Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups

Let $\Phi$ be a classical root system and $k$ be a field of sufficiently large characteristic. Let $G$ be the classical group over $k$ with the root system $\Phi$, $U$ be its maximal unipotent subgroup and $\mathfrak{u}$ be the Lie algebra of $U$. Let $D$ be an orthogonal subset of $\Phi$ and $\Omega$ be a coadjoint orbit of $U$ associated with $D$. We construct a polarization of $\mathfrak{u}$ at the canonical form on $\Omega$. We also find the dimension of $\Omega$ in terms of the Weyl group of $\Phi$. As a corollary, we determine all possible dimensions of irreducible complex represenations of the group $U$ for the case of finite field $k$.Comment: 11 page

Leptogenesis with Heavy Majorana Neutrinos Reexamined

The mass term for Majorana neutrinos explicitly violates lepton number. Several authors have used this fact to create a lepton asymmetry in the universe by considering CP violating effects in the one loop self-energy correction for the decaying heavy Majorana neutrino. We compare and comment on the different approaches used to calculate the lepton asymmetry including those using an effective Hamiltonian and resummed propagators. We also recalculate the asymmetry in the small mass difference limit.Comment: 16 pages, LaTex, 1 figure included. 2 footnotes and 1 reference adde

Protective effect of hypothermia on brain neurons in rats exposed to ionizing radiation

The protein-synthesizing system of hippocampal (CA1, CA3) and sensorimotor cortex neurons is damaged less and recovers much quicker in rats exposed to 8 Gy of gamma-radiation under hypoxia/hypercapnia (body temperature 16-18°C) than under usual conditions, as evidenced by microfluorimetry and electron microscopy. The radioprotective effect does not cover the membrane structures (endoplasmic reticulum and Golgi complex), and their restoration is not so prompt

Effect of ionizing radiation on the protein-synthesizing system of brain neurons of ground squirrels in different functional states

Using fluorescence and electron microscopy, it is shown that the physiological state of ground squirrels exposed to ionizing radiation at different stages of the torpor-awakeness (hypothermia-normothermia) cycle is the main factor responsible for changes in the protein-synthesizing system of neurons in the hippocampus (fields CA1 and CA3) and the sensomotor cortex. The neurons of animals irradiated in the state of awakeness are less radioresistant and recover more slowly than neurons of animals irradiated in torpor, with the difference being more distinct in neurons of the CA1 field. The effect of irradiation is weak in animals entering torpor and reaches a peak in awakening animals. It is proposed that the inhibition of protein synthesis in the latter case takes place at the elongation stage, with heavy polysomes formed in the cytoplasm of neurons