The geometry of polynomials explores geometrical relationships between the zeros and the coefficients of a polynomial. A classical problem in this theory is to locate the zeros of a given polynomial by determining disks in the complex plane in which all its zeros are situated. In this paper, we infer bounds for general polynomials and apply classical and new results to graph polynomials namely ...

The classical theory of statistical signal extraction presupposes lengthy data sequences, which are assumed, in theory, to be doubly infinite or semi-infinite— see Whittle (1983), for example. In many practical cases, and in most econometric applications, the available data are, to the contrary, both strongly trended and of a limited duration. This paper is concerned with the theory of finite-s...

Elliptic stochastic partial diierential equations (SPDE) with polynomial perturbation terms deened in terms of Nelson's Euclidean free eld on R d are studied using results by S. Kusuoka and A.S. Ust unel and M. Zakai concerning transformation of measures on abstract Wiener space. SPDEs of this type arise, in particular, in (Euclidean) quantum eld theory with interactions of the polynomial type....

Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. Presently, the input nonlinearity is allowed to be a memory operator of backlash type and both input and output nonlinearities are polynomial and may be noninvertible. The linear subsystem may be parametric or not, continuousor discrete-time. A two-stage identification method is develop...

In the language of mathematical chemistry, Fibonacci cubes can be defined as the resonance graphs of fibonacenes. Lucas cubes form a symmetrization of Fibonacci cubes and appear as resonance graphs of cyclic polyphenantrenes. In this paper it is proved that the Wiener index of Fibonacci cubes can be written as the sum of products of four Fibonacci numbers which in turn yields a closed formula f...

In this paper a three stage procedure is presented for deriving parameters bounds of SISOWiener models when the nonlinear block is modeled by a possibly noninvertible polynomial and the output measurement errors are bounded. First, using steady-state input–output data, parameters of the nonlinear part are bounded by a tight orthotope. Then, given the estimated uncertain nonlinearity and the out...

A generalized and automated process for the evaluation of system uncertainty using computer simulation is presented. Wiener–Askey polynomial chaos and generalized polynomial chaos expansions along with Galerkin projections, are used to project a resistive companion system representation onto a stochastic space. Modifications to the resistive companion modeling method that allow for individual m...

The Hosoya polynomial of a graph encompasses many of its metric properties, for instance the Wiener index (alias average distance) and the hyperWiener index. An expression is obtained that reduces the computation of the Hosoya polynomials of a graph with cut vertices to the Hosoya polynomial of the so-called primary subgraphs. The main theorem is applied to specific constructions including bouq...