply connected domains have been considered. Finally we will give some simple numerical simulations related to the Stommel model to see the importance of the corrector.     

Mesomorphic properties of a tetraphenylporphyrin metallomesogen with a weak hydrogen bond interaction between axial ligands: dihydroxo[5,10,15,20-tetrakis(4-n-dodecylphenyl)porphinato]silicon(IV)

A new metallomesogen, the dihydroxo[5,10,15,20-tetrakis(4-n-dodecylphenyl)porphinato]silicon(IV) complex, C₁₂TPPSi(OH)₂, was synthesized and its mesomorphism was investigated in terms of the axial hydrogen bond interaction in the stacked columnar structure. It was found that this compound exhibits a 3D plastic lamellar mesophase with a columnar structure, and the axial hydroxyl groups are connected by a very weak hydrogen bond interaction in the column. This causes a dramatic increase of the clearing point for the mesophase, even though the stacking periodicity is far larger (c. 9?Å) than that typically found for a columnar meosphase (c. 3.5?Å).     

Bandgap Modulation in Efficient n‐Thiophene Absorbers for Dye Solar Cell Sensitization

Five new sensitizers for dye sensitized solar cells have been designed consisting of conjugated thienylenevinylene units threaded with alkyl chains to improve solubility and cyanoacetic acid as anchoring group. The conjugation length was increased from 2 to 6 thienylenevinylene units, which resulted in a red‐shift of the optical absorption of the dyes from 550 to 750 nm, improving the spectral overlap with the solar spectrum. The photovoltaic performance of these dyes as sensitizers in mesoporous TiO₂ solar cells shows a clear correlation of increasing photocurrent with the extension of the conjugation up to an optimal length. Further extension of the conjugation increases the absorption but additional effects like self‐quenching or recombination processes reduce the photocurrent and photovoltages and consequently the overall efficiency of the DSC.     

Gemini amphiphilic pseudopeptides: synthesis and preliminary study of their self-assembling properties

The synthesis of a family of Gemini Amphiphilic Pseudopeptide (GAP) molecules by a reductive amination reaction has been carried out. The process is highly modular and can be efficiently performed with different pseudopeptidic diamines as well as aliphatic and aromatic aldehydes. Preliminary studies showed the abilities of the GAPs to self-assemble into supramolecular nanostructures.