Tensor FEM for Spectral Fractional Diffusion

Foundations of Computational Mathematics - We design and analyze several finite element methods (FEMs) applied to the Caffarelli–Silvestre extension that localizes the fractional powers of...     

The <Emphasis Type=Italic>p</Emphasis>-Daugavet property for function spaces

A natural extension of the Daugavet property for p-convex Banach function spaces and related classes is analysed. As an application, we extend the arguments given in the setting of the Daugavet property to show that no reflexive space falls into this class.     

A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts

Group decision making is a type of decision problem in which multiple experts acting collectively, analyze problems, evaluate alternatives, and select a solution from a collection of alternatives. As the natural language is the standard representation of those concepts that humans use for communication, it seems natural that they use words (linguistic terms) instead of numerical values to provide their opinions. However, while linguistic information is readily available, it is not operational and thus it has to be made usable though expressing it in terms of information granules. To do so, Granular Computing, which has emerged as a unified and coherent framework of designing, processing, and interpretation of information granules, can be used. The aim of this paper is to present an information granulation of the linguistic information used in group decision making problems defined in heterogeneous contexts, i.e., where the experts have associated importance degrees reflecting their ability to handle the problem. The granulation of the linguistic terms is formulated as an optimization problem, solved by using the particle swarm optimization, in which a performance index is maximized by a suitable mapping of the linguistic terms on information granules formalized as sets. This performance index is expressed as a weighted aggregation of the individual consistency achieved by each expert.     

On the approximate controllability of stochastic stokes systems

In this paper, we analyze the approximate controllability in quadratic mean of some systems governed by stochastic partial differential equations of the Stokes kind. When the noise is state-independent, we obtain satisfactory results, similar to those known for the corresponding deterministic system. In the more complicate case of a multiplicative noise, we are able to give (only) partial results. More precisely, we prove in this case that approximate controllability is equivalent to the unique continuation property for a particular backward (adjoint) stochastic system     

Measure-Preserving Functions and the Independence Copula

We solve a problem recently proposed by Kolesárová et al. Specifically, we prove that a necessary and sufficient condition for a given copula to be the independence or product copula is for the pair of measure-preserving transformations representing the copula to be independent as random variables.     

Adjustment boarding and alighting passengers on a bus transit line using qualitative information

Obtaining data to use in an urban public transport operation planning and analysis is problematic, particularly in urban bus transit lines. In an urban environment and for bus services, most ticketing methods can be used to record passengers getting on board but not getting off, and current methods are unable to make a proper adjustment of boardings and alightings based on the available data unless they do alighting counts. This paper presents a method whereby counts are made at fewer stops and qualitative information on alightings and/or vehicle loads between consecutive stops is used to make the boarding and alighting adjustment as a previous step to obtain the real origin and destination (O/D) of passengers allowing the O/D matrix calibration by using the loads between stops. Qualitative information can be obtained by the vehicle’s driver or an on board observer, avoiding the necessity of counting many stops in planning period. The method is applied to a real bus transit line in Malaga (Spain) and to a set of 50 different bus transit lines with number of stops ranging from 10 to 75. The results show that the proposed method reduces the adjustment errors with regard to traditional methods, such as Least Square Method, even in the situation where no qualitative information is used. When qualitative data is used on alightings and loadings, the reduction of the average error is over 50%.