We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it with quantum and probabilistic finite automata (QFA and PFA, respectively) with respect to three basic language recognition modes. We show that, in the cases of...

Given a bounded open subset ? of R n , we establish the weak closure affine ball B p A ( ) = { f ? W 0 1 : E ? } with respect to functional introduced by Lutwak, Yang and Zhang in [46] as well its compactness L for any ? . These points use strongly celebrated Blaschke-Santaló inequality. As counterpart, develop basic theory -Rayleigh quotients domains, case, More specifically, -affine versions ...

Affine spheres were introduced by Ţiţeica in [72, 73], and studied later by Blaschke, Calabi, and Cheng-Yau, among others. These are hypersurfaces in affine R which are related to real Monge-Ampère equations, to projective structures on manifolds, and to the geometry of Calabi-Yau manifolds. In this survey article, we will outline the theory of affine spheres their relationships to these topics...