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...

The distribution of the zeros of the partition function in the complex temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is studied for non-integer Q. On L × L self-dual lattices studied (L ≤ 8), no Fisher zero lies on the unit circle p0 = e iθ in the complex p = (e − 1)/√Q plane for Q < 1, while some of the Fisher zeros lie on the unit circle for Q > 1 and the number ...

Recently the existence of certain SU(2) BPS monopoles with the symmetries of the Platonic solids has been proved. Numerical results in an earlier paper suggest that one of these new monopoles, the tetrahedral 3-monopole, has a remarkable new property, in that the number of zeros of the Higgs field is greater than the topological charge (number of monopoles). As a consequence, zeros of the Higgs...

Since B (s) and d(s) are coprime, the proof is complete. From the lemma, the blocking zeros are seen to coincide with the roots, counting multiplicities, of q(s) = 0. For the sake of comparison, we remark that Rosenbrock [3] defines the zeros of G(s) to be the roots of cl(s)cz(s). . c,(s)=O. Desoer and Schulman [ I ] and Wolovich [2], without specifying multiplicities, identify the roots of c,...

This paper presents a method of numerically computing zeros of an analytic function for the specific application of computing eigenvalues of the Sturm-Liouville problem. The Sturm-Liouville problem is an infinite dimensional eigenvalue problem that often arises in solving partial differential equations, including the heat and wave equations. To compute eigenvalues of the Sturm-Liouville problem...

In this paper we consider the numerical problems faced by a blind dereverberation algorithm based on a multi-channel linear prediction. One hypothesis frequently incorporated in multimicrophone dereverberation algorithms is that channels do not share common zeros. However, it is known that real room transfer functions have a large number of zeros close to the unit circle on the z-plane, and thu...

We study the variation of the zeros of the Hermite function Hλ(t) with respect to the positive real variable λ. We show that, for each nonnegative integer n, Hλ(t) has exactly n + 1 real zeros when n < λ ≤ n + 1 and that each zero increases from −∞ to ∞ as λ increases. We establish a formula for the derivative of a zero with respect to the parameter λ; this derivative is a completely monotonic ...