This paper introduces a method for finding closed forms for certain sums involving squares of binomial coefficients. We use this method to present an alternative approach to a problem of evaluating a different type of sums containing squares of the numbers from Catalan's triangle.

This paper presents a construction for symmetric, non-negative polynomials, which are not sums of squares. It explicitly generalizes the Motzkin polynomial and the Robinson polynomials to families of non-negative polynomials, which are not sums of squares. The degrees of the resulting polynomials can be chosen in advance. 2000 Mathematics Subject Classification: 12Y05, 20C30, 12D10, 26C10, 12E10

This paper discusses the Sums of Squares “m” consecutive Woodall Numbers. These discussions are made from definition numbers. Also learn comparability numbers and other special An attempt to communicate formula for sums squares ‘m’ its matrix form discussed. Further, this study expresses some more correlations between

The relationship between nonnegative polynomials and sums of squares is one the central questions in real algebraic geometry. A modern approach to look at on a variety. We survey rich history this area focus recent developments highlighting unexpected links complex geometry commutative algebra.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 27 October 2020Accepted: 11 June 2021Published online: 14 2021Keywordssemidefinite programming, matrix completion, real algebraic geometryAMS Subject Headings90C22, 15A83, 14P99Publication DataISSN (online): 2470-6566Publisher: Society for Industrial and Applied Mathemati...