The constant density, spherically symmetric, perfect fluid solution to Einstein’s equations was given in 1916 by Schwarzschild[1]. Despite being a stalwart of introductory General Relativity, the source of much of the knowledge we have about the Schwarzschild star interior solution is shrouded in obscurity. When he was writing about it in 1971, Buchdahl[2] decried the fact that no standard text...

There is a requirement to find accurate parameters to accomplish precise dimensional accuracy, excellent surface integrity and maximum MRR. This work studies the influence of various cutting parameters on output parameters like Cutting force, Surface roughness, Flatness, and Material removal rate while face milling. A detailed finite element model was developed to simulate the face milling proc...

Let R be a commutative Noetherian ring. We give criteria for flatness of R-modules in terms of associated primes and torsion-freeness of certain tensor products. This allows us to develop a criterion for regularity if R has characteristic p, or more generally if it has a locally contracting endomorphism. Dualizing, we give criteria for injectivity of R-modules in terms of coassociated primes an...