In this paper we explore inequalities between symmetric homogeneous polynomials of degree four of three real variables and three nonnegative real variables. The main theorems describe the cases in which the smallest possible coefficient is not expressed by the other coefficients. The problem is resolved by introducing a parametric representation.Mathematics Subject Classication (2010): 26D05.Key words: Symmetric, homogeneous, polynomial, inequalities, degree four
The paper raises two problems on the homogeneous polynomial invariants for the cubic-homogeneous f...
This article presents several different methods for solving the problem of how to find a certain rel...
We study a natural extremal problem about the vector space consisting of all homogeneous polynomials...
Necessary and sufficient conditions for symmetric homogeneous polynomial inequalities of degree four...
Copyright 2012 c ⃝ Vasile Cirtoaje and Yuanzhe Zhou. This is an open access article distributed unde...
AbstractWe prove that homogeneous symmetric polynomial inequalities of degree p∈{4,5} in n positive1...
AbstractIn this paper, which is a continuation of [V. Timofte, On the positivity of symmetric polyno...
This thesis investigates the reducibility of trivariate homogeneous symmetric polynomials. For polyn...
The following very general result could have important implications for Quantifier Elimination theor...
This article addresses the problem of computing an upper bound of the degree d of a polynomial solut...
By means of algebraic, analytical and majorization theories, and under the proper hypotheses, we es...
We obtain quantitative bounds in the polynomial Szemerédi theorem of Bergelson and Leibman, provided...
Abstract. We prove some sufficient conditions implying l p inequalities of the form ||x||p ≤ ||y||p ...
AbstractThe symmetric complexity of a polynomial in n variables is defined as the number of times th...
We prove that a general polynomial vector (f1,f2,f3) in three homogeneous variables of degrees (3,3,...
The paper raises two problems on the homogeneous polynomial invariants for the cubic-homogeneous f...
This article presents several different methods for solving the problem of how to find a certain rel...
We study a natural extremal problem about the vector space consisting of all homogeneous polynomials...
Necessary and sufficient conditions for symmetric homogeneous polynomial inequalities of degree four...
Copyright 2012 c ⃝ Vasile Cirtoaje and Yuanzhe Zhou. This is an open access article distributed unde...
AbstractWe prove that homogeneous symmetric polynomial inequalities of degree p∈{4,5} in n positive1...
AbstractIn this paper, which is a continuation of [V. Timofte, On the positivity of symmetric polyno...
This thesis investigates the reducibility of trivariate homogeneous symmetric polynomials. For polyn...
The following very general result could have important implications for Quantifier Elimination theor...
This article addresses the problem of computing an upper bound of the degree d of a polynomial solut...
By means of algebraic, analytical and majorization theories, and under the proper hypotheses, we es...
We obtain quantitative bounds in the polynomial Szemerédi theorem of Bergelson and Leibman, provided...
Abstract. We prove some sufficient conditions implying l p inequalities of the form ||x||p ≤ ||y||p ...
AbstractThe symmetric complexity of a polynomial in n variables is defined as the number of times th...
We prove that a general polynomial vector (f1,f2,f3) in three homogeneous variables of degrees (3,3,...
The paper raises two problems on the homogeneous polynomial invariants for the cubic-homogeneous f...
This article presents several different methods for solving the problem of how to find a certain rel...
We study a natural extremal problem about the vector space consisting of all homogeneous polynomials...