772 research outputs found
Interpolating d-r.e. and REA degrees between r.e. degrees
We provide three new results about interpolating 2-r.e. (i.e. d-r.e.) or 2-REA (recursively enumerable in and above) degrees between given r.e. degrees: Proposition 1.13. If c < h are r.e., c is low and h is high, then there is an a < h which is REA in c but not r.e. Theorem 2.1. For all high r.e. degrees h < g there is a properly d-r.e. degree a such that h < a < g and a is r.e. in h. Theorem 3.1. There is an incomplete nonrecursive r.e. A such that every set REA in A and recursive in 0′ is of r.e. degree. The first proof is a variation on the construction of Soare and Stob (1982). The second combines highness with a modified version of the proof strategy of Cooper et al. (1989). The third theorem is a rather surprising result with a somewhat unusual proof strategy. Its proof is a 0‴ argument that at times moves left in the tree so that the accessible nodes are not linearly ordered at each stage. Thus the construction lacks a true path in the usual sense. Two substitute notions fill this role: The true nodes are the leftmost ones accessible infinitely often; the semitrue nodes are the leftmost ones such that there are infinitely many stages at which some extension is accessible. Another unusual feature of the construction is that it involves using distinct priority orderings to control the interactions of different parts of the construction
Interpolating d-r.e. and REA degrees between r.e. degrees
We provide three new results about interpolating 2-r.e. (i.e. d-r.e.) or 2-REA (recursively enumerable in and above) degrees between given r.e. degrees: Proposition 1.13. If c < h are r.e., c is low and h is high, then there is an a < h which is REA in c but not r.e. Theorem 2.1. For all high r.e. degrees h < g there is a properly d-r.e. degree a such that h < a < g and a is r.e. in h. Theorem 3.1. There is an incomplete nonrecursive r.e. A such that every set REA in A and recursive in 0′ is of r.e. degree. The first proof is a variation on the construction of Soare and Stob (1982). The second combines highness with a modified version of the proof strategy of Cooper et al. (1989). The third theorem is a rather surprising result with a somewhat unusual proof strategy. Its proof is a 0‴ argument that at times moves left in the tree so that the accessible nodes are not linearly ordered at each stage. Thus the construction lacks a true path in the usual sense. Two substitute notions fill this role: The true nodes are the leftmost ones accessible infinitely often; the semitrue nodes are the leftmost ones such that there are infinitely many stages at which some extension is accessible. Another unusual feature of the construction is that it involves using distinct priority orderings to control the interactions of different parts of the construction
Interpolating d-r.e. and REA degrees between r.e. degrees
We provide three new results about interpolating 2-r.e. (i.e. d-r.e.) or 2-REA (recursively enumerable in and above) degrees between given r.e. degrees: Proposition 1.13. If c < h are r.e., c is low and h is high, then there is an a < h which is REA in c but not r.e. Theorem 2.1. For all high r.e. degrees h < g there is a properly d-r.e. degree a such that h < a < g and a is r.e. in h. Theorem 3.1. There is an incomplete nonrecursive r.e. A such that every set REA in A and recursive in 0′ is of r.e. degree. The first proof is a variation on the construction of Soare and Stob (1982). The second combines highness with a modified version of the proof strategy of Cooper et al. (1989). The third theorem is a rather surprising result with a somewhat unusual proof strategy. Its proof is a 0‴ argument that at times moves left in the tree so that the accessible nodes are not linearly ordered at each stage. Thus the construction lacks a true path in the usual sense. Two substitute notions fill this role: The true nodes are the leftmost ones accessible infinitely often; the semitrue nodes are the leftmost ones such that there are infinitely many stages at which some extension is accessible. Another unusual feature of the construction is that it involves using distinct priority orderings to control the interactions of different parts of the construction
Interpolating d-r.e. and REA degrees between r.e. degrees
We provide three new results about interpolating 2-r.e. (i.e. d-r.e.) or 2-REA (recursively enumerable in and above) degrees between given r.e. degrees: Proposition 1.13. If c < h are r.e., c is low and h is high, then there is an a < h which is REA in c but not r.e. Theorem 2.1. For all high r.e. degrees h < g there is a properly d-r.e. degree a such that h < a < g and a is r.e. in h. Theorem 3.1. There is an incomplete nonrecursive r.e. A such that every set REA in A and recursive in 0′ is of r.e. degree. The first proof is a variation on the construction of Soare and Stob (1982). The second combines highness with a modified version of the proof strategy of Cooper et al. (1989). The third theorem is a rather surprising result with a somewhat unusual proof strategy. Its proof is a 0‴ argument that at times moves left in the tree so that the accessible nodes are not linearly ordered at each stage. Thus the construction lacks a true path in the usual sense. Two substitute notions fill this role: The true nodes are the leftmost ones accessible infinitely often; the semitrue nodes are the leftmost ones such that there are infinitely many stages at which some extension is accessible. Another unusual feature of the construction is that it involves using distinct priority orderings to control the interactions of different parts of the construction
On the jumps of degrees below an recursively enumerable degree
We consider the set of jumps below a Turing degree, given by JB(a) = {x(1) : x <= a}, with a focus on the problem: Which recursively enumerable (r.e.) degrees a are uniquely determined by JB(a)? Initially, this is motivated as a strategy to solve the rigidity problem for the partial order R of r.e. degrees. Namely, we show that if every high(2) r.e. degree a is determined by JB(a), then R cannot have a nontrivial automorphism. We then defeat the strategy-at least in the form presented-by constructing pairs a(0), a(1) of distinct r.e. degrees such that JB(a(0)) = JB(a(1)) within any possible jump class {x : x' = c}. We give some extensions of the construction and suggest ways to salvage the attack on rigidity
Charge Density Wave-Assisted Tunneling Between Hall Edge States
We study the intra-planar tunneling between quantum Hall samples separated by
a quasi one-dimensional barrier, induced through the interaction of edge
degrees of freedom with the charge density waves of a Hall crystal defined in a
parallel layer. A field theory formulation is set up in terms of bosonic
(2+1)-dimensional excitations coupled to (1+1)-dimensional fermions. Parity
symmetry is broken at the quantum level by the confinement of
soliton-antisoliton pairs near the tunneling region. The usual Peierls argument
allows to estimate the critical temperature , so that for mass
corrections due to longitudinal density fluctuations disappear from the edge
spectrum. We compute the gap dependence upon the random global phase of the
pinned charge density wave, as well as the effects of a voltage bias applied
across the tunneling junction.Comment: Additional references + 1 figure + more detailed discussions. To be
published in Phys. Rev.
Energy Spectra of Quantum Turbulence: Large-scale Simulation and Modeling
In simulation of quantum turbulence within the Gross-Pitaevskii
equation we demonstrate that the large scale motions have a classical
Kolmogorov-1941 energy spectrum E(k) ~ k^{-5/3}, followed by an energy
accumulation with E(k) ~ const at k about the reciprocal mean intervortex
distance. This behavior was predicted by the L'vov-Nazarenko-Rudenko bottleneck
model of gradual eddy-wave crossover [J. Low Temp. Phys. 153, 140-161 (2008)],
further developed in the paper.Comment: (re)submitted to PRB: 5.5 pages, 4 figure
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