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Nodal deformations of singularities.

Jorge A. González-Ramírez — 2002

Revista Matemática Complutense

In this note we study deformations of a plane curve singularity (C,P) to δ(C,P) nodes. We see that for some types of singularities the method of A'Campo can be carried on using parametric equations. For such singularities we prove that deformations to δ nodes can be made within the space of curves of the same degree.

Finite topological spaces.

Juan A. Navarro González — 1990

Extracta Mathematicae

We show that the study of topological T-spaces with a finite number of points agrees essentially with the study of polyhedra, by means of the geometric realization of finite spaces. In this paper all topological spaces are assumed to be T.

Topological games and product spaces

Salvador García-FerreiraR. A. González-SilvaArtur Hideyuki Tomita — 2002

Commentationes Mathematicae Universitatis Carolinae

In this paper, we deal with the product of spaces which are either 𝒢 -spaces or 𝒢 p -spaces, for some p ω * . These spaces are defined in terms of a two-person infinite game over a topological space. All countably compact spaces are 𝒢 -spaces, and every 𝒢 p -space is a 𝒢 -space, for every p ω * . We prove that if { X μ : μ < ω 1 } is a set of spaces whose product X = μ < ω 1 X μ is a 𝒢 -space, then there is A [ ω 1 ] ω such that X μ is countably compact for every μ ω 1 A . As a consequence, X ω 1 is a 𝒢 -space iff X ω 1 is countably compact, and if X 2 𝔠 is a 𝒢 -space, then all...

On completeness and direction in fuzzy relational systems.

The concepts of bounded subset, complete subset and directed subset, wich are well known in the context of partially ordered sets (X,≤), are extended in order to become appliable, with coherence, in fuzzy relational systems (X,R). The properties of these generalized structures are analyzed and operative exemples of them are presented.

Mathematical theory of musical scales.

M. J. Garmendia RodríguezJ. A. Navarro González — 1996

Extracta Mathematicae

Our aim is to look for precise definitions of musical concepts. In this work we present the concepts we have been able to derive from the concept of pitch (high-low aspect of musical sounds). Now, pitches being the primitive concept, they will not be defined from a previous concept, but from their mutual relationships.

About a family of naturally graded no p-filiform Lie algebras.

L. M. CamachoJ. R. GómezA. J. González — 2005

Extracta Mathematicae

The knowledge of the natural graded algebras of a given class of Lie algebras offers essential information about the structure of the class. So far, the classification of naturally graded Lie algebras is only known for some families of p-filiform Lie algebras. In certain sense, if g is a naturally graded Lie algebra of dimension n, the first case of no p-filiform Lie algebras it happens when the characteristic sequence is (n-3,2,1). We present the classification of a particular family of these algebras...

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