Let A and B be Banach algebras with bounded approximate identities let Φ:A→B a surjective continuous linear map which preserves two-sided zero products (i.e., Φ(a)Φ(b)=Φ(b)Φ(a)=0 whenever ab=ba=0). We show that Φ is weighted Jordan homomorphism provided product determined weakly amenable. These conditions are in particular fulfilled when the group algebra L1(G) G any locally compact group. also...

In this paper we study the birational rigidity problem for smooth Mori fibrations on del Pezzo surfaces of degree 1 and 2. For degree 1 we obtain a complete description of rigid and non-rigid cases. 1. Notions and results. Due to progress in the Minimal Model Program, the classification problem in the modern birational geometry for varieties of negative Kodaira dimension can be formulated as fo...

The palindromization map ψ in a free monoid A was introduced in 1997 by the first author in the case of a binary alphabet A, and later extended by other authors to arbitrary alphabets. Acting on infinite words, ψ generates the class of standard episturmian words, including standard ArnouxRauzy words. In this paper we generalize the palindromization map, starting with a given code X over A. The ...

This paper examines the concept of simulation from a modelling viewpoint. How can one Mealy machine simulate the other one? We create formalism for simulation of Mealy machines. The injective s–morphism of the machine semigroups induces the simulation of machines [1]. We present the example of s–morphism such that it is not a homomorphism of semigroups. The story for the surjective s–morphisms ...

A word is cubefree if it contains no non-empty subword of the form xxx. A morphism h : Σ * → Σ * is k-uniform if h(a) has length k for all a ∈ Σ. A morphism is cubefree if it maps cubefree words to cubefree words. We show that for all k ≥ 0 there exists a k-uniform cubefree binary morphism.

a toroidalization of a dominant morphism $varphi: xto y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $x$ and $y$. we give a proof of toroidalization of locally toroidal morphisms of 3-folds.

In this paper C denotes a category and o1, o2, o3 denote objects of C. Let C be a non empty category structure with units and let o be an object of C. Observe that 〈o, o〉 is non empty. The following propositions are true: (1) Let v be a morphism from o1 to o2, u be a morphism from o1 to o3, and f be a morphism from o2 to o3. If u = f · v and f −1 · f = id(o2) and 〈o1, o2〉 6= ∅ and 〈o2, o3〉 6= ∅...