We investigate the dynamics of semigroups generated by a family of polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is bounded. The Julia set of such a semigroup may not be connected in general. We show that for such a polynomial semigroup, if A and B are two connected components of the Julia set, then one of A and B surrounds the other. From this, it is...

Purpose – To propose a new computational approach for parameter estimation in the Bayesian framework. Aposteriori PDFs are obtained using the polynomial chaos theory for propagating uncertainties through system dynamics. The new method has the advantage of being able to deal with large parametric uncertainties, non-Gaussian probability densities, and nonlinear dynamics. Design/methodology/appro...

For every $1leq s< n$, the $s^{th}$ derivative of a polynomial $P(z)$ of degree $n$ is a polynomial $P^{(s)}(z)$ whose degree is $(n-s)$. This paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. Besides, our result gives interesting refinements of some well-known results.

Let G be a simple graph and (G,) denotes the number of proper vertex colourings of G with at most  colours, which is for a fixed graph G , a polynomial in  , which is called the chromatic polynomial of G . Using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some nanostars.

for a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, dewan et al [k. k. dewan, n. singh and a. mir, extension of some polynomial inequalities to the polar derivative, j. math. anal. appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). in this paper we improve and extend the above inequality. our result generalizes certai...

This thesis contributes to a better understanding of state and output dead-beat control problems and stability of zero output constrained dynamics for the class of discrete-time polynomial systems. Dead-beat controllability is one of the fundamental notions in control theory since it establishes the existence of control laws which can achieve a desired operating regime in finite time. The class...

In this brief paper the possibility to realize third-order chaotic system by using mixed analog-digital circuit synthesis is described and experimentally verified. A single third-order differential equation with quadratic and cubic polynomial function is utilized as original mathematical model. It is suggested that the proposed approach can be generalized for almost any dynamical system as long...