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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
Germanification, cultural mission, holocaust: theatre in Łódź during World War II
No abstract available
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