Abstract Let ( M , g ) denote a cosmological spacetime describing the evolution of universe which is isotropic and homogeneous on large scales, but highly inhomogeneous smaller scales. We consider two past lightcones, first, $${{\mathcal {C}}_{L}^{-}}(p, g)$$ CL...

For quasihomogeneous isolated hypersurface singularities, the logarithmic comparison theorem has been characterized explicitly by Holland and Mond. In the nonquasihomogeneous case, we give a necessary condition for the logarithmic comparison theorem in terms of the Gauss–Manin system of the singularity. It shows in particular that the logarithmic comparison theorem can hold for a nonquasihomoge...

in the present paper, the deformation zone of the ecae (equal channel angular extrusion) process was investigated using the upper bound theorem. for this purpose, the shape of the streamlines in the deformation zone was assumed to be cubic bezier curves. then, the force required for the ecae process was optimized with regard to the parameters defining the shape of streamlines by the upper bound...