A note on the application of wazewski’s topological method to an integro: differential equation of volterra type

The purpose of this note is to generalize the Wazewski’s Topological Method 11, originally stated for ordinary differential equations, to the integro – differential equation of Volterra type (1), under suitable conditions on the functions involved.Fil: Napoles Valdes, Juan Eduardo. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; ArgentinaFil: Velázquez, José R.. Universidad Nacional del Nordeste; ArgentinaFil: Lugo, Luciano Miguel. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; ArgentinaFil: Guzmán, Paulo Matias. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Some aspects of the energy cost linked to the IAQ. Impact of free-cooling and heat recovery in office buildings.

CLIMA 2000 (.1997.BRUSELAS)Increasing air exchange rate to improve IAQ may increase energy consumption, but this increase may be compensated for by strategies such as free cooling and heat recovery. The frame of the proposed paper is the examination of the potential at a regional level (the Iberian peninsula) of the different strategies mentioned above in typical office buildings. Based on a set of reference building morphologies, studies are conducted to evaluate the impact of increasing air ventilation rates for different orientations, quality of the envelope (opaque walls and glazing), operating schedules and indoor set-point temperatures. Then, the impact of the increased air ventilation rates is corrected by introducing the effect of free-cooling, air-to-air heat recovery devices of different types and finally, the combined effect of both energy savings strategies. The research provides Maps allowing: 1. To identify zones when heating or cooling regimes are dominant, in terms of both, peak load conditions and energy requirements. 2. To compare the expected performance of the two energy saving strategies at a certain locality. 3. To compare the potential benefit of applying a given strategy at different localities. 4. To indicate regions of recommendable application of the strategies and the expected energy savings achievable

Traumatic brain injury in pedestrian–vehicle collisions: Convexity and suitability of some functionals used as injury metrics

Background and Objective: Abrupt accelerations or decelerations can cause large strain in brain tissues and, consequently, different forms of Traumatic Brain Injury (TBI). In order to predict the effect of the accelerations upon the soft tissues of the brain, many different injury metrics have been proposed (typically, an injury metric is a real valued functional of the accelerations). The objective of this article is to make a formal and empirical comparison, in order to identify general criteria for reasonable injury metrics, and propose a general guideline to avoid ill-proposed injury metrics. Methods: A medium-size sample of vehicle-pedestrian collisions, from Post Mortem Human Subject (PMHS) tests, is analyzed. A statistical study has been conducted in order to determine the discriminant power of the usual metrics. We use Principal Component Analysis to reduce dimensionality and to check consistency among the different metrics. In addition, this article compares the mathematical properties of some of these functionals, trying to identify the desirable properties that any of those functionals needs to fulfill in order to be useful for optimization. Results: We have found a pair-wise consistency of all the currently used metrics (any two injury metrics are always positively related). In addition, we observed that two independent principal factors explain about 72.5% of the observed variance among all collision tests. This is remarkable because it indicates that despite high number of different injury metrics, a reduced number of variables can explain the results of all these metrics. With regard to the formal properties, we found that essentially all injury mechanisms can be accounted by means of scalable, differentiable and convex functionals (we propose to call minimization suitable injury metric to any metric having these three formal properties). In addition three useful functionals, usable as injury metrics, are identified on the basis of the empirical comparisons. Conclusions: The commonly used metrics are highly consistent, but also highly redundant. Formal minimal conditions of a reasonable injury metric have been identified. Future proposals of injury metrics can benefit from the results of this study.Peer ReviewedPostprint (author's final draft

Two species coagulation approach to consensus by group level interactions

We explore the self-organization dynamics of a set of entities by considering the interactions that affect the different subgroups conforming the whole. To this end, we employ the widespread example of coagulation kinetics, and characterize which interaction types lead to consensus formation and which do not, as well as the corresponding different macroscopic patterns. The crucial technical point is extending the usual one species coagulation dynamics to the two species one. This is achieved by means of introducing explicitly solvable kernels which have a clear physical meaning. The corresponding solutions are calculated in the long time limit, in which consensus may or may not be reached. The lack of consensus is characterized by means of scaling limits of the solutions. The possible applications of our results to some topics in which consensus reaching is fundamental, like collective animal motion and opinion spreading dynamics, are also outlined

Enhanced near infrared optical access to the brain with a transparent cranial implant and scalp optical clearing.

We report on the enhanced optical transmittance in the NIR wavelength range (900 to 2400 nm) offered by a transparent Yttria-stabilized zirconia (YSZ) implant coupled with optical clearing agents (OCAs). The enhancement in optical access to the brain is evaluated upon comparing ex-vivo transmittance measurements of mice native skull and the YSZ cranial implant with scalp and OCAs. An increase in transmittance of up to 50% and attenuation lengths of up to 2.4 mm (i.e., a five-fold increase in light penetration) are obtained with the YSZ implant and the OCAs. The use of this ceramic implant and the biocompatible optical clearing agents offer attractive features for NIR optical techniques for brain theranostics

Spectral Measures of Bipartivity in Complex Networks

We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which individual nodes and edges contribute to the global network bipartivity. It is shown that the bipartivity characterizes the network structure and can be related to the efficiency of semantic or communication networks, trophic interactions in food webs, construction principles in metabolic networks, or communities in social networks.Comment: 16 pages, 1 figure, 1 tabl

Boundedness and Stability Properties of Some Integrodifferential Systems

      In this paper we study the behavior of solutions of a Volterra integrodif­ferential system of the form (1). &nbsp

Boundedness and Stability Properties of Some Integrodifferential Systems

      In this paper we study the behavior of solutions of a Volterra integrodif­ferential system of the form (1).

Boundedness and Stability Properties of Some Integrodifferential Systems

      In this paper we study the behavior of solutions of a Volterra integrodif­ferential system of the form (1). &nbsp