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...

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

In the paper 10] (see also 2]), the authors construct a holomorphic map from the modular curve X(k) = H 2 =?(k), where ?(k) is the congruence subgroup of ? = PSL(2; Z), into the projective space C P (k?3 2) , via theta functions. This holomorphic map is equivariant with respect to the action of PSL(2; Z=k) on both factors, and extends to the conformal compactiication X(k). Thus, X(k) can be exh...

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...

We give explicitly the surgeries governing the changes of quotient manifolds of real algebraic surfaces in CP3. We also make a number of general observations regarding quotients of complex surfaces under antiholomorphic involutions.

BACKGROUND Productive thymopoiesis is essential for a robust and healthy immune system. Thymus unfortunately is acutely sensitive to stress resulting in involution and decreased T cell production. Thymic involution is a complication of many clinical settings, including infection, malnutrition, starvation, and irradiation or immunosuppressive therapies. Systemic rises in glucocorticoids and infl...