DSpace Collection:

Moyal and Rankin-Cohen deformations of algebras

2019-12-23T09:10:24Z

Title: Moyal and Rankin-Cohen deformations of algebras Authors: Volodymyr Lyubashenko Abstract: It is proven that Rankin-Cohen brackets form an associativedeformation of the algebra of polynomials whose coeffcients are holomorphicfunctions on the upper half-plane.

A calculation of periodic data of surface diffeomorphisms with one saddle orbit.

2019-12-23T09:11:14Z

Title: A calculation of periodic data of surface diffeomorphisms with one saddle orbit. Authors: Олена В'ячеславівна Ноздрінова, Ольга Віталіївна Починка Abstract: In the paper it is proved that any orientable surface admits an orientation-preserving diffeomorphism with one saddle orbit. It distinguishes in principle the considered class of systems from source-sink diffeomorphisms existing only on the sphere. It is shown that diffeomorphisms with one saddle orbit of a positive type on any surface have exactly three node orbits. In addition, all possible types of periodic data for such diffeomorphisms are established. Namely, formulas are found expressing the periods of the sources through the periods of the sink and the saddle.

Bypassing dynamical systems: a simple way to get the box-counting dimension of the graph of the Weierstrass function

2019-12-23T09:11:25Z

Title: Bypassing dynamical systems: a simple way to get the box-counting dimension of the graph of the Weierstrass function Authors: Claire David Abstract: In the following, bypassing dynamical systems tools, we propose a simple means of computing the box dimension of the graph of the classical Weierstrass function defined, for any real number~$x$, by[{mathcal W}(x)= sum_{n=0}^{+infty} lambda^n,cos left ( 2, pi,N_b^n,x right),]where $lambda$ and $N_b$ are two real numbers such that $0 1$, using a sequence a graphs that approximate the studied one.

On measures of nonplanarity of cubic graphs

2019-12-23T09:11:38Z

Title: On measures of nonplanarity of cubic graphs Authors: Leonid Plachta Abstract: We study two measures of nonplanarity of cubic graphs G, the genus γ (G), and the edge deletion number ed(G). For cubic graphs of small orders these parameters are compared with another measure of nonplanarity, the rectilinear crossing number (G). We introduce operations of connected sum, specified for cubic graphs G, and show that under certain conditions the parameters γ(G) and ed(G) are additive (subadditive) with respect to them.The minimal genus graphs (i.e. the cubic graphs of minimum order with given value of genus γ) and the minimal edge deletion graphs (i.e. cubic graphs of minimum order with given value of edge deletion number ed) are introduced and studied. We provide upper bounds for the order of minimal genus and minimal edge deletion graphs.