An algebro-geometric proof of Witten's conjecture

We present a new proof of Witten's conjecture. The proof is based on the analysis of the relationship between intersection indices on moduli spaces of complex curves and Hurwitz numbers enumerating ramified coverings of the 2-sphere.Comment: 12 pages, no figure

Star Formation and Tidal Encounters with the Low Surface Brightness Galaxy UGC 12695 and Companions

We present VLA H I observations of the low surface brightness galaxy UGC 12695 and its two companions, UGC 12687 and a newly discovered dwarf galaxy 2333+1234. UGC 12695 shows solid body rotation but has a very lopsided morphology of the H I disk, with the majority of the H I lying in the southern arm of the galaxy. The H I column density distribution of this very blue, LSB galaxy coincides in detail with its light distribution. Comparing the H I column density of UGC 12695 with the empirical (but not well understood) value of Sigma_c = 10E21 atoms/cm^2 found in, i.e., Skillman's 1986 paper shows the star formation to be a local affair, occurring only in those regions where the column density is above this star formation threshold. The low surface brightness nature of this galaxy could thus be attributed to an insufficient gas surface density, inhibiting star formation on a more global scale. Significantly, though, the Toomre criterion places a much lower critical density on the galaxy (+/-10E20 atoms/cm^2), which is shown by the galaxy's low SFR to not be applicable. Within a projected distance of 300kpc/30kms of UGC 12695 lie two companion galaxies - UGC 12687, a high surface brightness barred spiral galaxy, and 2333+1234, a dwarf galaxy discovered during this investigation. The close proximity of the three galaxies, combined with UGC 12695's extremely blue color and regions of localized starburst and UGC 12687's UV excess bring to mind mutually induced star formation through tidal activity.Comment: 14 pages, 8 figures (2 color), To be published in A.J., May 2000

Порівняльно-правовий аналіз інституту шлюбного договору за законодавством Німеччини та України

Казарян К. А. Порівняльно-правовий аналіз інституту шлюбного договору за законодавством Німеччини та України / К. А. Казарян // Правове життя сучасної України : матеріали Міжнар. наук. конф. проф.-викл. та аспірант. складу (м. Одеса, 16-17 травня 2013 р.) / відп. за вип. В. М. Дрьомін ; НУ "ОЮА". Півд. регіон. центр НАПрН України. - Одеса : Фенікс, 2013. - Т. 2. - С. 628-630

The combined use of imaging approaches to assess drug release from multicomponent solid dispersions

PURPOSE: Imaging methods were used as tools to provide an understanding of phenomena that occur during dissolution experiments, and ultimately to select the best ratio of two polymers in a matrix in terms of enhancement of the dissolution rate and prevention of crystallization during dissolution. METHODS: Magnetic resonance imaging, ATR-FTIR spectroscopic imaging and Raman mapping have been used to study the release mechanism of a poorly water soluble drug, aprepitant, from multicomponent amorphous solid dispersions. Solid dispersions were prepared based on the combination of two selected polymers - Soluplus, as a solubilizer, and PVP, as a dissolution enhancer. Formulations were prepared in a ratio of Soluplus:PVP 1:10, 1:5, 1:3, and 1:1, in order to obtain favorable properties of the polymer carrier. RESULTS: The crystallization of aprepitant during dissolution has occurred to a varying degree in the polymer ratios 1:10, 1:5, and 1:3, but the increasing presence of Soluplus in the formulation delayed the onset of crystallization. The Soluplus:PVP 1:1 solid dispersion proved to be the best matrix studied, combining the abilities of both polymers in a synergistic manner. CONCLUSIONS: Aprepitant dissolution rate has been significantly enhanced. This study highlights the benefits of combining imaging methods in order to understand the release process