The aim of this paper is to prove that, if R is a commutative regular ring in which 2 is a unit, then the reduced theory of quadratic forms with invertible coefficients in R, modulo a proper preorder T , satisfies Marshall’s signature conjecture and Milnor’s Witt ring conjecture (for precise statements, see Section 1 below). For that purpose we use the theory of special groups (abbreviated SG),...

One of the recently most developing fields of high energy heavy ion physics is the study of the underlying field theory at high temperatures. Despite of the naive picture of the quark gluon plasma as an ideal gas of quarks and gluons stemming from a given interpretation of early lattice gauge theory simulations it is since long clear that the continuum theory is plagued by serious infrared dive...

1.1 Introduction Environmental and genetic mutations can transform the cells in a cooperating healthy tissue into an ecosystem of individualistic tumour cells that compete for space and resources [1, 2, 3]. If we consider a tumour as an ecosystem it is possible to utilise tools traditionally used by ecologists to study the evolution of a population in which there is some degree of phenotypical ...