The reaper (rpr) and head involution defective (hid) genes mediate programmed cell death (PCD) during Drosophila development. We show that expression of either rpr or hid under control of a rhodopsin promoter induces rapid cell death of adult photoreceptor cells. Ultrastructural analysis revealed that the dying photoreceptor cells share morphological features with other cells undergoing PCD. Th...

In this paper we present a decomposition theorem for hermitian forms over fields of characteristic 2 refining the usual Witt decomposition in this case. We apply this decomposition to algebras with involution over fields of characteristic 2 to give a complete description of the effect of passing to a generic splitting field of the algebra on the isotropy of the involution.

We give a complete description of subdirectly irreducible rings with involution satisfying x = x for some positive integer n. We also discuss ways to apply this result for constructing lattices of varieties of rings with involution obeying an identity of the given type. MSC 2000: 16W10, 08B26, 08B15

We study a possibly integrable model of abelian gauge fields on a two-dimensional surface M , with volume form μ . It has the same phase space as ideal hydrodynamics, a coadjoint orbit of the volume-preserving diffeomorphism group of M . Gauge field Poisson brackets differ from the Heisenberg algebra, but are reminiscent of Yang-Mills theory on a null surface. Enstrophy invariants are Casimirs ...

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

In this note we give examples of division rings which posses an anti-automorphism but no involution. The motivation for such examples comes from geometry. If D is a division ring and V a finite-dimensional right D-vector space of dimension ≥ 3, then the projective geometry P(V ) has a duality (resp. polarity) if and only if D has an anti-automorphism (resp. involution) [2, p. 97, p. 111]. Thus,...