Related papers: On positive bivariate quartic forms
We present a Hilbert space geometric approach to the problem of characterizing the positive bivariate trigonometric polynomials that can be represented as the square of a two variable polynomial possessing a certain stability requirement,…
We state and prove an identity which represents the most general eta-products of weight 1 by binary quadratic forms. We discuss the utility of binary quadratic forms in finding a multiplicative completion for certain eta-quotients. We then…
The quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations. The quartic oscillator is sufficiently simple to allow a detailed study and comparison of various…
Schubert coefficients $c_{u,v}^w$ are structure constants describing multiplication of Schubert polynomials. Deciding positivity of Schubert coefficients is a major open problem in Algebraic Combinatorics. We prove a positive rule for this…
This paper extends previous work on linear correlations of representation functions of positive definite binary quadratic forms to allow indefinite forms.
In this paper we consider a one quartic operator on the $\mathbb{R}^2$ with positive coefficients. Positive fixed points for a quartic operator, were investigated. Theorems on number of positive fixed points of the quartic operator, are…
The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version of Gauss sum for arbitrary finite quadratic forms, which is an exponential sum…
We describe bivariate polynomial sequences orthogonal to a symmetric weight function in terms of several bivariate polynomial sequences orthogonal with respect to Christoffel transformations of the initial weight under a quadratic…
A Riemannian manifold is called geometrically formal if the wedge product of any two harmonic forms is again harmonic. We classify geometrically formal compact 4-manifolds with nonnegative sectional curvature. If the sectional curvature is…
The positivity of the Gram-Charlier probability density function has been a subject of extensive study for decades. Since Barton and Dennis (1952) introduced numerical positivity conditions, no analytic closed-form expression was available…
Cubic forms in three variables are parametrised by points of $\P^9$. We study the subvarieties in this space defined by decomposable forms. Specifically, we calculate the equivariant minimal resolutions of these varieties and describe their…
An integral quadratic polynomial (with positive definite quadratic part) is called almost universal if it represents all but finitely many positive integers. In this paper, we provide a characterization of almost universal ternary quadratic…
We obtain some criteria for a symmetric square-central element of a totally decomposable algebra with orthogonal involution in characteristic two, to be contained in an invariant quaternion subalgebra.
We prove a spectral summation formula for the product of four Fourier coefficients of half-integral weight cusp forms in Kohnen's subspace. The other side of the formula involves certain generalized class numbers of pairs of quadratic forms…
In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.
The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and study of a quadratic discrete Fourier…
Quantifier elimination of positive semidefinite cyclic ternary quartic forms is studied in this paper. We solve the problem by the theory of complete discrimination systems, function \RealTriangularize in Maple15 and the so-called…
Every linear, quadratic or cubic polynomial having all real zeros is the derivative of a polynomial having all real zeros. The statement is false for higher degree polynomials. In particular, not every fourth degree polynomial with real…
A quaternionic K\"ahler manifold M is called {\it positive} if it has positive scalar curvature. The main purpose of this paper is to prove several connectedness theorems for quaternionic immersions in a quaternionic K\"ahler manifold, e.g.…
There are many specific results, spread over the literature, regarding the dualisation of quadrics in projective spaces and quadratic forms on vector spaces. In the present work we aim at generalising and unifying some of these. We start…