GROUPS WITH QUADRATIC-NON-QUADRATIC DEHN FUNCTIONS

Groups with Quadratic-Non-Quadratic Dehn Functions

We construct a finitely presented group G with non-quadratic Dehn function f majorizable by a quadratic function on arbitrary long intervals.

Quadratic Functions on Torsion Groups

A quadratic function q on an Abelian groupG is a map, with values in an Abelian group, such that the map b : (x, y) 7→ q(x + y) − q(x) − q(y) is Z-bilinear. Such a map q satisfies q(0) = 0. If, in addition, q satisfies the relation q(nx) = nq(x) for all n ∈ Z and x ∈ G, then q is homogeneous. In general, a quadratic function cannot be recovered from the associated bilinear pairing b. Homogeneou...

Minimizing quadratic functions with separable quadratic constraints

This article deals with minimizing quadratic functions with a special form of quadratic constraints that arise in 3D contact problems of linear elasticity with isotropic friction [Haslinger, J., Kučera, R. and Dostál, Z., 2004, An algorithm for the numerical realization of 3D contact problems with Coulomb friction. Journal of Computational and Applied Mathematics, 164/165, 387–408.]. The propos...

Quadratic Functions, Optimization, and Quadratic Forms

Quadratic maps between groups

The notion of quadratic maps between arbitrary groups appeared at several places in the literature on quadratic algebra. Here a unified extensive treatment of their properties is given; the relation with a relative version of Passi’s polynomial maps and groups of degree 2 is established and used to study the structure of the latter. Introduction. Polynomial maps appear in nilpotent group theory...