We show that, possibly after a compactification of spacetime, constant functions are local maximizers the Tomas-Stein adjoint Fourier restriction inequality for cone and paraboloid in every dimension, sphere dimension up to 60. For we work from PDE framework, which enables use Penrose Lens transformations, map conjectured optimal into constants.

We consider the construction of a polyhedral Delaunay partition as limit sequence power diagrams (radical partitions). The dual Voronoi diagram is obtained weighted partitions. problem reduced to two convex polyhedra, inscribed and superscribed around circular paraboloid, pairs general polyhedra. primal polyhedra should converge polyhedron converges polyhedron. are interested in case when verti...

Heat transport over an upper paraboloid horizontal surface of revolution (UPHSR) has attracted much interest the researchers and aero dynamists. The flow fluid around pointed rocket, bullets, bonnet, fighting aircrafts exhibits flows in which engineering parameters like shear stresses Nusselt number significantly contributed. Therefore, study comprising heat generation/absorption, Lorentz force...

primary man in trying to find food went everywhere. but by forming ranching arranged a chain of places and became emigrant. by happening industrial revolution, human life was centralized on one place.  places that base on its advantages make different biologic and behavioral types. forming cities in seaboard, river shore, boundary of mountains and champaign cause to make different cultures that...

We demonstrate analytically and experimentally that a circular abruptly autofocusing (AAF) Airy beam can be generated by Fourier-transforming an appropriately apodized Bessel beam whose radial oscillations are chirped by a cubic phase term. Depending on the relation between the chirp rate and the focal distance of the Fourier-transforming lens, it is possible to generate AAF beams with one or t...