Title of dissertation: LENGTH SPECTRAL RIGIDITY OF NON-POSITIVELY CURVED SURFACES Jeffrey Frazier, Doctor of Philosophy, 2012 Dissertation directed by: Professor William Goldman Department of Mathematics Length spectral rigidity is the question of under what circumstances the geometry of a surface can be determined, up to isotopy, by knowing only the lengths of its closed geodesics. It is known...

The discriminatory power of ten factors has been explored in relation to the presence or absence of muscular rigidity in patients with Huntington's disease. The sex and neurological sign of an affected parent were the only two significant determinants of rigidity or choreoathetosis in offspring. It was shown, using the Mantel-Haenszel method of adjusting for confounding variables that the risk ...

MOTIVATION HIV-1 protease is a key drug target due to its role in the life cycle of the HIV-1 virus. Rigidity analysis using the software First is a computationally inexpensive method for inferring functional information from protein crystal structures. We evaluate the rigidity of 206 high-resolution (2 Å or better) X-ray crystal structures of HIV-1 protease and compare the effects of different...

We prove that bounded Beltrami fields are symmetric if a proportionality factor depends on two variables in the cylindrical coordinate and admits regular level set diffeomorphic to cylinder or torus.