23,800 research outputs found

    Some examples of Mahler measures as multiple polylogarithms

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    The Mahler measures of certain polynomials of up to five variables are given in terms of multiple polylogarithms. Each formula is homogeneous and its weight coincides with the number of variables of the corresponding polynomial.Comment: 21 pages, 1 figur

    Mahler measure of some n-variable polynomial families

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    The Mahler measures of some n-variable polynomial families are given in terms of special values of the Riemann zeta function and a Dirichlet L-series, generalizing the results of \cite{L}. The technique introduced in this work also motivates certain identities among Bernoulli numbers and symmetric functions

    Black hole formation in core-collapse supernovae and time-of-flight measurements of the neutrino masses

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    In large stars that have exhausted their nuclear fuel, the stellar core collapses to a hot and dense proto-neutron star that cools by the radiation of neutrinos and antineutrinos of all flavors. Depending on its final mass, this may become either a neutron star or a black hole. Black hole formation may be triggered by mass accretion or a change in the high-density equation of state. We consider the possibility that black hole formation happens when the flux of neutrinos is still measurably high. If this occurs, then the neutrino signal from the supernova will be terminated abruptly (the transition takes ≲0.5 ms). The properties and duration of the signal before the cutoff are important measures of both the physics and astrophysics of the cooling proto-neutron star. For the event rates expected in present and proposed detectors, the cutoff will generally appear sharp, thus allowing model-independent time-of-flight mass tests for the neutrinos after the cutoff. If black hole formation occurs relatively early, within a few (∼1) seconds after core collapse, then the expected luminosities are of order LBH=1052 erg/s per flavor. In this case, the neutrino mass sensitivity can be extraordinary. For a supernova at a distance D=10 kpc, SuperKamiokande can detect a ν̅e mass down to 1.8 eV by comparing the arrival times of the high-energy and low-energy neutrinos in ν̅e+p→e++n. This test will also measure the cutoff time, and will thus allow a mass test of νμ and ντ relative to ν̅e. Assuming that νμ and ντ are nearly degenerate, as suggested by the atmospheric neutrino results, masses down to about 6 eV can be probed with a proposed lead detector of mass MD=4 kton (OMNIS). Remarkably, the neutrino mass sensitivity scales as (D/LBHMD)1/2. Therefore, direct sensitivity to all three neutrino masses in the interesting few-eV range is realistically possible; there are no other known techniques that have this capability

    Photoerosion and the abundances of the light elements

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    The abundances of the rare light elements H-2, He-3, Li-7, and B-11 are shown to be potentially affected by photoerosion. That process, involving the interaction of high energy photons from galactic centers with atomic nuclei, will increase the abundances of H-2, He-3, and B-11 while lowering slightly those of Li-7 and He-4. In some regions of galaxies the effects may be large enough to impact their chemical evolution. In particular this process may have enhanced the H-2 and He-3 abundances near the center of our galaxy over and above those from the big bang, as well as the galactic B-11 abundance over that from cosmic-ray spallation

    Post Big Bang Processing of the Primordial Elements

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    We explore the Gnedin-Ostriker suggestion that a post-Big-Bang photodissociation process may modify the primordial abundances of the light elements. We consider several specific models and discuss the general features that are necessary (but not necessarily sufficient) to make the model work. We find that with any significant processing, the final D and 3^3He abundances, which are independent of their initial standard big bang nucleosynthesis (SBBN) values, rise quickly to a level several orders of magnitude above the observationally inferred primordial values. Solutions for specific models show that the only initial abundances that can be photoprocessed into agreement with observations are those that undergo virtually no processing and are already in agreement with observation. Thus it is unlikely that this model can work for any non-trivial case unless an artificial density and/or photon distribution is invoked.Comment: 12 page Latex file (AASTEX style). Tarred, gzipped, and uuencoded postscript files of seven figures. Also available (with ps file of paper) at ftp://www-physics.mps.ohio-state.edu/pub/nucex/phot

    Natural Kinds and Ceteris Paratis Generalizations: In Praise of Hunches

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    According to stereotypical logical empiricist conceptions, scientific findings are approximately true (or perhaps true ceteris paribus) law-like generalizations used to predict natural phenomena. They are deployed using topic-neutral, generally reliable inferential principles like deductive or statistical inferences. Natural kinds are the kinds in such generalizations. Chemical examples show that such conceptions are seriously incomplete. Some important chemical generalizations are true often enough, even though not usually true, and they are applied using esoteric topic- and discipline-specific inference rules. Their important methodological role is to underwrite often-enough reliable, often socially implemented, scientifically informed guessing about chemical phenomena. Some chemical natural kinds earn their naturalness mainly from participating in such generalizations. These results generalize: many scientific generalizations, inference rules, and natural kinds function to inform guessing, that is, to underwrite the generation of hunches
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