Combinatorics of BB-orbits and Bruhat--Chevalley order on involutions

Let $B$ be the group of invertible upper-triangular complex $n\times n$ matrices, $\mathfrak{u}$ the space of upper-triangular complex matrices with zeroes on the diagonal and $\mathfrak{u}^*$ its dual space. The group $B$ acts on $\mathfrak{u}^*$ by $(g.f)(x)=f(gxg^{-1})$, $g\in B$, $f\in\mathfrak{u}^*$, $x\in\mathfrak{u}$. To each involution $\sigma$ in $S_n$, the symmetric group on $n$ letters, one can assign the $B$-orbit $\Omega_{\sigma}\in\mathfrak{u}^*$. We present a combinatorial description of the partial order on the set of involutions induced by the orbit closures. The answer is given in terms of rook placements and is dual to A. Melnikov's results on $B$-orbits on $\mathfrak{u}$. Using results of F. Incitti, we also prove that this partial order coincides with the restriction of the Bruhat--Chevalley order to the set of involutions.Comment: 27 page

Cosmological models with interacting components and mass-varying neutrinos

A model for a homogeneous and isotropic spatially flat Universe, composed of baryons, radiation, neutrinos, dark matter and dark energy is analyzed. We infer that dark energy (considered to behave as a scalar field) interacts with dark matter (either by the Wetterich model, or by the Anderson and Carroll model) and with neutrinos by a model proposed by Brookfield et al.. The latter is understood to have a mass-varying behavior. We show that for a very-softly varying field, both interacting models for dark matter give the same results. The models reproduce the expected red-shift performances of the present behavior of the Universe.Comment: 8 pages, 5 figures, to be published in Gravitation and Cosmolog

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

Structure and State of Water in Branched N-Vinylpyrrolidone Copolymers as Carriers of a Hydrophilic Biologically Active Compound

Hydrated copolymers of N-vinylpyrrolidone (VP) with triethylene glycol dimethacrylate as a promising platform for biologically active compounds (BAC) were investigated by different physical chemical methods (dynamic light scattering, infrared spectroscopy, thermal gravimetric analysis, and differential scanning calorimetry) and the quantum chemical modeling of water coordination by the copolymers in a solution. According to the quantum chemical simulation, one to two water molecules can coordinate on one O-atom of the lactam ring of VP units in the copolymer. Besides the usual terminal coordination, the water molecule can form bridges to bind two adjacent C=O groups of the lactam rings of VP units. In addition to the first hydration shell, the formation of a second one is also possible due to the chain addition of water molecules, and its structure depends on a mutual orientation of C=O groups. We showed that N,N-dimethylbiguanidine hydrochloride (metformin) as a frontline drug for the treatment of type 2 diabetes mellitus can be associated in aqueous solutions with free and hydrated C=O groups of the lactam rings of VP units in studied copolymers. Based on the characteristics of the H-bonds, we believe that the level of the copolymer hydration does not affect the behavior and biological activity of this drug, but the binding of metformin with the amphiphilic copolymer will delight in the penetration of a hydrophilic drug across a cell membrane to increase its bioavailability