Almost Sure Approximation of the Superposition of the Random Processes

This article presents sufficient conditions, which provide almost sure (a.s.) approximation of the superposition of the random processes S(N(t)), when càd-làg random processes S(t) and N(t) themselves admit a.s. approximation by a Wiener or stable Lévy processes. Such results serve as a source of numerous strong limit theorems for the random sums under various assumptions on counting process N(t) and summands. As a consequence we obtain a number of results concerning the a.s. approximation of the Kesten–Spitzer random walk, accumulated workload input into queuing system, risk processes in the classical and renewal risk models with small and large claims and use such results for investigation the growth rate and fluctuations of the mentioned processes.     

Penultimate Approximations in Statistics of Extremes and Reliability of Large Coherent Systems

In reliability theory any coherent system can be represented as either a series-parallel or a parallel-series system. Its lifetime can thus be written as the minimum of maxima or the maximum of minima. For large-scale coherent systems it is sensible to assume that the number of system components goes to infinity. Then, the possible non-degenerate extreme value laws either for maxima or for minima are eligible candidates for the system reliability or at least for the finding of adequate lower and upper bounds for the reliability. The identification of the possible limit laws for the system reliability of homogeneous series-parallel (or parallel-series) systems has already been done under different frameworks. However, it is well-known that in most situations such non-degenerate limit laws are better approximated by an adequate penultimate distribution. Dealing with regular and homogeneous parallel-series systems, we assess both theoretically and through Monte-Carlo simulations the gain in accuracy when a penultimate approximation is used instead of the ultimate one.     

Using a cognitive architecture with a physiological substrate to represent effects of a psychological stressor on cognition

Adding a physiological representation to a cognitive architecture offers an attractive approach to modeling the effects of stress on cognition. We introduce ACT-R/Φ, an extended version of the ACT-R cognitive architecture that includes an integrative model of physiology. The extension allows the representation of how physiology and cognition interact. This substrate was used to represent potential effects of a startle response and task-based stress during a mental arithmetic (subtraction) task. We compare predictions from two models loaded into the new hybrid architecture to models previously developed within ACT-R. General behavior differed between models in that the ACT-R/Φ models had dynamic declarative memory noise over the course of the task based on varying epinephrine levels. They attempted more subtractions but were less accurate; this more closely matched human performance than the previous ACT-R models. Using ACT-R/Φ allows a more tractable integration of current physiological and cognitive perspectives on stress. ACT-R/Φ also permits further exploration of the interaction between cognition and physiology, and the emergent effects on behavior caused by the interaction among physiological subsystems. This extension is useful for anyone exploring how the human mind can occur in and be influenced by the physical universe.     

Deformations of Charged Axially Symmetric Initial Data and the Mass–Angular Momentum–Charge Inequality

We show how to reduce the general formulation of the mass–angular momentum–charge inequality, for axisymmetric initial data of the Einstein–Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to the basic inequality yielding a lower bound for the area of black holes in terms of mass, angular momentum, and charge. This extends previous work by the authors (Cha and Khuri, Ann Henri Poincaré, doi: 10.1007/s00023-014-0332-6, arXiv:1401.3384, 2014), in which the role of charge was omitted. Lastly, we improve upon the hypotheses required for the mass–angular momentum–charge inequality in the maximal case.     

A new rotating-disk sorptive extraction mode,with a copolymer of divinylbenzene and N-vinylpyrrolidone trapped in the cavity of the disk,used for determination of florfenicol residues in porcine plasma

A novel extraction approach was developed based on rotating-disk sorptive extraction (RDSE). In this approach the rotating-disk extraction device consists of a Teflon disk, with a cavity that is loaded with a commercial sorbent phase selected according to the polarity of the analyte. To avoid leakage of the sorbent, the cavity is covered with a fiberglass filter and sealed with a Teflon ring. The proposed novel analytical RDSE technique was used in this study to determine florfenicol levels in plasma as a model analyte, or sample system, to describe the pharmacokinetics of a veterinary formulation. The sorbent used for this application was the copolymer of divinylbenzene and N-vinylpyrrolidone (Oasis HLB), which was selected because the florfenicol molecule contains both hydrophilic and lipophilic moieties. After the extraction, final determination of the analyte was performed by HPLC–DAD. Calibration plots and other analytical features were obtained after 90 min of extraction. The calibration plot was linear over the interval 0.4–16 μg mL^?1 (n?=?6), with R ²?=?0.9999. Recovery and repeatability were determined using a blank plasma sample spiked with 4.8 μg mL^?1 florfenicol. A recovery of 91.5 %, with a relative standard deviation (RSD) of 8.8 %, was obtained when the extraction was evaluated using six different rotating-disk devices. Precision was also assessed, using the same disk (containing the same sorbent phase) for eight aliquots of the same sample. The RSD under these conditions was 10.2 %, clearly indicating that the sorptive phase could possibly be re-used. Accordingly, RDSE is a suitable sample preparation alternative to liquid–liquid extraction (LLE), solid-phase extraction (SPE), and stir-bar sorptive extraction (SBSE).     

Multi-Center Vector Field Methods for Wave Equations

We develop the method of vector-fields to further study Dispersive Wave Equations. Radial vector fields are used to get a-priori estimates such as the Morawetz estimate on solutions of Dispersive Wave Equations. A key to such estimates is the repulsiveness or nontrapping conditions on the flow corresponding to the wave equation. Thus this method is limited to potential perturbations which are repulsive, that is the radial derivative pointing away from the origin. In this work, we generalize this method to include potentials which are repulsive relative to a line in space (in three or higher dimensions), among other cases. This method is based on constructing multi-centered vector fields as multipliers, cancellation lemmas and energy localization.