549 research outputs found
New Lower Bounds for van der Waerden Numbers Using Distributed Computing
This paper provides new lower bounds for van der Waerden numbers. The number
is defined to be the smallest integer for which any -coloring
of the integers admits monochromatic arithmetic progression of
length ; its existence is implied by van der Waerden's Theorem. We exhibit
-colorings of that do not contain monochromatic arithmetic
progressions of length to prove that . These colorings are
constructed using existing techniques. Rabung's method, given a prime and a
primitive root , applies a color given by the discrete logarithm base
mod and concatenates copies. We also used Herwig et al's
Cyclic Zipper Method, which doubles or quadruples the length of a coloring,
with the faster check of Rabung and Lotts. We were able to check larger primes
than previous results, employing around 2 teraflops of computing power for 12
months through distributed computing by over 500 volunteers. This allowed us to
check all primes through 950 million, compared to 10 million by Rabung and
Lotts. Our lower bounds appear to grow roughly exponentially in . Given that
these constructions produce tight lower bounds for known van der Waerden
numbers, this data suggests that exact van der Waerden Numbers grow
exponentially in with ratio asymptotically, which is a new conjecture,
according to Graham.Comment: 8 pages, 1 figure. This version reflects new results and reader
comment
How to Probe for Dynamical Structure in the Collapse of Entangled States Using Nuclear Magnetic Resonance
The spin state of two magnetically inequivalent protons in contiguous atoms
of a molecule becomes entangeled by the indirect spin-spin interaction
(j-coupling). The degree of entanglement oscillates at the beat frequency
resulting from the splitting of a degeneracy. This beating is manifest in NMR
spectroscopy as an envelope of the transverse magnetization and should be
visible in the free induction decay signal. The period (approximately 1 sec) is
long enough for interference between the linear dynamics and collapse of the
wave-function induced by a Stern-Gerlach inhomogeneity to significantly alter
the shape of that envelope. Various dynamical collapse theories can be
distinguished by their observably different predictions with respect to this
alteration. Adverse effects of detuning due to the Stern-Gerlach inhomogeneity
can be reduced to an acceptable level by having a sufficiently thin sample or a
strong rf field.Comment: 6 pages, 4 figures, PDF, submitted to PR
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Peter Pan: A journey of imagination
This project explored ways in which a group of artists can encourage an audience to actively engage their imagination while producing a classical play based on a classic story. This paper discusses the techniques and approaches used to achieve conceptual goals as a director. The directors first goal was to accurately portray the main character. Secondly, he set out to create a Neverland that would allow the entire audience to engage their imagination and capture the joy of their youth
The Subtleties of Social Exclusion: Race, Social Class, and the Exclusion of Blacks in a Racially Mixed Neighborhood
We use interviews, content analysis, and surveys to describe how a neighborhood association in a racially mixed neighborhood in Portland, Oregon (USA) subtly excludes many blacks from being full members of the neighborhood. In contrast to explicit cases of social exclusion, this neighborhood association excludes blacks without ever referring to race. They instead justify their actions—e.g., helping close down a black social club and discouraging more affordable housing—based on such nonracial goals as increasing homeownership, minimizing crime, and maximizing “economic diversity.” We argue that without the inclusion of black residents and their neighborhood organizations (e.g., churches) in the decision-making process, mixed-race neighborhoods will continue to lose their diversity
Effect of Stator and Rotor Aspect Ratio on Transonic-Turbine Performance
The effect of stator and rotor aspect ratio on transonic-turbine performance was experimentally investigated. The stator aspect ratios covered were 1.6. 0.8, and 0.4, while the rotor aspect ratios investigated were 1.46 and 0.73. It was found that the observed variation in turbine design-point efficiency was negligible. Thus, within the range of aspect ratio investigated, these results verify for turbines operating in the transonic flow range the finding of a reference report, which showed analytically that, if blade shape and solidity are held constant, the aspect ratio may be varied over a wide range without appreciable change in turbine efficiency
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