Related papers: Note on the covering theorem for complex polynomia…
We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.
We give a simple proof of an explicit formula for Kerov polynomials. This formula is closely related to a formula of Goulden and Rattan.
In this paper, we study higher derivations of Jacobian type in positive characteristic. We give a necessary and sufficient condition for $(n-1)$-tuples of polynomials to be extendable in the polynomial ring in $n$ variables over an integral…
We estimate the density of tubes around the algebraic variety of decomposable univariate polynomials over the real and the complex numbers.
The generalized complex numbers can be realized in terms of $2\times2$ or higher-order matrices and can be exploited to get different ways of looking at the trigonometric functions. Since Chebyshev polynomials are linked to the power of…
In this paper we study the lattice point covering property of some regular polygons in dimension 2.
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.
In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.
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 define the covering gonality and separable covering gonality of varieties over arbitrary fields, generalizing the definition given by Bastianelli-de Poi-Ein-Lazarsfeld-Ullery for complex varieties. We show that over an arbitrary field a…
In this note we reconsider a familiar result in Vassiliev knot theory - that the coefficients of the Alexander-Conway polynomial determine the top row of the Kontsevich integral - from the point of view of Kazuo Habiro's clasper theory. We…
We give a criterion which characterizes a real multi-variate Laurent polynomial with full-dimensional smooth Newton polytope to have the property that all sufficiently large powers of the polynomial have fully positive coefficients. Here a…
A class P_{n,m,p}(x) of polynomials is defined. The combinatorial meaning of its coefficients is given. Chebyshev polynomials are the special cases of P_{n,m,p}(x). It is first shown that P_{n,m,p}(x) may be expressed in terms of…
In this paper we consider the extended q-Bernstein polynomials which are constructed by T. Kim and we investigate some properties.
We prove an extension of the Thue-Vinogradov Lemma and show some applications. This paper is another example for the application of the polynomial method.
Given a convergent sequence of nodes we present a one-dimensional-holomorphic-function version of the Newton interpolation method of polynomials. It also generalises the Taylor and the Laurent formula. In other words, we present an…
We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of…
The first aim of this paper is to prove a Gr\"uss-Voronovskaya estimate for Bernstein and for a class of Bernstein-Durrmeyer polynomials on $[0, 1]$. Then, Gr\"uss and Gr\"uss-Voronovskaya estimates for their corresponding operators of…
In the present paper a new mean value theorem for polynomials of special form is obtained. The case of sums on vertices of a regular polygon is studied. A criterion for a certain equation to be satisfied is obtained.