Let φ and ψ be endomorphisms of the projective line of degree at least 2, defined over a field F . From a dynamical perspective, a significant question is to determine whether φ and ψ are conjugate (or to answer the related question of whether a given rational function φ has a nontrivial automorphism). We construct efficient algorithms for computing the set of conjugating maps (resp., the group...

1 Measure Theory 2 1.1 σ-Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Dynkin Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Probability Measures . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Measurable Maps and Induced Measures . . . . . . . . . . . . . ....

We investigate certain classes of normal completely positive (CP) maps on the hyperfinite II1 factor A. Using the representation theory of a suitable irrational rotation algebra, we propose some computable invariants for such CP maps.

The problem of integrating territorial information within a multisensor vision system for autonomous-vehicle control is addressed. Environmental information is used to improve recognition results and to locate a vehicle's position in the coordinate reference frame of a map. To this end, a hypothesis-and-test search mechanism has been developed, which is based on an associative phase and a symbo...

We inve,tigate by ~tati,tical mechanical methods a uocha~tic analogue of the bidirectional a;sociative memone~ introduced by B. Kosko. We denve its ;torage capacity a~ a function of the total number of synapses and of the asymmetry of the network.

An explicit description of free strongly homotopy associative and free strongly homotopy Lie algebras is given. A variant of the Poincaré-Birkhoff-Witt theorem for the universal enveloping A(m)-algebra of a strongly homotopy Lie algebra is formulated. Introduction This note was originated many years ago as my reaction to questions of several people how free strongly homotopy algebras can be des...

1958 The words " some problems " in the title of this article mean primarily that the article considers absolutely no results about algebras of finite dimension. Among other questions that remain outside the scope of the article, we mention, for example, various theorems about decomposition of algebras (see for example [70, 47]) which are closely related to the theory of algebras of finite dime...