Hohenberg-Kohn Theorems in Electrostatic and Uniform Magnetostatic Fields

The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momentum. The proofs differ from the original HK proof, and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function.Comment: 16 pages; 1 Tabl

The ratio of VEGF/PEDF expression in bone marrow mesenchymal stem cells regulates neovascularization

Angiogenesis, or neovascularization, is a finely balanced process controlled by pro- and anti-angiogenic factors. Vascular endothelial growth factor (VEGF) is a major pro-angiogenic factor, whereas pigment epithelial-derived factor (PEDF) is the most potent natural angiogenesis inhibitor. In this study, the regulatory role of bone marrow stromal cells (BMSCs) during angiogenesis was assessed by the endothelial differentiation potential, VEGF/PEDF production and responses to pro-angiogenic and hypoxic conditions. The in vivo regulation of blood vessel formation by BMSCs was also explored in a SCID mouse model. Results showed that PEDF was expressed more prominently in BMSCs compared to VEGF. This contrasted with human umbilical vein endothelial cells (HUVECs) where the expression of VEGF was higher than that of PEDF. The ratio of VEGF/PEDF gene expression in BMSCs increased when VEGF concentration reached 40 ng/ml in the culture medium, but decreased at 80 ng/ml. Under CoCl2- induced hypoxic conditions, the VEGF/PEDF ratio of BMSCs increased significantly in both normal and angiogenic culture media. There was no expression of endothelial cell markers in BMSCs cultured in either pro-angiogenic or hypoxia culture conditions when compared with HUVECs. The in vivo study showed that VEGF/PEDF expression closely correlated with the degree of neovascularization, and that hypoxia significantly induced pro-angiogenic activity in BMSCs. These results indicate that, rather than being progenitors of endothelial cells, BMSCs play an important role in regulating the neovascularization process, and that the ratio of VEGF and PEDF may, in effect, be an indicator of the pro- or antiangiogenic activities of BMSCs

Transportation in McMinnville 100 Years Ago

Our project presents a historical view of transportation and its development in McMinnville in the 1910s, especially in 1912. McMinnville was incorporated as a town in 1876 and became a city in 1882. At the time, people still frequently rode horses (including stagecoaches), and the Yamhill River provided an early artery for pioneer travel and commerce. Then rails expanded in Oregon in the late 1800s and became a popular mode of transportation in the early 20th century. By the 1910s, horses, steamboats, rails, and cars were four major modes of transportation in McMinnville