In this manuscript, we are concerned with the problem of locating zeros some special quaternionic polynomials and regular functions restricted coefficients; namely coefficients whose real components or their moduli satisfy suitable inequalities. The obtained results for subclass produce extensions classical Enestr?m-Kakeya theorem its various variants from complex to setting.

Let $f(z)$ be an analytic function on the unit disk ${zinmathbb{C}, |z|leq 1}$, for each $q>0$, the $|f|_{q}$ is defined as followsbegin{align*}begin{split}&left|fright|_q:=left{frac{1}{2pi}int_0^{2pi}left|f(e^{itheta})right|^qdthetaright}^{1/q}, 0

for every $1leq s< n$, the $s^{th}$ derivative of a polynomial $p(z)$ of degree $n$ is a polynomial $p^{(s)}(z)$ whose degree is $(n-s)$. this paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. besides, our result gives interesting refinements of some well-known results.

The density conjecture of Katz and Sarnak predicts that, for natural families L-functions, the distribution zeros lying near real axis is governed by a group symmetry. In case universal family automorphic forms on totally definite quaternion algebra, we determine associated restricted class test functions in analytic conductor aspect. particular it leads to non-trivial results densities non-van...

The polar derivative of a polynomial P(z) degree n with respect to complex number ? is nP(z) + (??z)P?(z) at most n?1 and denoted by D?P(z). We consider the class polynomials = a0 ?n v=? avzv, 1, such that ?0 in |z| &lt; k, k 1 establish some upper bound estimates for maximum modulus D?P(z) on unit disk involving coefficients P(z). obtained results refine generalize well known inequalities.

Abstract Stenger conjectures are claims about the location of eigenvalues matrices whose elements certain integrals involving basic Lagrange interpolating polynomials supported on zeros orthogonal polynomials. In this paper, we show validity extended conjecture for families classical We also restricted Strenger a family Jacobi and generalized Laguerre A connection with -stability collocation Ru...

I compute exact partition function zeros of β hairpins, using both analytic and numerical methods, extending previous work [J. Lee, Phys. Rev. Lett. 110, 248101 (2013)] where only a restricted class of hairpins was considered. The zeros of β hairpins with an odd number of peptide bonds are computed and the difference of the distribution of zeros from those for an even number of peptide bonds is...

We use the method of interlacing families polynomials to derive a simple proof Bourgain and Tzafriri’s Restricted Invertibility Principle, then sharpen result in two ways. show that stable rank can be replaced by Schatten 4-norm tighter bounds hold when number columns matrix under consideration does not greatly exceed its rows. Our are derived from an analysis smallest zeros Jacobi associated L...

In resonator-coupled bandpass filter 3D design, it is a routine that the optimization methods are guided/supervised by designers’ experience to carry out an iterative design process. To realize automated or unsupervised optimization, new method, called hybrid surrogate model-assisted evolutionary algorithm for (H-SMEAFO), proposed. H-SMEAFO aims automatically obtain highly optimal without inter...