Third-order explicit autonomous differential equations in one scalar variable or, mechanically interpreted, jerky dynamics constitute an interesting subclass of dynamical systems that can exhibit many major features of regular and irregular or chaotic dynamical behavior. In this paper, we investigate the circumstances under which three dimensional autonomous dynamical systems possess at least o...

We study shapes given by polynomial lemniscates, and their fingerprints. We focus on the inflection points of fingerprints, their number and geometric meaning. Furthermore, we study dynamics of zeros of lemniscate-generic polynomials and their ‘explosions’ that occur by planting additional zeros into a defining polynomial at a certain moment, and then studying the resulting deformation. We call...

the topological index of a graph g is a numeric quantity related to g which is invariant underautomorphisms of g. the vertex pi polynomial is defined as piv (g)  euv nu (e)  nv (e).then omega polynomial (g,x) for counting qoc strips in g is defined as (g,x) =cm(g,c)xc with m(g,c) being the number of strips of length c. in this paper, a new infiniteclass of fullerenes is constructed. the ...

The problem of constructing standardized maximin D-optimal designs for weighted polynomial regression models is addressed. In particular it is shown that, by following the broad approach to the construction of maximin designs introduced recently by Dette, Haines and Imhof (2003), such designs can be obtained as weak limits of the corresponding Bayesian Φq-optimal designs. The approach is illust...