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Invariants and flow geometry

J. González-DávilaL. Vanhecke — 1999

Colloquium Mathematicae

We continue the study of Riemannian manifolds (M,g) equipped with an isometric flow ξ generated by a unit Killing vector field ξ. We derive some new results for normal and contact flows and use invariants with respect to the group of ξ-preserving isometries to charaterize special (M,g, ξ ), in particular Einstein, η-Einstein, η-parallel and locally Killing-transversally symmetric spaces. Furthermore, we introduce curvature homogeneous flows and flow model spaces and derive an algebraic characterization...

The index 2 F 1 -transform of generalized functions

N. HayekBenito J. González — 1993

Commentationes Mathematicae Universitatis Carolinae

In this paper the index transformation F ( τ ) = 0 f ( t ) 2 F 1 ( μ + 1 2 + i τ , μ + 1 2 - i τ ; μ + 1 ; - t ) t α d t 2 F 1 ( μ + 1 2 + i τ , μ + 1 2 - i τ ; μ + 1 ; - t ) being the Gauss hypergeometric function, is defined on certain space of generalized functions and its inversion formula established for distributions of compact support on 𝐈 = ( 0 , ) .

Invariant harmonic unit vector fields on Lie groups

J. C. González-DávilaL. Vanhecke — 2002

Bollettino dell'Unione Matematica Italiana

We provide a new characterization of invariant harmonic unit vector fields on Lie groups endowed with a left-invariant metric. We use it to derive existence results and to construct new examples on Lie groups equipped with a bi-invariant metric, on three-dimensional Lie groups, on generalized Heisenberg groups, on Damek-Ricci spaces and on particular semi-direct products. In several cases a complete list of such vector fields is given. Furthermore, for a lot of the examples we determine associated...

Cantor-Bernstein theorems for Orlicz sequence spaces

Carlos E. FinolMarcos J. GonzálezMarek Wójtowicz — 2014

Banach Center Publications

For two Banach spaces X and Y, we write d i m ( X ) = d i m ( Y ) if X embeds into Y and vice versa; then we say that X and Y have the same linear dimension. In this paper, we consider classes of Banach spaces with symmetric bases. We say that such a class ℱ has the Cantor-Bernstein property if for every X,Y ∈ ℱ the condition d i m ( X ) = d i m ( Y ) implies the respective bases (of X and Y) are equivalent, and hence the spaces X and Y are isomorphic. We prove (Theorems 3.1, 3.3, 3.5) that the class of Orlicz sequence spaces generated by regularly...

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...

Nash -equilibria for stochastic games with total reward functions: an approach through Markov decision processes

The main objective of this paper is to find structural conditions under which a stochastic game between two players with total reward functions has an ϵ -equilibrium. To reach this goal, the results of Markov decision processes are used to find ϵ -optimal strategies for each player and then the correspondence of a better answer as well as a more general version of Kakutani’s Fixed Point Theorem to obtain the ϵ -equilibrium mentioned. Moreover, two examples to illustrate the theory developed 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.

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