14,132 research outputs found
Fixed-Point Problems in Discrete Tomography: Case of Square Windows
A kind of fixed-point problem in the area of discrete tomography is proposed
and investigated. Our chief concern in this paper is the case of square windows
in the plane. Dealing with the arrays which are bounded, of polynomial growth,
and finite-ring-valued, one comes across several interesting phenomena of
combinatorial and arithmetic nature.Comment: 30 pages, 20 figure
Multiplicity of ground states in quantum field models: applications of asymptotic fields
The ground states of an abstract model in quantum field theory are
investigated. By means of the asymptotic field theory, we give a necessary and
sufficient condition for that the expectation value of the number operator of
ground states is finite, from which we obtain a wide-usable method to estimate
an upper bound of the multiplicity of ground states. Ground states of massless
GSB models and the Pauli-Fierz model with spin 1/2 are investigated as
examples
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