Lipschitz domains. Our presentations here will almost exclusively be for bounded Lipschitz domains. Roughly speaking, a domain (a connected open set) Ω ⊂ R is called a Lipschitz domain if its boundary ∂Ω can be locally represented by Lipschitz continuous function; namely for any x ∈ ∂Ω, there exists a neighborhood of x, G ⊂ R, such that G ∩ ∂Ω is the graph of a Lipschitz continuous function und...

We present a number of new characterizations of EP elements in rings with involution in purely algebraic terms. Then, we study equivalent conditions for an element a in a ring with involution to satisfy ana∗ = a∗an or a = (a∗)n for arbitrary n ∈ N . For n = 1, we present some new characterizations of normal and Hermitian elements in rings with involution.

A symplectic involution on a K3 surface is an involution which preserves the holomorphic 2-form. We prove that such a symplectic involution acts as the identity on the CH0 group of the K3 surface, as predicted by Bloch’s conjecture. 2010 Mathematics Subject Classification: 14C25, 14J28

We study the involution of the real line induced by the outer automorphism of the extended modular group PGL(2,Z). This ‘modular’ involution is discontinuous at rationals but satisfies a surprising collection of functional equations. It preserves the set of real quadratic irrationals mapping them in a non-obvious way to each other. It commutes with the Galois action on real quadratic irrational...

We give conditions that ensure an operator satisfying a Piestch domination in given setting also satisfies different setting. From this we derive bounded multilinear T T </mml:semant...

Abstract We prove that real topological Hochschild homology $\mathrm {THR}$ for schemes with involution satisfies base change and descent the ${\mathbb {Z}/2}$ -isovariant étale topology. As an application, we provide computations projective line (with without involution) higher-dimensional spaces.

For cubic pencils we define the notion of an involution curve. This is a curve which intersects each pencil in exactly one non-base point pencil. Involution curves can be used to construct integrable maps plane leave invariant

Morphogenetic cell movements mould the shape of the developing organism. These movements have been extensively studied during Drosophila embryonic development. In particular live imaging analyses have revealed the complexities underlying the comparatively simple processes of germband extension, retraction and dorsal closure. I am applying live imaging techniques to an apparently complex morphog...

If ∗ : G → G is an involution on the finite group G, then ∗ extends to an involution on the integral group ring Z[G]. In this paper, we consider whether bicyclic units u ∈ Z[G] exist with the property that the group 〈u, u∗〉, generated by u and u∗, is free on the two generators. If this occurs, we say that (u, u∗) is a free bicyclic pair. It turns out that the existence of u depends strongly upo...