Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples

Noether's Theorem for Control Problems on Time Scales

We prove a generalization of Noether's theorem for optimal control problems defined on time scales. Particularly, our results can be used for discrete-time, quantum, and continuous-time optimal control problems. The generalization involves a one-parameter family of maps which depend also on the control and a Lagrangian which is invariant up to an addition of an exact delta differential. We apply our results to some concrete optimal control problems on an arbitrary time scale.Comment: This is a preprint of a paper whose final and definite form is published in International Journal of Difference Equations ISSN 0973-6069, Vol. 9 (2014), no. 1, 87--10

Holder's and Hardy's Two Dimensional Diamond-alpha Inequalities on Time Scales

We prove a two dimensional Holder and reverse-Holder inequality on time scales via the diamond-alpha integral. Other integral inequalities are established as well, which have as corollaries some recent proved Hardy-type inequalities on time scales.Comment: Accepted for publication (October 21, 2009) in the journal "Annals of the University of Craiova, Mathematics and Computer Science Series" (http://inf.ucv.ro/~ami

Existence and uniqueness of a positive solution to generalized nonlocal thermistor problems with fractional-order derivatives

In this work we study a generalized nonlocal thermistor problem with fractional-order Riemann-Liouville derivative. Making use of fixed-point theory, we obtain existence and uniqueness of a positive solution.Comment: Submitted 17-Jul-2011; revised 09-Oct-2011; accepted 21-Oct-2011; for publication in the journal 'Differential Equations & Applications' (http://dea.ele-math.com

Beyond the "clash of ignorances": interculturality and postcolonialism

En el marco del estudio de la cuestión del conocimiento en la filosofía occidental, el artículo aborda la noción de «choque de ignorancias» que se está utilizando hoy en día en un gran número de debates académicos, religiosos y políticos para referirse a los choques o conflictos que surgen de la falta de comunicación y entendimiento intercultural. El artículo presenta algunos casos de normalización social de la ignorancia y propone, desde una perspectiva intercultural y post-colonial, algunas ideas que puedan ayudar a ir más allá de los choques que pueda causar la ignorancia normalizada socialmente en el ámbito interpersonal e intercultural.In the context of examining the question of knowledge in Western philosophy, the article discusses the notion of “clash of ignorance”, which is used today in a number of academic, religious and political debates to refer to clashes or conflicts arising from the lack of intercultural communication and understanding. It presents some cases of the social normalisation of ignorance and proposes, from an intercultural and post-colonial perspective, some ideas that could help overcome the clashes that the socially normalised ignorance may cause in the interpersonal and intercultural domain

Humanism Reconsidered: Post-colonial Humanistic Proposals

El artículo tiene como objetivo reflexionar sobre el ‘humanismo’ y presentar propuestas humanistas desde una perspectiva post-colonial. Comienza por examinar los supuestos que subyacen en la ciencia moderna e ilustrada para poner al descubierto su complicidad en la práctica colonial. A continuación, se analiza el humanismo para mostrar cómo se ha utilizado una noción altamente politizada del humanismo para justificar las prácticas y estructuras deshumanizantes del colonialismo. Este ejercicio crítico se complementa con la discusión de dos propuestas humanistas que tratan de presentar un humanismo alternativo que tiene como objetivo posibilitar una comunicación y entendimiento inclusivo, humanista y transcultural en un mundo que se hace cada vez más interrelacionado.The article aims to reconsider ‘humanism’ and to present humanistic proposals from a post-colonial perspective. It begins by examining the assumptions underlying the modern and enlightened science to expose its complicity in the colonial enterprise. It then analyses humanism to show how a highly politicised notion of humanism has been deployed to justify the dehumanising practices and structures of colonialism. This critical exercise is complemented by the discussion of two humanistic proposals that seek to present an alternative humanism that is geared to enabling an inclusive and humanistic trans-cultural communication and understanding in an increasingly interrelated world

Optimal Control for a Steady State Dead Oil Isotherm Problem

We study the optimal control of a steady-state dead oil isotherm problem. The problem is described by a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of mechanics of a continuous medium. Existence and regularity results of the optimal control are proved, as well as necessary optimality conditions.Comment: This is a preprint of a paper whose final and definitive form will appear in Control and Cybernetics. Paper submitted 24-Sept-2012; revised 21-March-2013; accepted for publication 17-April-2013. arXiv admin note: text overlap with arXiv:math/061237