The simplex dispersion ordering and its application to the evaluation of human corneal endothelia

A multivariate dispersion ordering based on random simplices is proposed in this paper. Given a R^d-valued random vector, we consider two random simplices determined by the convex hulls of two independent random samples of sizes d+1 of the vector. By means of the stochastic comparison of the Hausdorff distances between such simplices, a multivariate dispersion ordering is introduced. Main properties of the new ordering are studied. Relationships with other dispersion orderings are considered, placing emphasis on the univariate version. Some statistical tests for the new order are proposed. An application of such ordering to the clinical evaluation of human corneal endothelia is provided. Different analyses are included using an image database of human corneal endothelia.     

Counting bitangents with stable maps

This paper is an elementary introduction to the theory of moduli spaces of curves and maps. As an application to enumerative geometry, we show how to count the number of bitangent lines to a projective plane curve of degree d by doing intersection theory on moduli spaces.     

Subgame perfect equilibria in stopping games

Stopping games (without simultaneous stopping) are multi-player sequential games in which at every stage one of the players is chosen according to a stochastic process, and that player decides whether to continue the interaction or to stop it, whereby the terminal payoff vector is obtained by another stochastic process. We prove that if the payoff process is integrable, a $\delta $ -approximate subgame perfect ${\epsilon }$ -equilibrium exists for every $\delta ,\epsilon >0$ ; that is, there exists a strategy profile that is an ${\epsilon }$ -equilibrium in all subgames, except possibly in a set of subgames that occurs with probability at most $\delta $ (even after deviation by some of the players).     

The classification of homotopy classes of bounded curvature paths

A bounded curvature path is a continuously differentiable piecewise C² path with bounded absolute curvature that connects two points in the tangent bundle of a surface. In this note we give necessary and sufficient conditions for two bounded curvature paths, defined in the Euclidean plane, to be in the same connected component while keeping the curvature bounded at every stage of the deformation. Following our work in [3], [2] and [4] this work finishes a program started by Lester Dubins in [6] in 1961.     

The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics

This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator.

     

Ultrasonic micellar extraction of polycyclic aromatic hydrocarbons from marine sediments

In this present study the extraction of polycyclic aromatic hydrocarbons (PAHs) from marine sediments with a micellar medium of Polyoxyethylene 10 lauryl ether by an ultrasound-assisted method has been studied. Factorial design experiments were used in order to optimize the extraction parameters: extraction time, surfactant concentration and surfactant volume:amount of sediment relationship. The results suggest that surfactant concentration is statistically the most significant factor. The analysis of extracts has been carried out by HPLC with UV detection. Fortified sediments gave an average recovery between 86.7 and 106.6%, with relative standard deviation of 2.02-6.83% for PAHs with a ring number higher than three.     

Opposed-flow flame spread in microgravity-theoretical prediction of spread rate and flammability map

The spread rate formulas of de Ris in the thermal regime of opposed-flow flame spread are inarguably the most well-known formulas in the flame spread literature. Similar easy-to-use formulas are lacking in all other regimes of flame spread. This paper presents a simplified analysis leading to the development of closed-form expressions for spread rate for both thin and thick fuels in the microgravity regime of opposed-flow flame spread. The resulting formulas, expressed in terms of the thermal limit of spread rate and a radiation number that can be evaluated from the known parameters of the problem, are shown to reproduce the experimentally and numerically observed trends quite well at both limits of fuel thickness. These formulas are utilized to develop quantitative criterion to delineate thin and thick fuels in the microgravity and thermal regimes. The transition between the microgravity and thermal regimes is also explored. The flammability maps, derived from the spread rate expressions, are the first of their kind, establishing fuel thickness as one of the critical parameters.     

Free Superoxide is an Intermediate in the Production of H2O2 by Copper(I)‐Aβ Peptide and O2

Oxidative stress is considered as an important factor and an early event in the etiology of Alzheimer's disease (AD). Cu bound to the peptide amyloid‐β (Aβ) is found in AD brains, and Cu‐Aβ could contribute to this oxidative stress, as it is able to produce in vitro H₂O₂ and HO^. in the presence of oxygen and biological reducing agents such as ascorbate. The mechanism of Cu‐Aβ‐catalyzed H₂O₂ production is however not known, although it was proposed that H₂O₂ is directly formed from O₂ via a 2‐electron process. Here, we implement an electrochemical setup and use the specificity of superoxide dismutase‐1 (SOD1) to show, for the first time, that H₂O₂ production by Cu‐Aβ in the presence of ascorbate occurs mainly via a free O₂^.? intermediate. This finding radically changes the view on the catalytic mechanism of H₂O₂ production by Cu‐Aβ, and opens the possibility that Cu‐Aβ‐catalyzed O₂^.? contributes to oxidative stress in AD, and hence may be of interest.