Related papers: An inequality regarding differential polynomial
In the first part of this expository paper, we present and discuss the interplay of Dirichlet polynomials in some classical problems of number theory, notably the Lindel\"of Hypothesis. We review some typical properties of their means and…
In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.
Let $p(z)$ be a monic polynomial of degree $n$, with complex coefficients, and let $q(z)$ be its monic factor. We prove an asymptotically sharp inequality of the form $\|q\|_{E} \le C^n \|p\|_E$, where $\|\cdot\|_E$ denotes the sup norm on…
In the paper, the authors establish some interesting identities and inequalities involving the extended Weyl type fractional integrals.
A method for proving symmetrization inequalities for some elliptic p.d.e.'s on manifolds equipped with appropriate isoperimetric inequalities is outlined. The method is based on a modification of an approach of Baernstein. The question of…
We prove an explicit Chinese Remainder Theorem for one variable polynomials with complex coefficients, and derive some consequences.
In this note, we derive a Leibniz rule for difference quotient.
We give a variant of the Bohenblust-Hille inequality which, for certain families of polynomials, leads to constants with polynomial growth in the degree.
In this paper, we present certain new $L_p$ inequalities for $\mathcal B_{n}$-operators which include some known polynomial inequalities as special cases.
I prove new local inequality for divisors on smooth surfaces, describe its applications, and compare it to a similar local inequality that is already known by experts.
In this paper, we prove a number of results providing either necessary or sufficient conditions guaranteeing that the number of real roots of real polynomials of a given degree is either less or greater than a given number. We also provide…
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…
In this paper, the discriminant of homogeneous polynomials is studied in two particular cases: a single homogeneous polynomial and a collection of n-1 homogeneous polynomials in n variables. In these two cases, the discriminant is defined…
An expression for the subdifferential of the joint numerical radius is obtained. Its applications to the best approximation problems in the joint numerical radius are discussed.
Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…
The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of $n$ linear…
Recently, the non-linear Changhee differential equations were introduced in [5] and these differential equations turned out to be very useful for studying special polynomials and mathematical physics. Some interesting identities and…
In this paper, new refinements for integral and sum forms of H\"older inequality are established. We note that many existing inequalities related to the H\"older inequality can be improved via obtained new inequalities in here, we show this…
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness…