Search results for "22.05"
showing 6 items of 6 documents
Bounds for the relative n-th nilpotency degree in compact groups
2009
The line of investigation of the present paper goes back to a classical work of W. H. Gustafson of the 1973, in which it is described the probability that two randomly chosen group elements commute. In the same work, he gave some bounds for this kind of probability, providing information on the group structure. We have recently obtained some generalizations of his results for finite groups. Here we improve them in the context of the compact groups.
Representaciones escolares del Clima en el Paisaje fluvial del río Clariano
2020
Resumen:El conocimiento de la relación entre el clima y el paisaje convive con las dificultades propias del ámbito escolar. Para saber qué ocurre en su enseñanza, se analiza por medio del instrumento Evocation 2005 y los registros pictóricos, las representaciones sociales que tiene una parte del alumnado de 1º ESO. El estudio de caso sobre un paisaje fluvial en un ámbito local confirma la idealización del paisaje y la escasa presencia del clima en las representaciones del alumnado, esto junto con las dificultades de los docentes en su conocimiento disciplinar y su práctica nos conmina a quebrar las tradiciones y rutinas escolares para afrontar mejor las explicaciones de las transformaciones…
On Radon transforms on compact Lie groups
2016
We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to $S^1$ nor to $S^3$. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms from $S^1$.
On the quasi-isometric and bi-Lipschitz classification of 3D Riemannian Lie groups.
2021
AbstractThis note is concerned with the geometric classification of connected Lie groups of dimension three or less, endowed with left-invariant Riemannian metrics. On the one hand, assembling results from the literature, we give a review of the complete classification of such groups up to quasi-isometries and we compare the quasi-isometric classification with the bi-Lipschitz classification. On the other hand, we study the problem whether two quasi-isometrically equivalent Lie groups may be made isometric if equipped with suitable left-invariant Riemannian metrics. We show that this is the case for three-dimensional simply connected groups, but it is not true in general for multiply connec…
Entropy, Lyapunov exponents, and rigidity of group actions
2018
This text is an expanded series of lecture notes based on a 5-hour course given at the workshop entitled "Workshop for young researchers: Groups acting on manifolds" held in Teres\'opolis, Brazil in June 2016. The course introduced a number of classical tools in smooth ergodic theory -- particularly Lyapunov exponents and metric entropy -- as tools to study rigidity properties of group actions on manifolds. We do not present comprehensive treatment of group actions or general rigidity programs. Rather, we focus on two rigidity results in higher-rank dynamics: the measure rigidity theorem for affine Anosov abelian actions on tori due to A. Katok and R. Spatzier [Ergodic Theory Dynam. Systems…
CCDC 1918923: Experimental Crystal Structure Determination
2020
Related Article: Li‐Li Wang, Yi‐Kuan Tu, Arto Valkonen, Kari Rissanen, Wei Jiang|2019|Chin.J.Chem.|37|892|doi:10.1002/cjoc.201900233