Variable exponent Sobolev spaces associated with Jacobi expansions

In this paper we define variable exponent Sobolev spaces associated with Jacobi expansions. We prove that our generalized Sobolev spaces can be characterized as variable exponent potential spaces and as variable exponent Triebel-Lizorkin type spaces.Comment: 30 pages, small typos corrected in the introductio

Evidence for impulsivity in the Spontaneously Hypertensive Rat drawn from complementary response-withholding tasks

<p>Abstract</p> <p>Background</p> <p>The inability to inhibit reinforced responses is a defining feature of ADHD associated with impulsivity. The Spontaneously Hypertensive Rat (SHR) has been extolled as an animal model of ADHD, but there is no clear experimental evidence of inhibition deficits in SHR. Attempts to demonstrate these deficits may have suffered from methodological and analytical limitations.</p> <p>Methods</p> <p>We provide a rationale for using two complementary response-withholding tasks to doubly dissociate impulsivity from motivational and motor processes. In the lever-holding task (LHT), continual lever depression was required for a minimum interval. Under a differential reinforcement of low rates schedule (DRL), a minimum interval was required between lever presses. Both tasks were studied using SHR and two normotensive control strains, Wistar-Kyoto (WKY) and Long Evans (LE), over an overlapping range of intervals (1 – 5 s for LHT and 5 – 60 s for DRL). Lever-holding and DRL performance was characterized as the output of a mixture of two processes, timing and iterative random responding; we call this account of response inhibition the Temporal Regulation (TR) model. In the context of TR, impulsivity was defined as a bias toward premature termination of the timed intervals.</p> <p>Results</p> <p>The TR model provided an accurate description of LHT and DRL performance. On the basis of TR parameter estimates, SHRs were more impulsive than LE rats across tasks and target times. WKY rats produced substantially shorter timed responses in the lever-holding task than in DRL, suggesting a motivational or motor deficit. The precision of timing by SHR, as measured by the variance of their timed intervals, was excellent, flouting expectations from ADHD research.</p> <p>Conclusion</p> <p>This research validates the TR model of response inhibition and supports SHR as an animal model of ADHD-related impulsivity. It indicates, however, that SHR's impulse-control deficit is not caused by imprecise timing. The use of ad hoc impulsivity metrics and of WKY as control strain for SHR impulsivity are called into question.</p

Simulation study for investment decisions on the EcoBoost camshaft machining line

Design/redesign of manufacturing systems is a complex, risky, and expensive task. Ford Motor Company’s Valencia Engine Plant faces this challenge as it plans to upgrade its machining and assembly lines to introduce the new EcoBoost engines. The research project described in this paper aimed to support the transition process particularly at the camshaft machining line by using simulation modelling techniques. A series of experiments was carried out using the simulation model developed, and recommendations were proposed based on the results of these experiments to support the decision as to where to invest on the line. The outcomes from the research project indicated that investment is required in terms of increasing the capacity of two bottleneck operations through retooling and improving the conveyor routing logic in one key area. Keywords: simulation modelling, closed-loop network, automotive production system

In vitro increased respiratory activity of selected oral bacteria may explain competitive and collaborative interactions in the oral microbiome

Understanding the driving forces behind the shifts in the ecological balance of the oral microbiota will become essential for the future management and treatment of periodontitis. As the use of competitive approaches for modulating bacterial outgrowth is unexplored in the oral ecosystem, our study aimed to investigate both the associations among groups of functional compounds and the impact of individual substrates on selected members of the oral microbiome. We employed the Phenotype Microarray high-throughput technology to analyse the microbial cellular phenotypes of 15 oral bacteria. Multivariate statistical analysis was used to detect respiratory activity triggers and to assess similar metabolic activities. Carbon and nitrogen were relevant for the respiration of health-associated bacteria, explaining competitive interactions when grown in biofilms. Carbon, nitrogen, and peptides tended to decrease the respiratory activity of all pathobionts, but not significantly. None of the evaluated compounds significantly increased activity of pathobionts at both 24 and 48 h. Additionally, metabolite requirements of pathobionts were dissimilar, suggesting that collective modulation of their respiratory activity may be challenging. Flow cytometry indicated that the metabolic activity detected in the Biolog plates may not be a direct result of the number of bacterial cells. In addition, damage to the cell membrane may not influence overall respiratory activity. Our methodology confirmed previously reported competitive and collaborative interactions among bacterial groups, which could be used either as marker of health status or as targets for modulation of the oral environment

Chaotic dynamics around astrophysical objects with nonisotropic stresses

The existence of chaotic behavior for the geodesics of the test particles orbiting compact objects is a subject of much current research. Some years ago, Gu\'eron and Letelier [Phys. Rev. E \textbf{66}, 046611 (2002)] reported the existence of chaotic behavior for the geodesics of the test particles orbiting compact objects like black holes induced by specific values of the quadrupolar deformation of the source using as models the Erez--Rosen solution and the Kerr black hole deformed by an internal multipole term. In this work, we are interesting in the study of the dynamic behavior of geodesics around astrophysical objects with intrinsic quadrupolar deformation or nonisotropic stresses, which induces nonvanishing quadrupolar deformation for the nonrotating limit. For our purpose, we use the Tomimatsu-Sato spacetime [Phys. Rev. Lett. \textbf{29} 1344 (1972)] and its arbitrary deformed generalization obtained as the particular vacuum case of the five parametric solution of Manko et al [Phys. Rev. D 62, 044048 (2000)], characterizing the geodesic dynamics throughout the Poincar\'e sections method. In contrast to the results by Gu\'eron and Letelier we find chaotic motion for oblate deformations instead of prolate deformations. It opens the possibility that the particles forming the accretion disk around a large variety of different astrophysical bodies (nonprolate, e.g., neutron stars) could exhibit chaotic dynamics. We also conjecture that the existence of an arbitrary deformation parameter is necessary for the existence of chaotic dynamics.Comment: 7 pages, 5 figure

Minimal open sets on generalized topological space

We introduce the notion of minimal open sets in a generalized topological space (X μ). We investigate some of their fundamental properties and proved that any subset of a minimal open set on a GTS (X μ) is a μ-preopen se