THE AINU LANGUAGES: TRADITIONAL RECONSTRUCTION, EURASIAN AREAL LINGUISTICS, AND DIACHRONIC (HOLISTIC) TYPOLOGY

El objetivo principal de esta tesis doctoral es, en primer lugar, ofrecer una reconstrucción alternativa del protoainu para, en segundo lugar, aplicar conceptos de tipología diacrónicaholística con el fin de discernir algún patrón evolutivo que ayude a responder a la pregunta:¿por qué la lengua ainu es como es en su contexto geolingüístico (lengua AOV con prefijos),cuando en la región euroasiática lo normal es encontrar el perfil 'lengua AOV con sufijos'? En suma, se trata de explorar las posibilidades que ofrece la tipología diacrónica holística,combinada con métodos más tradicionales, en la investigación de las etapas prehistóricas delenguas aisladas, es decir, sin parientes conocidos, como el ainu, el vasco, el zuñi o elburushaski. Este trabajo se divide en tres grandes bloques con un total de ocho capítulos, unapéndice con las nuevas reconstrucciones protoainúes y la bibliografía.El primer bloque se abre con el capítulo 1, donde se hace una breve presentación delas lenguas ainus y su filología. El capítulo 2 está dedicado a la reconstrucción de la fonologíaprotoainu. La reconstrucción pionera pertenece a A. Vovin (1992), que de hecho sirve comobase sobre la que ampliar, corregir o modificar nuevos elementos. En el capítulo 3 se describela morfología histórica de las lenguas ainus. En el capítulo 4 se investiga esta opción dentrode un marco más amplio que tiene como objetivo analizar los patrones elementales deformación de palabras. El capítulo 5, con el que se inicia el segundo bloque, da cabida a lapresentación de una hipótesis tipológica diacrónica, a cargo de P. Donegan y D. Stampe, conla que especialistas en lenguas munda y mon-khmer han sido capaces de alcanzar unreconstrucción del protoaustroasiático según la cual el tipo aglutinante de las lenguas mundasería secundario, frente al original monosilábico de las lenguas mon-khmer. En el capítulo 6se retoma la perspectiva tradicional de la lingüística geográfica, pero no se olvidan algunas delas consideraciones tipológicas apuntadas en el capítulo anterior (el hecho de que la hipótesisde Donegan y Stampe no funcione con el ainu no significa que la tipología diacrónica nopueda ser todavía de utilidad). En el capítulo 7 se presentan algunas incongruencias queresultan tras combinar las supuestas evidencias arqueológicas con el escenario lingüísticodescrito en capítulos anteriores. Las conclusiones generales se presentan en el capítulo 8. Elapéndice es una tabla comparativa con las dos reconstrucciones disponibles a fecha de hoypara la lengua protoainu, es decir, las propuestas por A. Vovin en su estudio seminal de 1992y en el capítulo 3 de la presente tesis. Dicha tabla incluye 686 reconstrucciones (puedehacerse una sencilla referencia cruzada con Vovin, puesto que ambas están ordenadasalfabéticamente).

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

Evaluation of Two Alternative Carbon Capture and Storage Technologies: A Stochastic Model

30 p.

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.