Search results for "transitive"
showing 10 items of 98 documents
Generalizations of the periodicity Theorem of Fine and Wilf
2005
We provide three generalizations to the two-dimensional case of the well known periodicity theorem by Fine and Wilf [4] for strings (the one-dimensional case). The first and the second generalizations can be further extended to hold in the more general setting of Cayley graphs of groups. Weak forms of two of our results have been developed for the design of efficient algorithms for two-dimensional pattern matching [2, 3, 6].
Sylow permutable subnormal subgroups of finite groups II
2001
[EN] In this paper a local version of Agrawal's theorem about the structure of finite groups in which Sylow permutability is transitive is given. The result is used to obtain new characterisations of this class of finite groups.
Homogeneous three-dimensional Riemannian spaces
2020
The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit a transitive group of isometries are obtained. These conditions are Intrinsic, Deductive, Explicit and ALgorithmic, and they offer an IDEAL labeling of these geometries. It is shown that the transitive action of the group naturally falls into an unfolding of some of the ten types in the Bianchi-Behr classification. Explicit conditions, depending on the Ricci tensor, are obtained that characterize all these types.
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…
Periodic measures and partially hyperbolic homoclinic classes
2019
In this paper, we give a precise meaning to the following fact, and we prove it: $C^1$-open and densely, all the non-hyperbolic ergodic measures generated by a robust cycle are approximated by periodic measures. We apply our technique to the global setting of partially hyperbolic diffeomorphisms with one dimensional center. When both strong stable and unstable foliations are minimal, we get that the closure of the set of ergodic measures is the union of two convex sets corresponding to the two possible $s$-indices; these two convex sets intersect along the closure of the set of non-hyperbolic ergodic measures. That is the case for robustly transitive perturbation of the time one map of a tr…
Recurrence and genericity
2003
We prove a C^1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C^1-generic diffeomorphisms. For instance, C^1-generic conservative diffeomorphisms are transitive. Nous montrons un lemme de connexion C^1 pour les pseudo-orbites des diffeomorphismes des varietes compactes. Nous explorons alors les consequences pour les diffeomorphismes C^1-generiques. Par exemple, les diffeomorphismes conservatifs C^1-generiques sont transitifs.
Homeomorphic graph manifolds: A contribution to the μ constant problem
1999
Abstract We give a characterization, in terms of homological data in covering spaces, of those maps between (3-dimensional) graph manifolds which are homotopic to homeomorphisms. As an application we give a condition on a cobordism between graph manifolds that guarantees that they are homeomorphic. This in turn is applied to give a partial result on the μ -constant problem in (complex) dimension three.
Transitivity in coherence-based probability logic
2016
We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study selected probabilistic versions of classical categorical syllogisms and construct a new version of the squa…
A Neo2 bayesian foundation of the maxmin value for two-person zero-sum games
1994
A joint derivation of utility and value for two-person zero-sum games is obtained using a decision theoretic approach. Acts map states to consequences. The latter are lotteries over prizes, and the set of states is a product of two finite sets (m rows andn columns). Preferences over acts are complete, transitive, continuous, monotonie and certainty-independent (Gilboa and Schmeidler (1989)), and satisfy a new axiom which we introduce. These axioms are shown to characterize preferences such that (i) the induced preferences on consequences are represented by a von Neumann-Morgenstern utility function, and (ii) each act is ranked according to the maxmin value of the correspondingm × n utility …
A Neurocomputational Approach to Trained and Transitive Relations in Equivalence Classes
2017
A stimulus class can be composed of perceptually different but functionally equivalent stimuli. The relations between the stimuli that are grouped in a class can be learned or derived from other stimulus relations. If stimulus A is equivalent to B, and B is equivalent to C, then the equivalence between A and C can be derived without explicit training. In this work we propose, with a neurocomputational model, a basic learning mechanism for the formation of equivalence. We also describe how the relatedness between the members of an equivalence class is developed for both trained and derived stimulus relations. Three classic studies on stimulus equivalence are simulated covering typical and at…