Unachievable zeros

Is nursing becoming a political minefield of the unachievable?

Structural Zeros versus Sampling Zeros

Probabilistic sequence models estimated from large corpora typically require smoothing techniques to reserve some probability mass for unobserved events. These techniques fail to distinguish between events unobserved due to sampling limitations, sampling zeros, and those unobserved due to structural reasons such as syntactic constraints, structural zeros. We investigate the use of statistical t...

Monopole Zeros

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...

Some compact generalization of inequalities for polynomials with prescribed zeros

‎Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$‎, ‎$k^2 leq rRleq R^2$ and for $Rleq r leq k$‎. ‎Our results refine and generalize certain well-known polynomial inequalities‎.

Pólya's Theorem with zeros

Let R[X] := R[X1, . . . , Xn]. Pólya’s Theorem says that if a form (homogeneous polynomial) p ∈ R[X] is positive on the standard n-simplex ∆n, then for sufficiently large N all the coefficients of (X1 + · · ·+Xn)p are positive. This paper is the culmination of a project to characterize forms, possibly with zeros on ∆n, which satisfy a slightly relaxed version of Pólya’s Theorem (in which the co...