let g be a simple graph and (g,) denotes the number of proper vertex colourings of gwith at most  colours, which is for a fixed graph g , a polynomial in  , which is called thechromatic polynomial of g . using the chromatic polynomial of some specific graphs, weobtain the chromatic polynomials of some nanostars.

A bstract . The function h (z ) = ~ (z l i z ) is t he ewton map associated with the quadratic polynomial z 2 +1. The iterated dynamics of f on 3{ is usually st udied by exploit ing the conjugacy between f and the funct ion z f-> z2 In this paper we show how to use the technique of nested intervals t o yield a direct ana lysis of t he dynamics. We also show how to use the same technique to anal...

this paper presents a gain scheduled autopilot for pitch channel of a flying vehicle. the selected method is based on polynomial fuzzy systems. the method does not involve linearization about operating point. first the polynomial fuzzy model of pitch channel of the flight body is derived. next, using polynomial fuzzy system methodology the controller is design such that the outputs of the nonli...

The quantum dynamics of a driven single-band tight-binding model is considered. The relation between this Hamiltonian and Hamiltonian of the discrete-charge mesoscopic quantum circuits is investigated. It is shown that the former Hamiltonian, with closed boundary conditions, can be considered as a realization of the generalized para-fermionic polynomial algebras.

We formulate a sufficient condition on the mesh under which we prove the discrete maximum principle (DMP) for the one-dimensional Poisson equation with Dirichlet boundary conditions discretized by the hp-FEM. The DMP holds if a relative length of every element K in the mesh is bounded by a value H∗ rel(p) ∈ [0.9, 1], where p ≥ 1 is the polynomial degree of the element K. The values H∗ rel(p) ar...

We propose a model to analyze the dynamics of interacting proliferating and quiescent cell populations. The model includes age dependence of cell division, transitions between the two sub-populations and regulation of the recruitment of quiescent cells. We formulate the model as a pair of renewal equations and apply a rather recent general result to prove that (in-)stability of equilibria can b...

Design and analysis of residual generators for polynomial systems is considered. This paper presents a systematic procedure, given an input-output description of system dynamics, to design residual generators for fault diagnosis. The design procedure is based on standard elimination theory. The design procedure is applied in a simulation study on a non-linear system, where it is showed how mult...

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualit...

We study the convergence time of the best response dynamics in player-specific singleton congestion games. It is well known that this dynamics can cycle, although from every state a short sequence of best responses to a Nash equilibrium exists. Thus, the random best response dynamics, which selects the next player to play a best response uniformly at random, terminates in a Nash equilibrium wit...

in this paper, rst a design is proposed for representing fuzzy polynomials withinput fuzzy and output fuzzy. then, we sketch a constructive proof for existenceof such polynomial which can be fuzzy interpolation polynomial in a set given ofdiscrete points rather than a fuzzy function. finally, to illustrate some numericalexamples are solved.