It is well-known that a real analytic manifold X admits a complexification XC , a complex manifold that contains X as the fixed point set of an antiholomorphic involution. This can be seen as follows.The transition functions defining the manifold X are real-analytic local diffeomorphisms of Rn. The Taylor expansions of these transition functions can be considered as local biholomorphisms of Cn,...

The complexification of the compact group G is the group G whose Lie algebra is the complexification of the Lie algebra g of G and which satisfies π1(G ) = π1(G). The complexification G/K of G/K can be then identified (G-equivariantly) with the tangent bundle of G/K. We also remark that the Kähler form obtained in the Theorem is exact. This result has been proved in [9] for symmetric spaces of ...

Unravelling how the complexity of living systems can (have) emerge(d) from simple chemical reactions is one grand challenges in contemporary science. Evolving self-replicating molecules may hold key to this question. Here we show that, when a system replicators subjected regime where replication competes with replicator destruction, and fast give way more complex slower ones. The structurally w...

There is a subtle difference as far as the invariant subspace problem is concerned for operators acting on real Banach spaces and operators acting on complex Banach spaces. For instance, the classical hyperinvariant subspace theorem of V. I. Lomonosov [10] while true for complex Banach spaces is false for real Banach spaces. When one starts with a bounded operator on a real Banach space and the...

ION Modèle RESOLUTION Résultats Système réel COMPARAISON SIMPLIFICATION / COMPLEXIFICATION FIG. 1.1 – Processus de Modélisation Nous détaillons dans la section suivante la phase d’abstraction du système, en présentant différents formalismes de modélisation. 14 CHAPITRE

New type Paley–Wiener theorems for the modified multidimensional Mellin and inverse Mellin transforms are established. The supports of functions are described in terms of their modified Mellin (or inverse Mellin) transform without passing to the complexification.

Human civilisation has undergone a continuous trajectory of rising sociopolitical complexity since its inception; trend which dramatic recent acceleration. This phenomenon resulted in increasingly severe perturbation the Earth System, manifesting recently as global-scale effects such climate change. These create an increased risk global ‘de-complexification’ (collapse) event could undergo wides...

To increase the evolvability of larger search spaces, several indirect encoding strategies have been proposed. Among these, multicellular developmental systems are believed to offer great potential for the evolution of general, scalable, and self-repairing organisms. We reinforce this view, presenting the results achieved by such a model and comparing it against direct encoding. Extra effort ha...