13,083 research outputs found
On elliptic curves with an isogeny of degree 7
We show that if is an elliptic curve over with a
-rational isogeny of degree 7, then the image of the 7-adic Galois
representation attached to is as large as allowed by the isogeny, except
for the curves with complex multiplication by . The
analogous result with 7 replaced by a prime was proved by the first
author in [7]. The present case has additional interesting
complications. We show that any exceptions correspond to the rational points on
a certain curve of genus 12. We then use the method of Chabauty to show that
the exceptions are exactly the curves with complex multiplication. As a
by-product of one of the key steps in our proof, we determine exactly when
there exist elliptic curves over an arbitrary field of characteristic not 7
with a -rational isogeny of degree 7 and a specified Galois action on the
kernel of the isogeny, and we give a parametric description of such curves.Comment: The revision gives a complete answer to the question considered in
Version 1. Version 3 will appear in the American Journal of Mathematic
Variational Principle in the Algebra of Asymptotic Fields
This paper proposes a variational principle for the solutions of quantum
field theories in which the ``trial functions'' are chosen from the algebra of
asymptotic fields, and illustrates this variational principle in simple cases.Comment: 15 pages, Latex, no figure
Study made of corrosion resistance of stainless steel and nickel alloys in nuclear reactor superheaters
Experiments performed under conditions found in nuclear reactor superheaters determine the corrosion rate of stainless steel and nickel alloys used in them. Electropolishing was the primary surface treatment before the corrosion test. Corrosion is determined by weight loss of specimens after defilming
The Free Quon Gas Suffers Gibbs' Paradox
We consider the Statistical Mechanics of systems of particles satisfying the
-commutation relations recently proposed by Greenberg and others. We show
that although the commutation relations approach Bose (resp.\ Fermi) relations
for (resp.\ ), the partition functions of free gases are
independent of in the range . The partition functions exhibit
Gibbs' Paradox in the same way as a classical gas without a correction factor
for the statistical weight of the -particle phase space, i.e.\ the
Statistical Mechanics does not describe a material for which entropy, free
energy, and particle number are extensive thermodynamical quantities.Comment: number-of-pages, LaTeX with REVTE
Tidal Heating of Extra-Solar Planets
Extra-solar planets close to their host stars have likely undergone
significant tidal evolution since the time of their formation. Tides probably
dominated their orbital evolution once the dust and gas had cleared away, and
as the orbits evolved there was substantial tidal heating within the planets.
The tidal heating history of each planet may have contributed significantly to
the thermal budget that governed the planet's physical properties, including
its radius, which in many cases may be measured by observing transit events.
Typically, tidal heating increases as a planet moves inward toward its star and
then decreases as its orbit circularizes. Here we compute the plausible heating
histories for several planets with measured radii, using the same tidal
parameters for the star and planet that had been shown to reconcile the
eccentricity distribution of close-in planets with other extra-solar planets.
Several planets are discussed, including for example HD 209458 b, which may
have undergone substantial tidal heating during the past billion years, perhaps
enough to explain its large measured radius. Our models also show that GJ 876 d
may have experienced tremendous heating and is probably not a solid, rocky
planet. Theoretical models should include the role of tidal heating, which is
large, but time-varying.Comment: Accepted for publication to Ap
Dynamical mapping method in nonrelativistic models of quantum field theory
The solutions of Heisenberg equations and two-particles eigenvalue problems
for nonrelativistic models of current-current fermion interaction and model are obtained in the frameworks of dynamical mapping method. The
equivalence of different types of dynamical mapping is shown. The connection
between renormalization procedure and theory of selfadjoint extensions is
elucidated.Comment: 14 page
Some economic benefits of a synchronous earth observatory satellite
An analysis was made of the economic benefits which might be derived from reduced forecasting errors made possible by data obtained from a synchronous satellite system which can collect earth observation and meteorological data continuously and on demand. User costs directly associated with achieving benefits are included. In the analysis, benefits were evaluated which might be obtained as a result of improved thunderstorm forecasting, frost warning, and grain harvest forecasting capabilities. The anticipated system capabilities were used to arrive at realistic estimates of system performance on which to base the benefit analysis. Emphasis was placed on the benefits which result from system forecasting accuracies. Benefits from improved thunderstorm forecasts are indicated for the construction, air transportation, and agricultural industries. The effects of improved frost warning capability on the citrus crop are determined. The benefits from improved grain forecasting capability are evaluated in terms of both U.S. benefits resulting from domestic grain distribution and U.S. benefits from international grain distribution
The chameleon groups of Richard J. Thompson: automorphisms and dynamics
The automorphism groups of several of Thompson's countable groups of
piecewise linear homeomorphisms of the line and circle are computed and it is
shown that the outer automorphism groups of these groups are relatively small.
These results can be interpreted as stability results for certain structures of
PL functions on the circle. Machinery is developed to relate the structures on
the circle to corresponding structures on the line
Search for exchange-antisymmetric two-photon states
Atomic two-photon J=0 J'=1 transitions are forbidden for
photons of the same energy. This selection rule is related to the fact that
photons obey Bose-Einstein statistics. We have searched for small violations of
this selection rule by studying transitions in atomic Ba. We set a limit on the
probability that photons are in exchange-antisymmetric states:
.Comment: 5 pages, 4 figures, ReVTeX and .eps. Submitted to Phys. Rev. Lett.
Revised version 9/25/9
Generalized Fock Spaces, New Forms of Quantum Statistics and their Algebras
We formulate a theory of generalized Fock spaces which underlies the
different forms of quantum statistics such as ``infinite'', Bose-Einstein and
Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems
that cannot be mapped into single-indexed systems are studied. Our theory is
based on a three-tiered structure consisting of Fock space, statistics and
algebra. This general formalism not only unifies the various forms of
statistics and algebras, but also allows us to construct many new forms of
quantum statistics as well as many algebras of creation and destruction
operators. Some of these are : new algebras for infinite statistics,
q-statistics and its many avatars, a consistent algebra for fractional
statistics, null statistics or statistics of frozen order, ``doubly-infinite''
statistics, many representations of orthostatistics, Hubbard statistics and its
variations.Comment: This is a revised version of the earlier preprint: mp_arc 94-43.
Published versio
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