Discontinuous information in the worst case and randomized settings

We believe that discontinuous linear information is never more powerful than continuous linear information for approximating continuous operators. We prove such a result in the worst case setting. In the randomized setting we consider compact linear operators defined between Hilbert spaces. In this case, the use of discontinuous linear information in the randomized setting cannot be much more powerful than continuous linear information in the worst case setting. These results can be applied when function evaluations are used even if function values are defined only almost everywhere

Magnetic relaxation in metallic films: Single and multilayer structures

The intrinsic magnetic relaxations in metallic films will be discussed. It will be shown that the intrinsic damping mechanism in metals is caused by incoherent scattering of itinerant electron-hole pair excitations by phonons and magnons. Berger [L. Berger, Phys. Rev. B 54, 9353 (1996)] showed that the interaction between spin waves and itinerant electrons in multilayers can lead to interface Gilbert damping. Ferromagnetic resonance (FMR) studies were carried out using magnetic single and double layer films. The FMR linewidth of the Fe films in the double layer structures was found to always be larger than the FMR linewidth measured for the single Fe films having the same thickness. The increase in the FMR linewidth scaled inversely with the film thickness, and was found to be linearly dependent on the microwave frequency. These results are in agreement with Berger's predictions. (C) 2002 American Institute of Physics

The Relativity of Existence

Despite the success of modern physics in formulating mathematical theories that can predict the outcome of experiments, we have made remarkably little progress towards answering the most fundamental question of: why is there a universe at all, as opposed to nothingness? In this paper, it is shown that this seemingly mind-boggling question has a simple logical answer if we accept that existence in the universe is nothing more than mathematical existence relative to the axioms of our universe. This premise is not baseless; it is shown here that there are indeed several independent strong logical arguments for why we should believe that mathematical existence is the only kind of existence. Moreover, it is shown that, under this premise, the answers to many other puzzling questions about our universe come almost immediately. Among these questions are: why is the universe apparently fine-tuned to be able to support life? Why are the laws of physics so elegant? Why do we have three dimensions of space and one of time, with approximate locality and causality at macroscopic scales? How can the universe be non-local and non-causal at the quantum scale? How can the laws of quantum mechanics rely on true randomness