2,127 research outputs found
Takeuti's Well-Ordering Proof: Finitistically Fine?
If it could be shown that one of Gentzen's consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert's program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen's second proof can be finitistically justified. In particular, the focus is on Takeuti's purportedly finitistically acceptable proof of the well-ordering of ordinal notations in Cantor normal form.
The paper begins with a historically informed discussion of finitism and its limits, before introducing Gentzen and Takeuti's respective proofs. The rest of the paper is dedicated to investigating the finitistic acceptability of Takeuti's proof, including a small but important fix to that proof. That discussion strongly suggests that there is a philosophically interesting finitist standpoint that Takeuti's proof, and therefore Gentzen's proof, conforms to
Autocatalytic plume pinch-off
A localized source of buoyancy flux in a non-reactive fluid medium creates a
plume. The flux can be provided by either heat, a compositional difference
between the fluid comprising the plume and its surroundings, or a combination
of both. For autocatalytic plumes produced by the iodate-arsenous acid
reaction, however, buoyancy is produced along the entire reacting interface
between the plume and its surroundings. Buoyancy production at the moving
interface drives fluid motion, which in turn generates flow that advects the
reaction front. As a consequence of this interplay between fluid flow and
chemical reaction, autocatalytic plumes exhibit a rich dynamics during their
ascent through the reactant medium. One of the more interesting dynamical
features is the production of an accelerating vortical plume head that in
certain cases pinches-off and detaches from the upwelling conduit. After
pinch-off, a new plume head forms in the conduit below, and this can lead to
multiple generations of plume heads for a single plume initiation. We
investigated the pinch-off process using both experimentation and simulation.
Experiments were performed using various concentrations of glycerol, in which
it was found that repeated pinch-off occurs exclusively in a specific
concentration range. Autocatalytic plume simulations revealed that pinch-off is
triggered by the appearance of accelerating flow in the plume conduit.Comment: 10 figures. Accepted for publication in Phys Rev E. See also
http://www.physics.utoronto.ca/nonlinear/papers_chemwave.htm
Takeuti's Well-Ordering Proof: Finitistically Fine?
If it could be shown that one of Gentzen's consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert's program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen's second proof can be finitistically justified. In particular, the focus is on Takeuti's purportedly finitistically acceptable proof of the well-ordering of ordinal notations in Cantor normal form.
The paper begins with a historically informed discussion of finitism and its limits, before introducing Gentzen and Takeuti's respective proofs. The rest of the paper is dedicated to investigating the finitistic acceptability of Takeuti's proof, including a small but important fix to that proof. That discussion strongly suggests that there is a philosophically interesting finitist standpoint that Takeuti's proof, and therefore Gentzen's proof, conforms to
Quaternion-Octonion SU(3) Flavor Symmetry
Starting with the quaternionic formulation of isospin SU(2) group, we have
derived the relations for different components of isospin with quark states.
Extending this formalism to the case of SU(3) group we have considered the
theory of octonion variables. Accordingly, the octonion splitting of SU(3)
group have been reconsidered and various commutation relations for SU(3) group
and its shift operators are also derived and verified for different iso-spin
multiplets i.e. I, U and V- spins.
Keywords: SU(3), Quaternions, Octonions and Gell Mann matrices
PACS NO: 11.30.Hv: Flavor symmetries; 12.10-Dm: Unified field theories and
models of strong and electroweak interaction
The falling chain of Hopkins, Tait, Steele and Cayley
A uniform, flexible and frictionless chain falling link by link from a heap
by the edge of a table falls with an acceleration if the motion is
nonconservative, but if the motion is conservative, being the
acceleration due to gravity. Unable to construct such a falling chain, we use
instead higher-dimensional versions of it. A home camcorder is used to measure
the fall of a three-dimensional version called an -slider. After
frictional effects are corrected for, its vertical falling acceleration is
found to be . This result agrees with the theoretical
value of for an ideal energy-conserving -slider.Comment: 17 pages, 5 figure
The t W- Mode of Single Top Production
The t W- mode of single top production is proposed as an important means to
study the weak interactions of the top quark. While the rate of this mode is
most likely too small to be observed at Run II of the Fermilab Tevatron, it is
expected to be considerably larger at the CERN LHC. In this article the
inclusive t W- rate is computed, including O(1 / log (m_t^2 / m_b^2))
corrections, and when combined with detailed Monte Carlo simulations including
the top and W decay products, indicate that the t W- single top process may be
extracted from the considerable t tbar and W+ W- j backgrounds at low
luminosity runs of the LHC.Comment: 16 pages, 4 figure
Top Pair Production Beyond Double-Pole Approximation: pp, pp~ --> 6 Fermions and 0, 1 or 2 Additional Partons
Hadron collider cross sections for tt~ production and di-lepton,
single-lepton and all-jet decays with up to 2 additional jets are calculated
using complete LO matrix elements with 6-, 7- and 8-particle final states. The
fixed-width, complex-mass and overall-factor schemes (FWS, CMS & OFS) are
employed and the quality of narrow-width and double-pole approximations (NWA &
DPA) is investigated for inclusive production and suppressed backgrounds to new
particle searches. NWA and DPA cross sections differ by 1% or less. The
inclusion of sub- and non-resonant amplitudes effects a cross section increase
of 5-8% at pp supercolliders, but only minor changes at the Tevatron. On-shell
tt~/Wtb backgrounds for the H --> WW decay in weak boson fusion, the hadronic
\tau decay of a heavy H^\pm and the \phi --> hh --> \tau\tau bb~ radion decay
at the LHC are updated, with corrections ranging from 3% to 30%. FWS and CMS
cross sections are uniformly consistent, but OFS cross sections are up to 6%
smaller for some backgrounds.Comment: 20 pages, 6 tables, 1 figur
Top Background Extrapolation for H -> WW Searches at the LHC
A leading order (LO) analysis is presented that demonstrates that key top
backgrounds to H -> W^+W^- -> l^\pm l^\mp \sla{p}_T decays in weak boson fusion
(WBF) and gluon fusion (GF) at the CERN Large Hadron Collider can be
extrapolated from experimental data with an accuracy of order 5% to 10%. If LO
scale variation is accepted as proxy for the theoretical error, parton level
results indicate that the tt~j background to the H -> WW search in WBF can be
determined with a theoretical error of about 5%, while the tt~ background to
the H -> WW search in GF can be determined with a theoretical error of better
than 1%. Uncertainties in the parton distribution functions contribute an
estimated 3% to 10% to the total error.Comment: 17 pages, 9 tables, 4 figures; LO caveat emphasized, version to be
published in Phys. Rev.
Discovery of mating in the major African livestock pathogen Trypanosoma congolense
The protozoan parasite, Trypanosoma congolense, is one of the most economically important pathogens of livestock in Africa and, through its impact on cattle health and productivity, has a significant effect on human health and well being. Despite the importance of this parasite our knowledge of some of the fundamental biological processes is limited. For example, it is unknown whether mating takes place. In this paper we have taken a population genetics based approach to address this question. The availability of genome sequence of the parasite allowed us to identify polymorphic microsatellite markers, which were used to genotype T. congolense isolates from livestock in a discrete geographical area of The Gambia. The data showed a high level of diversity with a large number of distinct genotypes, but a deficit in heterozygotes. Further analysis identified cryptic genetic subdivision into four sub-populations. In one of these, parasite genotypic diversity could only be explained by the occurrence of frequent mating in T. congolense. These data are completely inconsistent with previous suggestions that the parasite expands asexually in the absence of mating. The discovery of mating in this species of trypanosome has significant consequences for the spread of critical traits, such as drug resistance, as well as for fundamental aspects of the biology and epidemiology of this neglected but economically important pathogen
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