In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.

The zeros of generalized Krawtchouk polynomials are studied. Some interlacing theorems for the zeros are given. A new infinite family of integral zeros is given, and it is conjectured that these comprise most of the non-trivial zeros. The integral zeros for two families of q-Krawtchouk polynomials are classified.

We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval (−1, 1) are asymptotically independent of the zeros outside of this interval, and that the straightened zeros have the same limit translation invariant correlations. Then we calculate the correlations between the straightened zeros of the SO(2) random p...

The notions separability and normality are related to this characterisation. In the case of skew fields polynomials often have infinitely many zeros, so a different way of counting zeros as distinct is needed. The well-known theorem of Gordon and Motzkin [Z] states that a polynomial of degree n has zeros in at most n conjugacy classes. This suggests one should count zeros of a polynomial by the...

Abstract We propose a novel statistical inference methodology for multiway count data that is corrupted by false zeros are indistinguishable from true zero counts. Our approach consists of zero-truncating the Poisson distribution to neglect all values. This simple truncated dispenses with need distinguish between and counts reduces amount be processed. Inference accomplished via tensor completi...

Abstract The Cauchy radius of a scalar polynomial is an upper bound on the magnitude its zeros, and it optimal among all bounds depending only moduli coefficients. It has disadvantage being implicit because requires solution nonlinear equation. In this note, simple explicit are derived that useful approximations to radius. general approach obtain aforementioned embed polynomials into larger fra...

We derive non-abelian Toda field theories (NATFTs) from a 4d Chern-Simons (CS) theory with two order defects by employing certain asymptotic boundary condition. The CS is characterized meromorphic 1-form $\omega$\,. adopt $\omega$ simple poles and no zeros, each of the located at pole. As result, an anisotropy parameter $\beta^2$ can be identified distance between defects. examples, we (complex...

In the noncommutative case also a version of (1) can be proved; see for instance [S, Proposition A.33. In that case, in general, such an N is not finitely generated over K. What (2) means for the noncommutative case depends on how one defines the phrase “constructing by repeatedly adding zeros of p until p has a complete set of zeros.” The adding of zeros may be done by forming field coproducts...

Polynomials with perturbed coefficients, which can be regarded as interval polynomials, are very common in the area of scientific computing due to floating point operations in a computer environment. In this paper, the zeros of interval polynomials are investigated. We show that, for a degree n interval polynomial, the number of interval zeros is at most n and the number of complex block zeros ...