The concept of a coset-preserving skew-morphism is a generalization of the widely studied t-balanced skew-morphisms of regular Cayley maps which are in turn generalizations of group automorphisms. In case of abelian groups, all skew-morphisms of regular Cayley maps are roots of coset-preserving skew-morphisms, and therefore, classification of cosetpreserving skew-morphisms of finite abelian gro...

Let S = {ki,ki, ...} be an increasing sequence of positive integers. We call S strongly ergodic if for every measure preserving transformation T on a probability space (Cl, J, P) and every / £ Li(f2) we have limn-»oo(l/n) J^^j f(TkiuJ) = Pf(w) a.e. where Pf is the appropriate limit guaranteed by the individual ergodic theorem. We give sufficient conditions for a sequence S to be strongly ergodi...

The methods of defining and evaluating evolution of information in economic systems are often based on abstract measuretheoretic mean-preserving transformations (MPTs), also known as second-order stochastic dominance. This study first points out that such abstract MPTs have distributional equivalents and then shows that the distributional MPTs often provide analytical settings that are more acc...

In this work, we study the (2 + 1)-dimensional Zoomeron equation which is an extension of the famous (1 + 1)-dimensional Zoomeron equation that has been studied extensively in the literature. Using classical Lie point symmetries admitted by the equation, for the first time we develop an optimal system of one-dimensional subalgebras. Based on this optimal system, we obtain symmetry reductions an...

A band-dominant function on the Euclidean sphere embedded in R is the restriction to this sphere of an entire function of q + 1 complex variables having a finite exponential type in each of its variables. We develop a method to represent such a function using finitely many bits, using the values of the function at scattered sites on the sphere. The number of bits required in our representation ...

Consider a measure-preserving action Γ y (X,μ) of a countable group Γ and a measurable cocycle α : X × Γ → Aut(Y ) with countable image, where (X,μ) is a standard Lebesgue space and (Y, ν) is any probability space. We prove that if the Koopman representation associated to the action Γ y X is non-amenable, then there does not exist a countable-to-one Borel homomorphism from the orbit equivalence...

T h e purpose of the present paper is to study the metric entropy h((j),J\r) of an F-measure preserving transformation relative to a cr-algebra M of an F-dynamical system. Concepts of sufficient families and generators are introduced and a few results are proved. Finally, the entropy of the inverse limit of an inverse spectrum of F-dynamical systems is obtained.

We construct a family of integrable volume-preserving maps in R with a bidimensional heteroclinic connection of spherical shape between two fixed points of saddle-focus type. In other contexts, such structures are called Hill’s spherical vortices or spheromaks. We study the splitting of the separatrix under volume-preserving perturbations using a discrete version of the Melnikov method. Firstly...

This paper proposes a nonparametric FPE-like procedure based on the smooth backfitting estimator when the additive structure is a priori known. This procedure can be expected to perform well because of its well-known finite sample performance of the smooth backfitting estimator. Consistency of our procedure is established under very general conditions, including heteroskedasticity.

We study mappings obtained as s-periodic reductions of the lattice Korteweg-De Vries equation. For small s ∈ N we establish upper bounds on the growth of the degree of the numerator of their iterates. These upper bounds appear to be exact. Moreover, we conjecture that for s1, s2 co-prime the growth is ∼ (2s1s2)−1n2, except when s1 + s2 = 4 where the growth is linear ∼ n. Also, we conjecture the...