Related papers: Bernstein polynomials and spectral numbers for lin…
The free resolution and the Alexander dual of squarefree monomial ideals associated with certain subsets of distributive lattices are studied.
We prove a four dimensional version of the Bernstein Theorem, with complex polynomials being replaced by quaternionic polynomials. We deduce from the theorem a quaternionic Bernstein's inequality and give a formulation of this last result…
Exact ground truth invariant polynomial systems can be written for arbitrarily correlated binary classifiers. Their solutions give estimates for sample statistics that require knowledge of the ground truth of the correct labels in the…
Using similarity transformations we construct explicit solutions of the nonlinear Schrodinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their…
The accurate solution of some of the main problems in numerical linear algebra (linear system solving, eigenvalue computation, singular value computation and the least squares problem) for a totally positive Bernstein-Vandermonde matrix is…
In this paper we study q-Bernoulli numbers and polynomials related to q-Stirling numbers. From thsese studying we investigate some interesting q-stirling numbers' identities related to q-Bernoulli numbers.
This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some…
We present a quite efficient method to calculate the roots of Bernstein-Sato polynomial for a defining polynomial $f$ of a projective hypersurface $Z\subset{\mathbb P}^{n-1}$ of degree $d$ having only weighted homogeneous isolated…
We introduce a multivariate analogue of Bernoulli polynomials and give their fundamental properties: difference and differential relations, symmetry, explicit formula, inversion formula, multiplication theorem, and binomial type formula.…
We classify the discriminantly separable polynomials of degree two in each of three variables, defined by a property that all the discriminants as polynomials of two variables are factorized as products of two polynomials of one variable…
Lower bounds are given for the number of non-real zeros of a second order linear differential polynomial with constant coefficients in a real entire function with finitely many non-real zeros.
We introduce and study symmetric polynomials, which as very special cases include polynomials related to the supersymmetric eight-vertex model, and other elliptic lattice models with $\Delta=\pm 1/2$. There is also a close relation to…
We show that the polytopes obtained from the Birkhoff polytope by imposing additional inequalities restricting the "longest increasing subsequence" have Ehrhart quasi-polynomials which are honest polynomials, even though they are just…
In this paper new criteria are established for the existence of positive radial solutions of a semilinear elliptic system depending on the gradient. These criteria are determined by some relationships between the upper and lower bounds on…
We establish a necessary and sufficient condition for all zeros of a self-reciprocal polynomial to lie on the unit circle. Moreover, we relate the necessary and sufficient condition with a canonical system of linear differential equations…
Finding eigenvalue distributions for a number of sparse random matrix ensembles can be reduced to solving nonlinear integral equations of the Hammerstein type. While a systematic mathematical theory of such equations exists, it has not been…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
Several families of sharp Bernstein inequalities are established on the weighted $L^2$ space over parabolic domains, which include bounded or unbounded rotational paraboloids and parabolic surfaces. The main tool is a second-order…
We develop a unified construction of matrix-valued orthogonal polynomials associated with discrete weights, yielding bispectral sequences as eigenfunctions of second-order difference operators. This general framework extends the discrete…
We consider multivariable polynomials over a fixed number field, linear in some of the variables. For a system of such polynomials satisfying certain technical conditions we prove the existence of search bounds for simultaneous zeros with…