Complex Analogues of the Rolle's Theorem

2000 Mathematics Subject Classification: 30C10.

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

* The authors thank the “Swiss National Science Foundation” for its support.

Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

Development of Procedures of Recognition of Objects with Usage Multisensor Ontology Controlled Instrumental Complex

The ontological approach to structuring knowledge and the description of data domain of knowledge is considered. It is described tool ontology-controlled complex for research and developments of sensor systems. Some approaches to solution most frequently meeting tasks are considered for creation of the recognition procedures.

Fractal Analysis for Cancer Research: Case Study and Simulation of Fractals

2010 Mathematics Subject Classification: 65D18.