We prove an extension of a theorem of Barta then we make few geometric applications. We extend Cheng’s lower eigenvalue estimates of normal geodesic balls. We generalize Cheng-Li-Yau eigenvalue estimates of minimal submanifolds of the space forms. We prove an stability theorem for minimal hypersurfaces of the Euclidean space, giving a converse statement of a result of Schoen. Finally we prove a...

Literature Review If one uses the structure-processoutcome framework that is often used to measure quality of various parts of the health care system, the literature on staffing can be summarized by looking at the various structure-process-outcome variables. Most of the studies on nurse staffing in hospitals have focused on (1) patient outcomes such as pneumonia, urinary tract infections, failu...

ln previous work I have developed an equation explaining votes for president in the United States that seems to have remarkable explanatory paver. The purpose of this paper is to update this equation through the 1984 election and then use it to predict the 1988 election. The history of the equation is as follows. The original work was &one in 1976 and published in Fair (1978). In this work I te...

We introduce a concept of tree-graded metric space and we use it to show quasi-isometry invariance of certain classes of relatively hyperbolic groups, to obtain a characterization of relatively hyperbolic groups in terms of their asymptotic cones, to find geometric properties of Cayley graphs of relatively hyperbolic groups, and to construct the first example of finitely generated group with a ...