Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces

It is well known that the complexity of the Delaunay triangulation of $n$ points in $\RR ^d$, i.e., the number of its simplices, can be $\Omega (n^{\lceil {d}/{2}\rceil })$. In particular, in $\RR ^3$, the number of tetrahedra can be quadratic. Put another way, if the points are uniformly distributed in a cube or a ball, the expected complexity of the Delaunay triangulation is only linear. The case of points distributed on a surface is of great practical importance in reverse engineering since most surface reconstruction algorithms first construct the Delaunay triangulation of a set of points measured on a surface. In this paper we bound the complexity of the Delaunay triangulation of points distributed on the boundary of a given polyhedron. Under a mild uniform sampling condition, we provide deterministic asymptotic bounds on the complexity of the three-dimensional Delaunay triangulation of the points when the sampling density increases. More precisely, we show that the complexity is $O(n^{1.8})$ for general polyhedral surfaces and $O(n\sqrt{n})$ for convex polyhedral surfaces. Our proof uses a geometric result of independent interest that states that the medial axis of a surface is well approximated by a subset of the Voronoi vertices of the sample points.     

The Structural Nature of the Nerve Functor for n-Groupoids

Given a left exact category B, the construction of the nerve functor _n for n-groupoids in B is related to a certain property of the category S-S i m p l _{n – 1} B of the split (n – 1)-truncated simplicial objects in B, which allows us to define the split n-truncated simplicial objects in B completely internally to S-S i m p l _{n – 1} B and thus to construct intrisincally from it the category S-S i m p l _n B.     

Ultrasound-assisted microencapsulation of jackfruit extract in eco-friendly powder particles: characterization and antiproliferative activity

The aim of the article was to develop stable and safe eco-friendly microcapsules and evaluate their physicochemical properties and their efficiency to protect a jackfruit extract. Eco-friendly microcapsules were produced by ultrasound and spray drying using only three safe ingredients: sucrose ester (SE), miglyol and maltodextrin (DE = 10). Some physicochemical properties, particle morphology, FT-IR, differential scanning calorimetry and antiproliferative activity were determined for microcapsules loaded or not with the jackfuit extract. The results revealed that the encapsulation process by spray drying produced stable microcapsules, with adequate physicochemical and fluid properties for a powder product. The cell viability on the proliferation of M12.C3.F6 cell line was not affected by powder microcapsules without jackfruit extract, indicating that capsules are not toxic for these cells. However, microcapsules with jackfruit extract (100 μg/ml) were able to inhibit significantly the proliferation of M12.C3.F6 cells. These microcapsules can be used for the protection of different compounds sensitive to light, oxygen and/or heat and displaying a very low aqueous solubility.     

“Vapor-liquid” equilibrium measurements and modeling for the cyclohexane + n-hexanoic acid binary system

To simulate cyclohexane to cyclohexanol oxidation reactors, the acquisition and modeling of vapor-liquid equilibria of the key components, under the process conditions, are essential. n-Hexanoic acid is a co-product of the reaction. Vapor-liquid equilibrium data are reported for the cyclohexane + n-hexanoic acid binary system at four temperatures: 413, 423, 464 and 484 K. All measurements have been carried out using an apparatus based on the “static-analytic” method, with two ROLSI™ pneumatic capillary samplers. The generated data are successfully correlated using two equations of state, the Peng-Robinson (PR) and the Perturbed Chain Statistical Association Fluid Theory (PC-SAFT). Both models are capable of representing the experimental data, but the PC-SAFT EoS uses less binary interaction parameters.     

Three different β‐cyclodextrins direct the emulsion copolymerization of a highly fluorinated methacrylate toward distinctive nanostructured particle morphologies

Stable colloidal dispersions of nanostructured semifluorinated acrylic particles with an unfluorinated core and an outer layer consisting of copolymers of the highly hydrophobic and lipophobic heptadecafluorodecyl methacrylate (FMA) were successfully synthesized with the assistance of three different cyclodextrins as phase‐transfer catalysts: β‐cyclodextrin (β‐CD), hydroxypropyl β‐cyclodextrin (HpCD), and methyl β‐cyclodextrin (MeCD). While all the cyclodextrins form a stable inclusion complex (IC) with FMA, only the ICs with the more hydrophilic HpCD and MeCD are soluble in water. Nevertheless, incorporation of FMA in the particle shell copolymer could be achieved also when using β‐CD. On the other hand, the morphology of the nanostructured particles was characterized by a “patchy” fluorinated shell dependent on the cyclodextrin used, the best results being obtained with MeCD. A monomer‐starved semicontinuous emulsion polymerization procedure was essential to favor the CD‐mediated incorporation of FMA into the copolymer structure and to achieve a stable colloidal dispersion even in the presence of small amounts of mixed anionic–nonionic surfactants. The thermal and surface properties of the latex films showed a good correlation with the shell composition and patchy nanostructured morphology of the particles. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Polysaccharide Based Vaccines for The Prevention of Pneumococcal Infections

1. INTRODUCTION

Streptococcus pneumoniae remains an important cause of infections in this end of the 20th century and is responsible for invasive diseases - pneumonia, meningitis, bacteremia, septicemia - as well as for noninvasive diseases such as pharyngitis, conjunctivitis, otitis media.^1,2     

Measurement of Total and Unbound Mycophenolic Acid and Its Glucuronide by LC Coupled with MS. Application to a Pharmacokinetic Study of Mycophenolate Mofetil in Patients with Autoimmune Diseases

Liquid chromatography coupled with mass spectrometry for the determination of total and unbound mycophenolic acid and its major metabolite in human plasma has been developed. Sample preparations were based on a fully automated solid-phase extraction process and ultrafiltration. Mass spectrometric data were acquired in a single-ion monitoring method. The analytes and nevirapine (internal standard) were well separated in an isocratic mode over 8 min. Validation study exhibited excellent linearity, with intra- and inter-day precision and accuracy of less than 12%. The assay was successfully applied to the pharmacokinetic study of mycophenolic acid in patients with autoimmune diseases.     

Electronic core levels of hydroxyls at the surface of chromia related to their XPS O 1s signature: A DFT + U study

The Cr 2p and O 1s binding energy (BE) levels have been calculated by first principles methods for different models of hydroxylated (0001)-Cr₂O₃ surfaces. Several surface terminations have been considered. The calculations allow us to reproduce the O 1s shifts between O in oxide and OH groups. It is found that two main effects account for the OH binding energy shifts. On the one hand, the increased covalency of the O–H bond with respect to the Cr–O bond, lowers the electronic O (1s and 2p) energy, and in consequence the BE of the core levels (O 1s) are higher. On the other hand, the lower the OH coordination number, the higher the valence and core levels energy, and the lower the BE. Consequently, mono-coordinated hydroxyls have a binding energy near that of O^2? in the oxide (ΔBE_OH–O = ? 0.2–0.0 eV). Two-fold coordinated hydroxyls have a slightly higher BE (ΔBE_OH–O = + 0.3 eV). Three-fold coordinated OH groups have a higher binding energy (ΔBE_OH–O = + 0.6?0.7 eV), corresponding to that experimentally measured for OH groups. Finally, water adsorbed above OH groups exhibits a still higher BE (ΔBE_HOH–O = + 0.9–1.0 eV). The ΔBE are slightly under-estimated under the initial state approximation, and overestimated under the final state (Z + 1) approximation.     

Multiscale dynamics of 1H and 19F in confined ionogels for lithium batteries

We present the first results of the nuclear magnetic relaxation dispersion (NMRD) of the confined proton-bearing cation (BMI) and fluorine-bearing anion (TFSI) pair of ionic liquids (Li⁺-ionogels) confined within a silica-like mesoporous matrices designed for lithium batteries. These results are in favour of a very-correlated dynamical motion of the anion–cation pair within the solid and disordered silica matrix.