Using potential theoretic methods we give extension results for functions in various Hardy classes and in the Nevanlinna class in C". Our exceptional sets are polar or slightly larger n-small sets depending whether the majorant is a harmonic or separately hyperharmonic function.

Zeilberger’s original approach My original approach was to teach the computer some elementary ‘logical reasoning’, and find enumeration schemes that way. This was done in a Maple package (still available from my website) called WILF. To check the ‘logical’ program, I also wrote an empirical program, called HERB. The Maple package HERB found enumeration schemes by testing them for permutations o...

Investigation of desertification trend requires an understanding of phenomena that create changes singly or action and reaction together in an area that these changes were led to the desertification and land degradation. In the investigation of pedological criterion affecting on land degradation in Alluvial Fans, first, the map of units was created by overlaying and crossing maps of slope class...

In this paper an alternative model allowing the extension of the Debye-Hückel Theory (DHT) considering time dependence explicitly is presented. From the Electro-Quasistatic approach (EQS) introduced in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles (ions) in electrolytes. This leads t...

Definition 1.3. Let C be a monster model of a theory interpretable in o-minimal structure. • A set φ(x) is finite by o-minimal if there is some definable equivalence relation E with finite classes and domain φ(C and a definable binary relation < such that (φ(C)/E,<) together with the C-induced structure is an ominimal ordered set. • A type p(x) is finite by o-minimal if there is some finite by ...

The notions separability and normality are related to this characterisation. In the case of skew fields polynomials often have infinitely many zeros, so a different way of counting zeros as distinct is needed. The well-known theorem of Gordon and Motzkin [Z] states that a polynomial of degree n has zeros in at most n conjugacy classes. This suggests one should count zeros of a polynomial by the...

This contribution is concerned with a generalization of Itoh and Tsujii’s algorithm for inversion in extension fields GF (q). Unlike the original algorithm, the method introduced here uses a standard (or polynomial) basis representation. The inversion method is generalized for standard basis representation and relevant complexity expressions are established, consisting of the number of extensio...

This paper introduces a programming language that makes it convenient to extend large software systems and even to compose them in a modular way. JX/MI supports multiple nested inheritance, building on earlier work on nested inheritance in the language JX. Nested inheritance permits modular, type-safe extension of a package (including nested packages and classes), while preserving existing type...

This paper describes an extension for logic programming. We propose a flexible logical language that combines overloading and higher-order polymorphism by means of a type classes system. Our proposal consists in classifying the logical predicates, collecting the set of types which share predicates with common application domains in the same type class and particularising more specific applicati...

This paper demonstrates that the novel combination of type classes and existential types adds significant expressive power to a language, requiring only a minor syntactic change. We explore this combination in the context of higher-order functional languages with static typing, parametric polymorphism, algebraic data types, and Hindley-Milner type inference. Since we have examined the underlyin...