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...

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...

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.

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.

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...

We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely spaced zeros. This gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields.

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...