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...

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.

We have derived orbital basis sets from scattering theory. They are expressed as polynomial approximations to the energy dependence of a set of partial waves, in quantized form. The corresponding matrices, as well as the Hamiltonian and overlap matrices, are specified by the values on the energy mesh of the screened resolvent and its first energy derivative. These orbitals are a generalization ...

ALEXANDRE L. MADUREIRA Abstract. We use variational techniques to derive a class of two-dimensional models for three-dimensional linearly elastic piezoelectric plates. The models result from a mixed formulation for the original problem within spaces of functions with polynomial dependence in the transverse direction. We show that the resulting system of equations is well-posed, and then discuss...

We define and study semimatroids, a class of objects which abstracts the dependence properties of an affine hyperplane arrangement. We show that geometric semilattices are precisely the posets of flats of semimatroids. We define and investigate the Tutte polynomial of a semimatroid. We prove that it is the universal Tutte-Grothendieck invariant for semimatroids, and we give a combinatorial inte...

Contrary to the expected behavior, we show the existence of noninvertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint module. A criterion to decide whether a given deformation is invertible or not is given in dependence of the Poincaré polynomial. PACS numbers: 02.20Sv, 02.20Qs, 9...

The problem of identifying a linear time invariant system with bilinear dependence on two unknown parameters is considered. An algorithm which , uses measurements of the input and output and knowledge of the polynomial coefficients of the bilinear combinations of the unknown parameters is described. Persistence of excitation conditions an the input for computability of the algorithm are derived...

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...

Using density-functional calculations, we obtain the ~001! biaxial strain dependence of the valence and conduction band energies of GaN, GaP, GaAs, InN, InP, and InAs. The results are fit to a convenient-to-use polynomial and the fits provided in tabular form. Using the calculated biaxial deformation potentials in large supercell empirical pseudopotential calculations, we demonstrate that epita...

Abstract: The paper presents the solution of the time optimal control with the help of Gröbner Bases theory. First the set of polynomial equations for the triple integrator system with unknowns corresponding to the switching times is constructed and later it is solved in the computer algebra system Maple using the Groebner library. In dependence of resulting switching times the control action i...