Given a proper cone K?Rn, multivariate polynomial f?C[z]=C[z1,…,zn] is called K-stable if it does not have root whose vector of the imaginary parts contained in interior K. If K non-negative orthant, then K-stability specializes to usual notion stability polynomials. We study conditions and certificates for given f, especially case determinantal polynomials as well quadratic A particular focus ...

In a recent paper, Guo, Mező, and Qi proved an identity representing the Bernoulli polynomials at non-negative integer points m in terms of the m-Stirling numbers of the second kind. In this note, using a new representation of the Bernoulli polynomials in the context of the Zeon algebra, we give an alternative proof of the aforementioned identity.

Let q ≥ 2 be a positive integer, B be a fractional Brownian motion with Hurst index H ∈ (0, 1), Z be an Hermite random variable of index q, and Hq denote the Hermite polynomial having degree q. For any n ≥ 1, set Vn = ∑n−1 k=0 Hq(Bk+1 − Bk). The aim of the current paper is to derive, in the case when the Hurst index verifies H > 1 − 1/(2q), an upper bound for the total variation distance betwee...

Combining the approach to Thom polynomials via classifying spaces of singularities with the Fulton-Lazarsfeld theory of cone classes and positive polynomials for ample vector bundles, we show that the coefficients of the Schur function expansions of the Thom polynomials of stable singularities are nonnegative with positive sum.

Polynomials defined recursively over the integers such as Dickson polynomials, Chebychev polynomials, Fibonacci polynomials, Lucas polynomials, Bernoulli polynomials, Euler polynomials, and many others have been extensively studied in the past. Most of these polynomials have some type of relationship between them and share a large number of interesting properties. They have been also found to b...