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 ...

When massaging differential-algebraic equations during an index reduction process, one usually keeps track of structural zeros in order to be able to detect when non-differential equations appear. However, in a numerical setting structural zeros may turn out as small numbers, impossible to distinguish from zero when numerical precision is taken into account. Such coefficients are referred to as...

Zeros frequently appear in economic data. Zeros in economic data come from different sources and the source affects the choice of an estimator. This paper surveys the literature on dealing with zeros from the perspective of an applied economist, discusses alternative estimators, and offers some illustrative examples.

Let ρ = β ′ + iγ ′ denote the zeros of ζ (s), s = σ + i t . It is shown that there is a positive proportion of the zeros of ζ (s) in 0 < t < T satisfying β ′ − 1/2 (log T )−1. Further results relying on the Riemann hypothesis and conjectures on the gaps between the zeros of ζ(s) are also obtained.

We study the monotonicity with respect to a parameter of zeros of orthogonal polynomials. Our method uses the tridiagonal (Jacobi) matrices arising from the three-term recurrence relation for the polynomials. We obtain new results on monotonicity of zeros of associated Laguerre, Al-Salam-Carlitz, Meixner and PoJlaczek polynomials. We also derive inequalities for the zeros of the Al-Salam-Carlit...

We study the zeros of the partition function in the complex β plane (Fisher’s zeros) in SU(2) and SU(3) gluodynamics. We discuss their effects on the asymptotic behavior of the perturbative series for the average plaquette. We present new methods to infer the existence of these zeros in region of the complex β plane where MC reweighting is not reliable. These methods are based on the assumption...

In this paper, some zeros and non-zeros in the character tables of symmetric groups are displayed partition forms. particular, more self conjugate partitions beside odd permutations heavily investigated.

a compact and sharp-rejection ultra-wideband (uwb) microstrip bandpass filter (bpf) is presented. the proposed filter is constructed with multiple-mode resonator (mmr) and split ring resonator (srr). moreover, proposed structure consists of two doublets parallel coupling gaps at each side of a microstrip ring. in comparison with some other filters, this structure shows a significantly wider pas...

We investigate the radiation amplitude zeros exhibited by many Standard Model amplitudes for triple weak gauge boson production processes. We show thatWZγ production amplitudes have especially rich structure in terms of zeros, these amplitudes have zeros originating from several different sources. It is also shown that TYPE I current null zone is the special case of the equality of the specific...

We use the behavioural approach to de®ne and characterize control-lable and uncontrollable poles and zeros of multidimensional (nD) linear systems. We show a strong relationship between controllable poles and zeros and properties of the transfer function matrix, and we give characterizations of uncontrollable poles and zeros, in particular demonstrating that these have an input decoupling prope...