Geometric Quantization on a Coset Space G/H

Geometric quantization on a coset space $G/H$ is considered, intending to recover Mackey's inequivalent quantizations. It is found that the inequivalent quantizations can be obtained by adopting the symplectic 2-form which leads to Wong's equation. The irreducible representations of $H$ which label the inequivalent quantizations arise from Weil's theorem, which ensures a Hermitian bundle over $G/H$ to exist.Comment: 12 pages, LateX2

Constraint on the ejecta mass for a black hole-neutron star merger event candidate S190814bv

We derive the upper limit to the ejecta mass of S190814bv, a black hole-neutron star merger candidate, through the radiative transfer simulations for kilonovae with the realistic ejecta density profile as well as the detailed opacity and heating rate models. The limits to the ejecta mass strongly depend on the viewing angle. For the face-on observations ($\le45^\circ$), the total ejecta mass should be smaller than $0.1\,M_\odot$ for the average distance of S190814bv ($D=267$ Mpc), while larger mass is allowed for the edge-on observations. We also derive the conservative upper limits of the dynamical ejecta mass to be $0.02\,M_\odot$, $0.03\,M_\odot$, and $0.05\,M_\odot$ for the viewing angle $\le 20^\circ$, $\le 50^\circ$, and for $\le 90^\circ$, respectively. We show that the {\it iz}-band observation deeper than $22$ mag within 2 d after the GW trigger is crucial to detect the kilonova with the total ejecta mass of $0.06\,M_\odot$ at the distance of $D=300$ Mpc. We also show that a strong constraint on the NS mass-radius relation can be obtained if the future observations put the upper limit of $0.03\,M_\odot$ to the dynamical ejecta mass for a BH-NS event with the chirp mass smaller than $\lesssim 3\,M_\odot$ and effective spin larger than $\gtrsim 0.5$.Comment: 16 pages, 15 figure

Complement regulatory proteins in glomerular diseases

Complement regulatory proteins in glomerular diseases. Complement activation plays a critical role in the pathogenesis of many forms of glomerulonephritis. Complement activation leads to tissue injury through various mechanisms including the generation of chemotactic factors and activation of the resident glomerular cells following C5b-9 insertion. Recent advances have disclosed the mechanisms of regulation of complement activation by discovery of a number of complement regulatory proteins. Decay accelerating factor (DAF), membrane cofactor protein (MCP), and complement receptor type 1 (CR1) act by inactivating C3/C5 convertase. They belong to the gene superfamily known as the regulators of complement activation (RCA), and share a common structural motif called a short consensus repeat (SCR). In contrast, CD59 works by inhibiting formation of C5b-9. The glomerulus is particularly well endowed with these membrane-bound complement regulatory proteins. DAF, MCP, and CD59 are ubiquitously expressed by all three resident glomerular cells, while CR1 is localized exclusively in podocytes. Expression of complement regulatory proteins can be changed by many factors including complement attack itself, and their expression levels are affected in various glomerular disorders. Studies utilizing cultured glomerular cells and animal models of glomerular diseases suggest important protective roles of complement regulatory proteins against immune-mediated renal injury. Recent progress in molecular biological techniques has made new therapeutic strategy feasible. Systemic administration of soluble recombinant complement regulatory proteins and local overexpression of complement regulatory proteins are promising therapeutic approaches