1,235 research outputs found
Harmonic analysis and the Riemann-Roch theorem
This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and
arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from
these papers and two-dimensional adelic theory we obtain the Riemann-Roch
formula on a projective smooth algebraic surface over a finite field.Comment: 7 pages; to appear in Doklady Mathematic
Harmonic analysis on local fields and adelic spaces I
We develop a harmonic analysis on objects of some category of
infinite-dimensional filtered vector spaces over a finite field. It includes
two-dimensional local fields and adelic spaces of algebraic surfaces defined
over a finite field. The main result is the theory of the Fourier transform on
these objects and two-dimensional Poisson formulas.Comment: 69 pages; corrected typos and inserted some changes into the last
sectio
Interpretable collective intelligence of non-rational human agents
We outline how to create a mechanism that provides an optimal way to elicit,
from an arbitrary group of experts, the probability of the truth of an
arbitrary logical proposition together with collective information that has an
explicit form and interprets this probability. Namely, we provide strong
arguments for the possibility of the development of a self-resolving prediction
market with play money that incentivizes direct information exchange between
experts. Such a system could, in particular, motivate experts from all over the
world to collectively solve scientific or medical problems in a very efficient
manner. In our main considerations about real experts, they are not assumed to
be Bayesian and their behavior is described by utilities that satisfy the von
Neumann--Morgenstern axioms only locally.Comment: 41 pages, 4 figures, 3 table
Quantum Oscillations of the Critical Current of Asymmetric Aluminum Loops in Magnetic Field
The periodical dependencies in magnetic field of the asymmetry of the
current-voltage curves of asymmetric aluminum loop are investigated
experimentally at different temperatures below the transition into the
superconducting state T < Tc. The obtained periodical dependencies of the
critical current on magnetic field allow to explain the quantum oscillations of
the dc voltage as consequence of the rectification of the external ac current
and to calculate the persistent current at different values of magnetic flux
inside the loop and temperatures.Comment: 2 pages, 2 figures, will be published in the Proceedings of the 24th
International Conference on Low Temperature Physic
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