9,916 research outputs found
Maximal almost disjoint families, determinacy, and forcing
We study the notion of -MAD families where is a
Borel ideal on . We show that if is an arbitrary
ideal, or is any finite or countably iterated Fubini product of
ideals, then there are no analytic infinite -MAD
families, and assuming Projective Determinacy there are no infinite projective
-MAD families; and under the full Axiom of Determinacy +
there are no infinite -mad families.
These results apply in particular when is the ideal of finite sets
, which corresponds to the classical notion of MAD families. The
proofs combine ideas from invariant descriptive set theory and forcing.Comment: 40 page
Relativistic Chiral Mean Field Model for Finite Nuclei
We present a relativistic chiral mean field (RCMF) model, which is a method
for the proper treatment of pion-exchange interaction in the nuclear many-body
problem. There the dominant term of the pionic correlation is expressed in
two-particle two-hole (2p-2h) states with particle-holes having pionic quantum
number, J^{pi}. The charge-and-parity-projected relativistic mean field
(CPPRMF) model developed so far treats surface properties of pionic correlation
in 2p-2h states with J^{pi} = 0^{-} (spherical ansatz). We extend the CPPRMF
model by taking 2p-2h states with higher spin quantum numbers, J^{pi} = 1^{+},
2^{-}, 3^{+}, ... to describe the full strength of the pionic correlation in
the intermediate range (r > 0.5 fm). We apply the RCMF model to the ^{4}He
nucleus as a pilot calculation for the study of medium and heavy nuclei. We
study the behavior of energy convergence with the pionic quantum number,
J^{pi}, and find convergence around J^{pi}_{max} = 6^{-}. We include further
the effect of the short-range repulsion in terms of the unitary correlation
operator method (UCOM) for the central part of the pion-exchange interaction.
The energy contribution of about 50% of the net two-body interaction comes from
the tensor part and 20% comes from the spin-spin central part of the
pion-exchange interaction.Comment: 22 pages, 12 figure
Failure criterion of glass fabric reinforced plastic laminates
Failure criteria are derived for several modes of failure (in unaxial tensile or compressive loading, or biaxial combined tensile-compressive loading) in the case of closely woven plain fabric, coarsely-woven plain fabric, or roving glass cloth reinforcements. The shear strength in the interaction formula is replaced by an equation dealing with tensile or compressive strength in the direction making a 45 degree angle with one of the anisotropic axes, for the uniaxial failure criteria. The interaction formula is useful as the failure criterion in combined tension-compression biaxial failure for the case of closely woven plain fabric laminates, but poor agreement is obtained in the case of coarsely woven fabric laminates
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