Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH) circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed....

We describe computations which show that each of the first 12069 zeros of the Ramanujan τ -Dirichlet series of the form σ + it in the region 0 < t < 6397 is simple and lies on the line σ = 6. The failures of Gram’s law in this region are also noted. The first 5018 zeros and 2228 successive zeros beginning with the 20001st zero are also calculated. The distribution of the normalized spacing of t...

This paper describes efficient algorithms for the computation of dominant zeros of large scale transfer functions. The transfer function zeros are demonstrated to be equal to the poles of a new inverse system, which is valid even for the strictly proper case. This is a new finding, which is important from practical as well as theoretical viewpoints. Hence, the dominant zeros can be computed as ...

The complex field zeros of the Random Energy Model are analytically determined. For T < Tc they are distributed in the whole complex plane with a density that decays very fast with the real component of H. For T > Tc a region is found which is free of zeros and is associated to the paramagnetic phase of the system. This region is separated from the former by a line of zeros. The real axis is fo...

Over the past ten years, many examples of natural polynomial families from combinatorics and number theory have emerged whose zeros for high degrees appear to converge to intriguing curves in the complex plane. One interesting collection of examples appears on the website [16] of Richard Stanley which includes chromatic polynomials of complete partite graphs, q-analogue of Catalan numbers, Bern...

Inequalities satisfied by the zeros of the solutions of second order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among o...

ing the origin, the theorem from Polya-Szegö may be applied with the F(z) of the theorem taken as A (z). Theorem 111(b) then follows immediately. As an application of Theorem III, let us consider the polynomial F(z)=jy~oakG(k+p)z where p>0 and G(z)=T(z)~ = ^ n * = i ( l + n~'z)e~} the reciprocal of the gamma function. Since J> = 0 and all the zeros of G(z-\-p) are negative, any sector wi ̂ arg z...

Let q be a pattern and let Sn q c be the number of n-permutations having exactly c copies of q. We investigate when the sequence Sn q c c≥0 has internal zeros. If q is a monotone pattern it turns out that, except for q = 12 or 21, the nontrivial sequences (those where n is at least the length of q) always have internal zeros. For the pattern q = 1 l + 1 l 2 there are infinitely many sequences w...

. The wavefunctions in phase-space representation can be expressed as entire functions of their zeros if the phase space is compact. These zeros seem to hide a lot of relevant and explicit information about the underlying classical dynamics. Besides, an understanding of their statistical properties may prove useful in the analytical calculations of the wavefunctions in quantum chaotic systems. ...

Lee-Yang zeros are points on the complex plane of physical parameters where the partition function of a system vanishes and hence the free energy diverges. Lee-Yang zeros are ubiquitous in many-body systems and fully characterize their thermodynamics. Notwithstanding their fundamental importance, Lee-Yang zeros have never been observed in experiments, due to the intrinsic difficulty that they w...