R-endomorphisms ofR[[X]] are essentially continuous

On Essentially Absolutely Continuous Plane Transformations

Endomorphisms of stable continuous-trace C-algebras

We classify spectrum-preserving endomorphisms of stable continuoustrace C∗-algebras up to inner automorphism by a surjective multiplicative invariant taking values in finite dimensional vector bundles over the spectrum. Specializing to automorphisms, this gives a different approach to results of Phillips and Raeburn. 2000 Mathematics Subject Classification: 46L05, 46M20

Intersecting Families are Essentially Contained in Juntas

A family J of subsets of {1, . . . , n} is called a j-junta if there exists J ⊆ {1, . . . , n}, with |J | = j, such that the membership of a set S in J depends only on S ∩ J . In this paper we provide a simple description of intersecting families of sets. Let n and k be positive integers with k < n/2, and let A be a family of pairwise intersecting subsets of {1, . . . , n}, all of size k. We sh...

Completely Integrable Differential Systems Are Essentially Linear

Let ẋ = f(x) be a C autonomous differential system with k ∈ N ∪ {∞, ω} defined in an open subset Ω of R. Assume that the system ẋ = f(x) is C completely integrable, i.e. there exist n−1 functionally independent first integrals of class C with 2 ≤ r ≤ k. If the divergence of system ẋ = f(x) is non–identically zero, then any Jacobian multiplier is functionally independent of the n − 1 first integ...

Semirings whose additive endomorphisms are multiplicative

A ring or an idempotent semiring is associative provided that additive endomorphisms are multiplicative.