Proper holomorphic mappings between symmetrized ellipsoids

We characterize the existence of proper holomorphic mappings in the special class of bounded $(1,2,...,n)$-balanced domains in $\mathbb{C}^n$, called the symmetrized ellipsoids. Using this result we conclude that there are no non-trivial proper holomorphic self-mappings in the class of symmetrized ellipsoids. We also describe the automorphism groupof these domains.Comment: 10 pages, some modification

Three-body non-additive forces between spin-polarized alkali atoms

Three-body non-additive forces in systems of three spin-polarized alkali atoms (Li, Na, K, Rb and Cs) are investigated using high-level ab initio calculations. The non-additive forces are found to be large, especially near the equilateral equilibrium geometries. For Li, they increase the three-atom potential well depth by a factor of 4 and reduce the equilibrium interatomic distance by 0.9 A. The non-additive forces originate principally from chemical bonding arising from sp mixing effects.Comment: 4 pages, 3 figures (in 5 files

Effect of oral calcium carbonate on aortic calcification in apolipoprotein E-deficient (apoE-/-) mice with chronic renal failure.

BACKGROUND: In chronic kidney disease (CKD) patients, the intake of calcium-based phosphate binders is associated with a marked progression of coronary artery and aortic calcification, in contrast to patients receiving calcium-free phosphate binders. The aim of this study was to reexamine the role of calcium carbonate in vascular calcification and to analyse its effect on aortic calcification-related gene expression in chronic renal failure (CRF). METHODS: Mice deficient in apolipoprotein E underwent either sham operation or subtotal nephrectomy to create CRF. They were then randomly assigned to one of the three following groups: a control non-CRF group and a CRF group fed on standard diet, and a CRF group fed on calcium carbonate enriched diet, for a period of 8 weeks. Aortic atherosclerotic plaque and calcification were evaluated using quantitative morphologic image processing. Aortic gene and protein expression was examined using immunohistochemistry and Q-PCR methods. RESULTS: Calcium carbonate supplementation was effective in decreasing serum phosphorus but was associated with a higher serum calcium concentration. Compared with standard diet, calcium carbonate enriched diet unexpectedly induced a significant decrease of both plaque (p<0.05) and non-plaque-associated calcification surface (p<0.05) in CRF mice. It also increased osteopontin (OPN) protein expression in atherosclerotic lesion areas of aortic root. There was also a numerical increase in OPN and osteoprotegerin gene expression in total thoracic aorta but the difference did not reach the level of significance. Finally, calcium carbonate did not change the severity of atherosclerotic lesions. CONCLUSION: In this experimental model of CRF, calcium carbonate supplementation did not accelerate but instead decreased vascular calcification. If our observation can be extrapolated to humans, it appears to question the contention that calcium carbonate supplementation, at least when given in moderate amounts, necessarily enhances vascular calcification. It is also compatible with the hypothesis of a preponderant role of phosphorus over that of calcium in promoting vascular calcification in CRF