5,159 research outputs found
A bounded jump for the bounded Turing degrees
We define the bounded jump of A by A^b = {x | Exists i <= x [phi_i (x)
converges and Phi_x^[A|phi_i(x)](x) converges} and let A^[nb] denote the n-th
bounded jump. We demonstrate several properties of the bounded jump, including
that it is strictly increasing and order preserving on the bounded Turing (bT)
degrees (also known as the weak truth-table degrees). We show that the bounded
jump is related to the Ershov hierarchy. Indeed, for n > 1 we have X <=_[bT]
0^[nb] iff X is omega^n-c.e. iff X <=_1 0^[nb], extending the classical result
that X <=_[bT] 0' iff X is omega-c.e. Finally, we prove that the analogue of
Shoenfield inversion holds for the bounded jump on the bounded Turing degrees.
That is, for every X such that 0^b <=_[bT] X <=_[bT] 0^[2b], there is a Y
<=_[bT] 0^b such that Y^b =_[bT] X.Comment: 22 pages. Minor changes for publicatio
Relatively computably enumerable reals
A real X is defined to be relatively c.e. if there is a real Y such that X is
c.e.(Y) and Y does not compute X. A real X is relatively simple and above if
there is a real Y <_T X such that X is c.e.(Y) and there is no infinite subset
Z of the complement of X such that Z is c.e.(Y). We prove that every nonempty
Pi^0_1 class contains a member which is not relatively c.e. and that every
1-generic real is relatively simple and above.Comment: 5 pages. Significant changes from earlier versio
Qualitative Assessment of Risk for Monkeypox Associated with Domestic Trade in Certain Animal Species, United States
TOC summary: The probability of further human infection is low and the risk is further mitigated by rodent import restrictions
Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods
We report large-scale computer simulations of the hard-disk system at high
densities in the region of the melting transition. Our simulations reproduce
the equation of state, previously obtained using the event-chain Monte Carlo
algorithm, with a massively parallel implementation of the local Monte Carlo
method and with event-driven molecular dynamics. We analyze the relative
performance of these simulation methods to sample configuration space and
approach equilibrium. Our results confirm the first-order nature of the melting
phase transition in hard disks. Phase coexistence is visualized for individual
configurations via the orientational order parameter field. The analysis of
positional order confirms the existence of the hexatic phase.Comment: 9 pages, 8 figures, 2 table
Bariatric surgery and its impact on cardiovascular disease and mortality : A systematic review and meta-analysis
Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.Peer reviewedPostprin
Stability of exact solutions of the defocusing nonlinear Schrodinger equation with periodic potential in two dimensions
The cubic nonlinear Schrodinger equation with repulsive nonlinearity and
elliptic function potential in two-dimensions models a repulsive dilute gas
Bose--Einstein condensate in a lattice potential. A family of exact stationary
solutions is presented and its stability is examined using analytical and
numerical methods. All stable trivial-phase solutions are off-set from the zero
level. Our results imply that a large number of condensed atoms is sufficient
to form a stable, periodic condensate.Comment: 12 pages, Latex, High resolution version available at
http://www.amath.washington.edu/~kutz/research.htm
- …