Theorem 1.1. There exists a holomorphic map σ of C of the form ξ → λξ + O(2), η → λη + O(2), with λ not a root of unity and |λ| = 1, such that σ is reversible by an antiholomorphic involution and by a formal holomorphic involution, and is however not reversible by any C-smooth involution of which the linear part is holomorphic. In particular, the σ is not reversible by any holomorphic involution.

The thymus is the organ devoted to T-cell production. The thymus undergoes multiple rounds of atrophy and redevelopment before degenerating with age in a process known as involution. This process is poorly understood, despite the influence the phenomenon has on peripheral T-cell numbers. Here we have investigated the FVB/N mouse strain, which displays premature thymic involution. We find multip...

The main goal of this paper is to propose an approach inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO involution-reflection. Our based reduction problem matrix form and solution Sturm-Liouville operator by developing method mappings. obtained contains weight, which causes qualitative difficulties in study ...

We show that over a field of characteristic 2 a central simple algebra with orthogonal involution that decomposes into a product of quaternion algebras with involution is either anisotropic or metabolic. We use this to define an invariant of such orthogonal involutions in characteristic 2 that completely determines the isotropy behaviour of the involution. We also give an example of a non-total...

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a carefull analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate th...

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a careful analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate the...

The question of the existence of an analogue, in the framework of central simple algebras with involution, of the notion of Pfister form is raised. In particular, algebras with orthogonal involution which split as a tensor product of quaternion algebras with involution are studied. It is proven that, up to degree 16, over any extension over which the algebra splits, the involution is adjoint to...

in this paper, we define the notions of ultra and involution ideals in $bck$-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative $bck$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $bck$-semilattice, the not...