2 H design of decoupled control systems is treated in the generalized plant model. The existence condition of a decoupling controller is stated and a parameterized form of all achievable decoupled closed loop transfer matrices is presented by using the directional interpolation approaches under the assumption of simple transmission zeros. The class of all decoupling controllers that yield finit...

We study Bernstein polynomials for simple nonsmooth rational module functions. show that these can be represented as special sums of regular structure. For historical reasons, the representations found are naturally called “generalized Popoviciu expansions.” To write generalized expansions, we develop a formalism based on combinatorial calculations. Based formulas obtained, propose complete des...

We present an algorithm to decompose a polynomial system into a finite set of normal ascending sets such that the set of the zeros of the polynomial system is the union of the sets of the regular zeros of the normal ascending sets. If the polynomial system is 0-dimensional, the set of the zeros of the polynomials is the union of the sets of the zeros of the normal ascending sets.

In this paper, an algorithm that determines a real algebraic curve is outlined. Its basic step is to divide the plane into subdomains that include only simple branches of the algebraic curve without singular points. Each of the branches is then stably and efficiently traced in the particular subdomain. Except for the tracing, the algorithm requires only a couple of simple operations on polynomi...

We develop some of the finer details of the location of the zeros of the weight two Eisenstein series. These zeros are the same as the zeros of the derivative of the Ramanujan delta function.

Received: January 27, 2011 Accepted: February 12, 2011 doi:10.5539/jmr.v3n3p130 Abstract The purpose of this work is to study the zeros of linear recurrence sequence, with constant coefficients. We give a simple proof of well known Skolem-Mahler-Lech theorem. The advantage of this work is similar to the one done by V. Halava and collaborators, but in a simple way. We study the problem when the ...

Abstract – 2 H design of decoupled control systems is treated in the generalized plant model. The existence condition of a decoupling controller is stated and a parameterized form of all achievable decoupled closed loop transfer matrices is presented by using the directional interpolation approaches under the assumption of simple transmission zeros. The class of all decoupling controllers that ...

Abstract. We extend Aziz and Mohammad’s result that the zeros, of a polynomial P (z) = ∑n j=0 ajz , taj > aj−1 > 0, j = 2, 3, . . . , n for certain t ( > 0), with moduli greater than t(n − 1)/n are simple, to polynomials with complex coefficients. Then we improve their result that the polynomial P (z), of degree n, with complex coefficients, does not vanish in the disc |z − ae| < a/(2n); a > 0,...

In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting   0 f x   near the root. The main advantage of our methods is that they perform better and moreover, have the same efficiency indices as that of existing multipoint iterative methods. Furthermore, the convergence analysis of ...

Let Ψn(x) be the monic polynomial having precisely all non-primitive nth roots of unity as its simple zeros. One has Ψn(x) = (x n − 1)/Φn(x), with Φn(x) the nth cyclotomic polynomial. The coefficients of Ψn(x) are integers that like the coefficients of Φn(x) tend to be surprisingly small in absolute value, e.g. for n < 561 all coefficients of Ψn(x) are ≤ 1 in absolute value. We establish variou...