相关论文: A Refinement of Vietoris Inequality for Cosine Pol…
Recently the author established an improvement of the classical Vietoris sine inequality to include sine polynomials with non-monotone coefficients. In this paper two further improvements are presented admitting sine polynomials with…
In this work, a Vietoris type theorem for the positivity of sine and cosine sum for a particular sequence of real numbers is provided. In this connection, the positivity of a particular type of sine sum involving ratio of some parameters is…
In a recent work, the authors established a refinement of the well-known 1958 result of Vietoris on nonnegative cosine polynomials. In four places of the proof, use was made of the classical Sturm Theorem on determining the number of real…
We present two extensions of the one dimensional free Poincar\'e inequality similar in spirit to two classical refinements.
We establish refinements of the classical Kato inequality for sections of a vector bundle which lie in the kernel of a natural injectively elliptic first-order linear differential operator. Our main result is a general expression which…
Given a positive linear combination of five (respectively seven) cosines, where the angles are positive and sum to pi, the aim of this article is to express the sharp bound of the combination as a Positive Real Fraction in the coefficients…
A refinement of the Hardy inequality has been presented by use of superquadratic function.
We refine upper bounds for the classical exponents of uniform approximation for a linear form on the Veronese curve in dimension from $3$ to $9$. For dimension three, this in particular shows that a bound previously obtained by two…
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
In the paper, some lower bounds for polygamma functions are refined.
Let $Z(N)$ denote the minimum number of zeros in $[0,2\pi]$ that a cosine polynomial of the form $$f_A(t)=\sum_{n\in A}\cos nt$$ can have when $A$ is a finite set of non-negative integers of size $|A|=N$. It is an old problem of Littlewood…
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…
Coxeter polynomials are important homological invariants that are defined for a large class of finite-dimensional algebras. It is of particular interest to develop methods to compute these polynomials. We define the notion of insertion of a…
A refinement of the q-trinomial coefficients is introduced, which has a very powerful iterative property. This ``T-invariance'' is applied to derive new Virasoro character identities related to the exceptional simply-laced Lie algebras…
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…
We give some new refinements and reverses Young inequalities in both additive-type and multiplicative-type for two positive numbers/operators. We show our advantages by comparing with known results. A few applications are also given. Some…
The more then hundred years old Bernstein inequality states that the supremum norm of the derivative of a trigonometric polynomial of fixed degree can be bounded from above by supremum norm of the polynomial itself. The reversed Bernstein…
This is a brief review of recent progress in constructing solutions to the matrix model Virasoro equations. These equations are parameterized by a degree n polynomial W_n(x), and the general solution is labeled by an arbitrary function of…
We show that even mild improvements of the Polya-Vinogradov inequality would imply significant improvements of Burgess' bound on character sums. Our main ingredients are a lower bound on certain types of character sums (coming from works of…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…