Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy

Pairs of $n\times n$ matrices whose commutator differ from the identity by a matrix of rank $r$ are used to construct bispectral differential operators with $r\times r$ matrix coefficients satisfying the Lax equations of the Matrix KP hierarchy. Moreover, the bispectral involution on these operators has dynamical significance for the spin Calogero particles system whose phase space such pairs represent. In the case $r=1$, this reproduces well-known results of Wilson and others from the 1990's relating (spinless) Calogero-Moser systems to the bispectrality of (scalar) differential operators. This new class of pairs $(L, \Lambda)$ of bispectral matrix differential operators is different than those previously studied in that $L$ acts from the left, but $\Lambda$ from the right on a common $r\times r$ eigenmatrix.Comment: 16 page

Effects of proteins on the permeability of monolayers of cultured bovine arterial endothelium.

1. Monolayers of arterial endothelium on porous membranes were exposed to a pressure of 15 cmH2O at 37 degrees C, or of 30 cmH2O at 0 degree C. At constant pressure, the rate of liquid flow per unit area (Jv/A) through each monolayer decreased with time, in the way previously described for cultured endothelium. This phenomenon has been called sealing. After Jv/A stabilized, the pressure was reduced and the hydraulic permeability (Lp) of the endothelium was calculated from the relationship between Jv/A and pressure. Endothelium was seen to be damaged after some experiments at 37 degrees C, but appeared undamaged after experiments at 0 degree C. 2. Bovine serum albumin (BSA) did not influence the Lp of cultured endothelium. At 37 degrees C, the mean (+/- S.E.M.) endothelial Lp was 47.2 +/- 7.3 x 10(-7) cm s-1 cmH2O-1 (n = 10) in the presence of BSA (5 g (100 ml)-1). This is not significantly different from the mean (+/- S.E.M.) Lp of 53.4 +/- 9.0 x 10(-7) cm s-1 cmH2O-1 (n = 9) in the absence of added protein (P greater than 0.10). At 0 degree C also, there was no significant difference between mean Lps in the presence of BSA (0.1 g (100 ml)-1) and in the absence of added protein. 3. Solutions of BSA (5 g (100 ml)-1 or of the neutral polymer Ficoll 70 (4 g (100 ml)-1) did not exert any effective osmotic pressure across endothelium at 37 or 0 degrees C, respectively. 4. BSA (0.1 g (100 ml)-1) did not enable solutions of Ficoll 70 (4 g (100 ml)-1) to exert an effective osmotic pressure across endothelium at 0 degree C. 5. The mean Lp of endothelium at 0 degree C was significantly lower in the presence of cationized ferritin (CF; 0.1 g (100 ml)-1) than in the absence of added protein (P less than 0.001). Native ferritin (NF; 0.1 g (100 ml)-1) had no effect on Lp. 6. In the presence of CF (0.1 g (100 ml)-1), solutions of Ficoll 70 (4 g (100 ml)-1) exerted a mean effective osmotic pressure of 27.7 cmH2O (n = 5) across endothelium at 0 degree C. The mean effective osmotic pressure exerted across endothelium by solutions of Ficoll 70 (4 g (100 ml)-1) plus NF (0.1 g (100 ml)-1) was 1.2 cmH2O (n = 4)