‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

Digital maps are used, for example, in car navigation systems and web-based map services. As digital data, digital maps are easy to update, duplicate, and distribute. At the same time, illegal duplication and distribution or forgery of the maps is also easy. This paper proposes a digital watermarking algorithm for vector digital maps as a method to counter such abuses of the maps. A watermark b...

Abstract. We consider perturbations of quadratic maps fa admitting an absolutely continuous invariant probability measure, where a is in a certain positive measure set A of parameters, and show that in any neighborhood of any such an fa, we find a rich fauna of dynamics. There are maps with periodic attractors as well as non-periodic maps whose critical orbit is absorbed by the continuation of ...

In particular, (6) implies that the functions/i, • • • , /„ are all regular in the domain (7) a > 0, i wi\ < r, • • • ,| to„| < r. In these notations, the following theorem will be proved: Theorem. In the domain (7), let fx, • ■ • ,fnbe regular functions of the form (1) with uniformly almost periodic coefficient functions defined on (2) having Fourier expansions of the type (3), satisfying (4)....

We show that a completely multiplicative automatic function, which dos not have 0 as value, is almost periodic.

This paper studies some sufficient conditions for the existence and uniqueness of a pseudo almost periodic mild solution to abstract hyperbolic differential equations with infinite delay. Applications include the existence and uniqueness of a pseudo almost periodic mild solution to the heat equation.

Abstract We establish a sufficient condition for continuous map, acting on compact metric space, to have Baire residual set of points exhibiting historic behavior (also known as irregular points). This criterion applies, instance, minimal and non-uniquely ergodic map; maps preserving two distinct probability measures with full support; non-trivial homoclinic classes; some non-uniformly expandin...