The mod 4 valued quadratic forms defined by E. H. Brown, Jr. are studied. A classification theorem is proven which states that these forms are determined by two things: whether or not their associated bilinear form is alternating, and the rj-invariant of Brown (which generalizes the Arf invariant of an ordinary quadratic form). Particular attention is paid to a generalization of Witt's extensio...

• A quadratic space is a pair (V,B) where V is a finite-dimensional vector space over a field K and B : V × V → K is a symmetric bilinear form. • For quadratic spaces (V,B) and (V ′, B′), a map τ : V → V ′ is an isometry iff τ is a linear isomorphism and ∀~v, ~ w ∈ V : B(~v, ~ w) = B′(τ(~v), τ(~ w)). In this case V and V ′ are isometric. • The quadratic form determined by B and basis β := {~v1,...

multi objective quadratic fractional programming (moqfp) problem involves optimization of several objective functions in the form of a ratio of numerator and denominator functions which involve both contains linear and quadratic forms with the assumption that the set of feasible solutions is a convex polyhedral with a nite number of extreme points and the denominator part of each of the object...

In this paper we are concerned with classical polar spaces, i. e. with the set of points and lines of some vector space W on which a non–degenerate (σ, )-hermitian form or pseudo-quadratic form vanishes. To state the Main Theorem we introduce some notation. Let L be a division ring and W be a (left–)vector space over L endowed with a (σ, )–hermitian form or a pseudo–quadratic form q (with assoc...

This paper is a sequel to [6], in which we introduced quadratic forms on a module over a supertropical semiring R and analyzed the set of bilinear companions of a single quadratic form V → R in case the module V is free. Any (semi)module over a semiring gives rise to what we call its minimal ordering, which is a partial order iff the semiring is “upper bound.” Any polynomial map q (or quadratic...