First steps towards total reality of meromorphic functions

It was earlier conjectured by the second and the third authors that any rational curve $g:{\mathbb C}P^1\to {\mathbb C}P^n$ such that the inverse images of all its flattening points lie on the real line ${\mathbb R}P^1\subset {\mathbb C}P^1$ is real algebraic up to a linear fractional transformation of the image ${\mathbb C}P^n$. (By a flattening point $p$ on $g$ we mean a point at which the Frenet $n$-frame $(g',g'',...,g^{(n)})$ is degenerate.) Below we extend this conjecture to the case of meromorphic functions on real algebraic curves of higher genera and settle it for meromorphic functions of degrees $2,3$ and several other cases.Comment: 10 pages, 1 figur

An Analysis of Early Renal Transplant Protocol Biopsies - the High Incidence of Subclinical Tubulitis

To investigate the possibility that we have been underestimating the true incidence of acute rejection, we began to perform protocol biopsies after kidney transplantation. This analysis looks at the one-week biopsies. Between March 1 and October 1, 1999, 100 adult patients undergoing cadaveric kidney or kidney/pancreas transplantation, or living donor kidney transplantation, underwent 277 biopsies. We focused on the subset of biopsies in patients without delayed graft function (DGF) and with stable or improving renal function, who underwent a biopsy 8.2 ± 2.6 d (range 3-18 d) after transplantation (n = 28). Six (21%) patients with no DGF and with stable or Improving renal function had borderline histopathology, and 7 (25%) had acute tubulitis on the one-week biopsy. Of the 277 kidney biopsies, there was one (0.4%) serious hemorrhagic complication, in a patient receiving low molecular weight heparin; she ultimately recovered and has normal renal function. Her biopsy showed Banff 1B tubulitis. In patients with stable or improving renal allograft function early after transplantation, subclinical tubulitis may be present in a substantial number of patients. This suggests that the true incidence of rejection may be higher than is clinically appreciated

Majorana states in a p-wave superconducting ring

The spectrum of excitations of the chiral superconducting ring with internal and external radii, comparable with coherence length, trapping a unit flux is calculated. We find within the Bogoliubov-deGennes approach that there exists a pair of precisely zero energy states. They are not protected by topology, but are stable under certain deformations of the system. We discuss the ways to tune the system so that it grows into such a "Majorana disk". This condition has a character of a resonance phenomenon