Existence for the steady problem of a mixture of two power-law fluids

The steady problem resulting from a mixture of two distinct fluids of power-law type is analyzed in this work. Mathematically, the problem results from the superposition of two power laws, one for a constant power-law index with other for a variable one. For the associated boundary-value problem, we prove the existence of very weak solutions, provided the variable power-law index is bounded from above by the constant one. This result requires the lowest possible assumptions on the variable power-law index and, as a particular case, extends the existence result by Ladyzhenskaya dated from 1969 to the case of a variable exponent and for all zones of the pseudoplastic region. In a distinct result, we extend a classical theorem on the existence of weak solutions to the case of our problem.Comment: 22. arXiv admin note: substantial text overlap with arXiv:1203.679

Parabolic reaction-diffusion systems with nonlocal coupled diffusivity terms

In this work we study a system of parabolic reaction-diffusion equations which are coupled not only through the reaction terms but also by way of nonlocal diffusivity functions. For the associated initial problem, endowed with homogeneous Dirichlet or Neumann boundary conditions, we prove the existence of global solutions. We also prove the existence of local solutions but with less assumptions on the boundedness of the nonlocal terms. The uniqueness result is established next and then we find the conditions under which the existence of strong solutions is assured. We establish several bow-up results for the strong solutions to our problem and we give a criterium for the convergence of these solutions towards a homogeneous state.CAPES [BEX 2478-12-8]; MEC/MCTI/CAPES/CNPq/FAPs, Brazil [71/2013, 88881.030388/2013-01]; Fundacao para a Ciencia e a Tecnologia, Portugal [UID/MAT/04561/2013-2015]info:eu-repo/semantics/publishedVersio

The Second Order Traffic Fine: Temporal Reasoning in European Transport Regulations

We argue that European transport regulations can be formalized within the Sigma^1_1 fragment of monadic second order logic, and possibly weaker fragments including linear temporal logic. We consider several articles in the regulation to verify these claims

Traces of Lorentz symmetry breaking in a Hydrogen atom at ground state

Some traces of a specific Lorentz symmetry breaking scenario in the ground state of the Hydrogen atom are investigated. It is used standard Rayleigh-Schr\"odinger perturbation theory in order to obtain the corrections to the the ground state energy and wave function. It is shown that an induced four-pole moment arises, due to the Lorentz symmetry breaking. The model considered is the one studied in reference Eur. Phys. J. C {\bf 74}, 2937 (2014), where the Lorentz symmetry is broken in the electromagnetic sector.Comment: 8 Latex pages, 2 figure

Study on behavioral impedance for route planning techniques from the pedestrian's perspective: some findings and considerations

The multi-disciplinary characteristics of transportation force a new design of geographic information systems, within which these characteristics are considered. In this context, geographic information systems for transportation are the result of the integration of transportation information systems and conventional geographic information systems. An interesting research area in geographic information systems for transportation is constraint management in route planning algorithms from the pedestrian s perspective. Constraint management becomes more complex when route planning takes into account an integrated public transportation network (i.e. a multimodal network). A study on the theoretical contextualization and taxonomy of a pedestrian s behavioral impedance has been developed in order to improve the constraint management from the pedestrian s perspective. This study entails strategies of travel reduction by private transport (e.g. travel by car) through switching to or substitution by alternative public transport (e.g. travel by walk, bus or rail). The grounded theory method has been used to develop the proposed taxonomy. Using the partial results of a questionnaire applied to a reduced group of people from Barcelona as a starting point, important data are being collected to define the mathematical model of the behavioral impedance domain. The goal of this paper is to provide some considerations about theoretical contextualization on identification and management of constraints regarding the behavioral impedance domain from the pedestrian s perspective within the urban public transportation context. The research project where this work is included is composed of six major phases. The first phase represents a continuous bibliographic review. The second phase was a study on sidewalks in the university zone of Barcelona. In this phase, an experimental application has been proposed and the management, map and route modules have been implemented on the ArcInfo GIS package and C++. This paper reports the partial work of the third phase, which is composed of two parts. The first part was a theoretical study on behavioral impedance for route planning techniques, in which taxonomy was proposed. The results of the second part are partially presented in this paper. The fourth (i.e. design and implementation), fifth (i.e. calibration and validation) and sixth (i.e. generalization of the results) phases are characterized by the application of the prototype regarding the multimodal network model for urban public transportation from the pedestrian s perspective. The main contribution of this article is the behavioral impedance taxonomy review from the pedestrian s perspective, which will allow designing a mathematical model and be used to implement a constraint management algorithm. Within this context, the proposed taxonomy could be used to model cost functions more precisely.Postprint (published version