Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spaces

We extend the theory of weighted norm inequalities on variable Lebesgue spaces to the case of bilinear operators. We introduce a bilinear version of the variable \A_\pp condition, and show that it is necessary and sufficient for the bilinear maximal operator to satisfy a weighted norm inequality. Our work generalizes the linear results of the first author, Fiorenza and Neugebauer \cite{dcu-f-nPreprint2010} in the variable Lebesgue spaces and the bilinear results of Lerner {\em et al.} \cite{MR2483720} in the classical Lebesgue spaces. As an application we prove weighted norm inequalities for bilinear singular integral operators in the variable Lebesgue spaces.Comment: Revised based on anonymous referee's reports. A number of typos and small errors corrected. One conjecture added to introductio

A Virtual Element Method for a Nonlocal FitzHugh-Nagumo Model of Cardiac Electrophysiology

We present a Virtual Element Method (VEM) for a nonlocal reaction-diffusion system of the cardiac electric field. To this system, we analyze an $H^1(\Omega)$-conforming discretization by means of VEM which can make use of general polygonal meshes. Under standard assumptions on the computational domain, we establish the convergence of the discrete solution by considering a series of a priori estimates and by using a general $L^p$ compactness criterion. Moreover, we obtain optimal order space-time error estimates in the $L^2$ norm. Finally, we report some numerical tests supporting the theoretical results

Using a damper amplification factor to increase energy dissipation in structures

AbstractFluid dampers are an important tool for dissipating unwanted vibrations in a range of engineering structures. This paper examines the effects of amplifying the displacements transferred to a non-linear damper, to increase the effectiveness of the damper in a range of situations commonly encountered in civil engineering structures. These include, (i) the ability to “fine tune” the required damping for a particular size damper, (ii) the ability to have a set of the same size dampers, but with different amplification factors to achieve a specific damping task, and (iii) to increase the sensitivity of the damper to small movements which effectively extends the range over which the damper works. Through numerical simulations and experimental tests conducted on a non-linear damper, we quantify the potential advantages of adding an amplification factor and the range of parameters where the benefit to this device is significant. The example of a two-storey structure is used as a test case and real-time dynamic substructuring tests are used to assess the complete system performance using a range of different amplification factors. The results show that the structural performance is most improved for frequencies close to resonance and that the amplification factor has an effective limit that for the case considered in this study is of approximately 3. The effects of the mechanism compliance are also assessed

Supporting brace sizing in structures with added linear viscous fluid dampers: A filter design solution

Viscous fluid dampers have proved to be effective in suppressing unwanted vibrations in a range of engineering structures. When dampers are fitted in a structure, a brace is typically used to attach them to the main structure. The stiffness of this brace can significantly alter the effectiveness of the damper, and in structures with multiple dampers, this can be a complex scenario to model. In this paper, we demonstrate that the effects of the brace compliance on the damper performance can be modelled by way of a first-order filter. We use this result to formulate a procedure that calculates the stiffness required by the supporting brace to provide a specified effectiveness of the damping action. The proposed procedure assumes that viscous dampers have been sized in a previous design step based on any optimal methodology in which, as is usually the case, the presence of supporting braces and their dynamic effects were neglected. Firstly considering a one degree-of-freedom system, we show that the proposed method ensures a desired level of damper efficiency for all frequencies within a selected bandwidth. Then the analysis is extended to the case of multi-degree-of-freedom systems to show that the design criteria can be applied in a straightforward and successful manner to more complex structures

Estimating the Self-depuration Capacity of a Reach of the Luján River

A 3-km reach of the Luján River was studied by establishing 6 sampling stations, which were from 300 to 500 m apart. The first station was the control reading for river nutrients and particulate material. The second station measured the continuous effluent from a wastewater treatment plant flow of the city of Luján and was, therefore, considered a continuous addition point of nutrients. The other 4 stations were used to evaluate whether the river captured phosphorus as phosphate, nitrogen as ammonium, nitrite or nitrates, and the suspended particulate material, both organic and inorganic. These data were used to calculate material uptake (U), uptake velocity (Vf), and net distance Snet under two different hydrological situations, during low and high flow, during the same season of the same year. Results indicate that phosphate ions as well as organic matter are retained for less than 2 km in both high and low flow situations. In the case of ammonium, the results appear similar to those of phosphate ions but it may be transformed into nitrates and transported in the latter form for greater distances. It is concluded that this river, in the reach under study, has a variable retention speed according to its flow but the retention capacity is no less than 900 m and as much as 2000 m. Therefore, a 2 km distance must be considered as the minimum distance before another effluent of nutrients or organic matter is added.Fil: Piccinini, Mauricio. Provincia de Buenos Aires. Municipalidad de Lujan; ArgentinaFil: Sánchez Caro, Anibal. Universidad Nacional de Luján. Instituto de Ecología y Desarrollo Sustentable. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Ecología y Desarrollo Sustentable; Argentina. Universidad Nacional de Luján. Departamento de Ciencias Básicas; ArgentinaFil: Gultermiriam, M.L.. Universidad Nacional de Tucumán. Facultad de Ciencias Naturales e Instituto Miguel Lillo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Giorgi, Adonis David Nazareno. Universidad Nacional de Luján. Instituto de Ecología y Desarrollo Sustentable. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Ecología y Desarrollo Sustentable; Argentina. Universidad Nacional de Luján. Departamento de Ciencias Básicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

CONSEQUENCES OF TRADE LIBERALIZATION ON POVERTY AND INCOME DISTRIBUTION IN BRAZIL

This study evaluates the regional short run impacts of reduction in import tariffs in Brazil on poverty and distribution of income related to recent free trade area agreements. Results show that trade can reduce inter-regional income inequality, but poor urban households lose with trade liberalization. In order to compensate welfare losses for the poor, this study designs and evaluates a combination of trade and tax policies, which effectively contributes to improve welfare for poor urban households.International Relations/Trade,