Some aspects of grid generation

New results concerning the development of a universal method for grid generation based on the numerical solution of the inverted Beltrami and diffusion equations with respect to the monitor metric are obtained. In order to build monitor metrics, layer-type functions are used. Algorithms for generating smoothly matched block grids are proposed. Examples of two-and three-dimensional grids for the tokamak edge region, for calculation of a passive impurity in the atmosphere, and for the numerical solution of two-dimensional singularly perturbed problems are presented.     

Some aspects of Riesz multimorphisms

We study the behavior of Riesz multimorphisms on Archimedean f-algebras with unit element and focus on their different multiplicative aspects.     

Some aspects of Property for

In this paper, we discuss the invariance property of Property under holomorphic maps on any compact subset in . An obstruction to Property of any compact subset regarding the fine topology is also given, which generalizes a classical result of N. Sibony on the complex plane.     

Some mathematical aspects of reinsurance

In two earlier papers, Waters (1979) and Andreadakis and Waters (1980), the effect on an insurer as a result of varying his retention limits has been studied. This present paper represents an extension of this earlier work. In particular we investigate whether it is possible to prove some of the results of the earlier papers without making restrictive assumptions about the distribution of annual claims or about the way in which the reinsurance premium is calculated. It will be shown that this is possible in the case of proportional but not possible in the case of non-proportional reinsurance.     

Some aspects of topological descent

The paper deals with (effective) descent morphisms for subfibrations X of the basic fibration Top/X, for topological spaces X and classes of continuous functions stable under pullback. For a category with pullbacks, we prove the stability under pullback of effective -descent morphisms for a class satisfying some suitable conditions. This plays a rôle in relating effective -descent to effective global-descent and enables us to obtain a criterion for effective étale-descent. We also show that the inclusion of the class of effective global-descent maps in the class surjective effective étale-descent is strict.Partial financial support by Centro de Matemática da Universidade de Coimbra is gratefully acknowledged.     

Some aspects of narrative method

The idea of abstracting and/or generalising the structure of a narrative (i.e. a set of weakly connected human actions) using a mapping rule which creates either a tolerance (a symmetric reflexive relationship) or an equivalence on the domain set is explored. The paper is an extension of earlier work by the author. A detailed example of the use of narrative analysis is provided which links the analysis into a game‐theoretic context.

… for each of us is a biography, a story. Each of us is a singular narrative, which is constructed, continually, unconsciously, by, through, and in us—through our perceptions, our feelings, our thoughts, our actions; and not least, our discourse, our spoken narrations. Biologically, physiologically, we are not so different from each other; historically, as narratives—we are each of us unique. To be ourselves we must have ourselves—possess, if needs be re‐possess, our life stories. We must “recollect” ourselves, recollect the inner drama, the narrative of ourselves. A man needs such a narrative

Oliver Sacks The Man Who Mistook His Wife for a Hat, 1985.     

Some aspects of Hermitian Jacobi forms

We introduce a certain differential (heat) operator on the space of Hermitian Jacobi forms of degree 1, show its commutation with certain Hecke operators and use it to construct a map from elliptic cusp forms to Hermitian Jacobi cusp forms. We construct Hermitian Jacobi forms as the image of the tensor product of two copies of Jacobi forms and also from the differentiation of the variables. We determine the number of Fourier coefficients that determine a Hermitian Jacobi form and use the differential operator to embed a certain subspace of Hermitian Jacobi forms into a direct sum of modular forms for the full modular group.     

Some aspects of intuitionistic fuzzy sets

We first discuss the significant role that duality plays in many aggregation operations involving intuitionistic fuzzy subsets. We then consider the extension to intuitionistic fuzzy subsets of a number of ideas from standard fuzzy subsets. In particular we look at the measure of specificity. We also look at the problem of alternative selection when decision criteria satisfaction is expressed using intuitionistic fuzzy subsets. We introduce a decision paradigm called the method of least commitment. We briefly look at the problem of defuzzification of intuitionistic fuzzy subsets.     

Some set-theoretical aspects of differentiation theory

We study the behaviour under uncountable products of some structures of interest in the Frölicher-Kriegel calculus of differentiation theory: the Mackey closure topology, the compactly and sequentially generated topologies and bornologies. Some properties turn out to be independent from ZFC+(CH).     

Some aspects of elliptic variational inequalities

In this paper we study an existence and the approximation of the solution of the elliptic variational inequality from an abstract axiomatic point of view. We discuss convergence results and give an error estimate for the difference of the two solutions in an appropriate norm. Also, we present some computational results by using fixed point method.