The zeros of the derivative of a complex polynomial p are functions of the zeros of p itself. In general we do not know explicit expressions for these functions. So approximate localizations of the derivative zeros in terms of the given zeros of p are of interest. A question of this type is the famous conjecture of Bl. Sendov which goes back to 1959 and took place in Hayman’s booklet on problem...

In this paper, we study a more general pair correlation function, F h (x, T), of the zeros of the Riemann zeta function. It provides information on the distribution of larger differences between the zeros.

In this paper, we present certain results concerning the location of the zeros of lacunarytpye polynomials which generalize and refine some known Cauchy type bounds for the zeros of polynomials.

While attempting to clarify the confusion concerning the conceptualization of "blocking zeros" in state space in the recent literature, some new observations are made on the relationship between pole-zero cancellation and transmission blocking. An important distinction between uncontrollable and unobservable eigenvalue s is pointed out; and it is argued that the description of a Blocking Zero, ...

In this paper, we consider a proximal point algorithm for finding a common zero of a finite family of maximal monotone operators in real Hilbert spaces. Also, we give a necessary and sufficient condition for the common zero set of finite operators to be nonempty, and by showing that in this case, this iterative sequence converges strongly to the metric projection of some point onto the set of c...

We consider interlacing properties satisfied by the zeros of Jacobi polynomials in quasi-orthogonal sequences characterised by α > −1, −2 < β < −1. We give necessary and sufficient conditions under which a conjecture by Askey, that the zeros of Jacobi polynomials P (α,β) n and P (α,β+2) n are interlacing, holds when the parameters α and β are in the range α > −1 and −2 < β < −1. We prove that t...

The sparse hypermatrix storage scheme produces a recursive 2D partitioning of a sparse matrix. Data subblocks are stored as dense matrices. Since we are dealing with sparse matrices some zeros can be stored in those dense blocks. The overhead introduced by the operations on zeros can become really large and considerably degrade performance. In this paper, we present several techniques for reduc...

We show that a large class of sets of leptonic texture zeros considered in the literature imply the vanishing of certain CP-odd weak-basis invariants. These invariant conditions enable one to recognize a flavour model corresponding to a set of texture zeros, when written in an arbitrary weak-basis where the zeros are not manifest. We also analyse the rôle of texture zeros in allowing for a conn...

We investigate the Laplacian Abelian gauge on the sphere S in the background of a single ‘t Hooft instanton. To this end we solve the eigenvalue problem of the covariant Laplace operator in the adjoint representation. The ground state wave function serves as an auxiliary Higgs field. We find that the ground state is always degenerate and has nodes. Upon diagonalisation, these zeros induce toplo...

Consider an operator dQ(f) = d dxk (Q(x)f(x)) where Q(x) is some fixed polynomial of degree k. One can easily see that dQ has exactly one polynomial eigenfunction pn(x) in each degree n ≥ 0 and its eigenvalue λn,k equals (n+k)! n! . A more intriguing fact is that all zeros of pn(x) lie in the convex hull of the set of zeros to Q(x). In particular, if Q(x) has only real zeros then each pn(x) enj...