In the literature of time series analysis since Whittle (1953), many authors (for example, Dunsmuir and Hannan (1976), Dunsmuir (1979), and Hosoya and Taniguchi (1982)) have considered an approach using Whittle’s log-likelihood, which is an approximation of Gaussian log-likelihood of the data, and have developed the asymptotic properties of an estimator that maximizes Whittle’s loglikelihood. T...

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.

Double hexagonal chains” can be considered as benzenoids constructed by successive fusions of successive naphthalenes along a zig-zag sequence of triples of edges as appear on opposite sides of each naphthalene unit. In this paper, we discuss the numbers of k-matchings and k-independent sets of double hexagonal chains, as well as Hosoya indices and Merrifield–Simmons indices, and obtain some ex...

This paper investigates the effects of wealth−enhanced social status using an optimizing monetary growth model with non−separable utility function between consumption and wealth. Within this framework, we first arrive a conclusion that, in the case of no wealth effects, an increase in the rate of money growth does not stimulate the steady−state growth rate. Moreover, in the case of existing wea...

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...

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.