Tail Behavior of a Threshold Autoregressive Stochastic Volatility Model

We consider a threshold autoregressive stochastic volatility model where the driving noises are sequences of iid regularly random variables. We prove that both the right and the left tails of the marginal distribution of the log-volatility process (α_t)_t are regularly varying with tail exponent −α with α > 0. We also determine the exact values of the coefficients in the tail behaviour of the process (α_t)_t. AMS 2000 Subject Classification. Primary—62G32, 62PO5     

Nonlinear synthesis of input signals in ultrasonic experimental setups

A method is proposed to find the digital input signals to enter in nonlinear acoustical systems (power amplifiers, transducers, etc.) in order to obtain desired arbitrary response signals. The searched input signals are found by performing a Monte Carlo search guided by a simulated annealing process applied to a hidden model with a small number of parameters. The physical system is actually used in the optimization procedure, in a real-time manner, so that no theoretical model of the system response is required. The main aspects of the algorithm are described and illustrated with several examples.     

Detection of acoustic waves by NMR using a radiofrequency field gradient

A B(1) field gradient-based method previously described for the detection of mechanical vibrations has been applied to detect oscillatory motions in condensed matter originated from acoustic waves. A ladder-shaped coil generating a quasi-constant RF-field gradient was associated with a motion-encoding NMR sequence consisting in a repetitive binomial 13;31; RF pulse train (stroboscopic acquisition). The NMR response of a gel phantom subject to acoustic wave excitation in the 20-200 Hz range was investigated. Results showed a linear relationship between the NMR signal and the wave amplitude and a spectroscopic selectivity of the NMR sequence with respect to the input acoustic frequency. Spin displacements as short as a few tens of nanometers were able to be detected with this method.     

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