24,708 research outputs found
Detailed Abundances of 15 Stars in the Metal-Poor Globular Cluster NGC 4833
We have observed 15 red giant stars in the relatively massive, metal-poor
globular cluster NGC 4833 using the Magellan Inamori Kyocera Echelle
spectrograph at Magellan. We calculate stellar parameters for each star and
perform a standard abundance analysis to derive abundances of 43 species of 39
elements, including 20 elements heavier than the iron group. We derive
= -2.25 +/- 0.02 from Fe I lines and = -2.19 +/- 0.013 from Fe II
lines. We confirm earlier results that found no internal metallicity spread in
NGC 4833, and there are no significant star-to-star abundance dispersions among
any elements in the iron group (19 <= Z <= 30). We recover the usual abundance
variations among the light elements C, N, O, Na, Mg, Al, and possibly Si. The
heavy-element distribution reflects enrichment by r-process nucleosynthesis
([Eu/Fe] = +0.36 +/- 0.03), as found in many other metal-poor globular
clusters. We investigate small star-to-star variations found among the
neutron-capture elements, and we conclude that these are probably not real
variations. Upper limits on the Th abundance, log epsilon (Th/Eu) < -0.47 +/-
0.09, indicate that NGC 4833, like other globular clusters where Th has been
studied, did not experience a so-called "actinide boost."Comment: Accepted for publication in MNRAS. Version 2 adds final publication
referenc
Differential and Functional Identities for the Elliptic Trilogarithm
When written in terms of -functions, the classical
Frobenius-Stickelberger pseudo-addition formula takes a very simple form.
Generalizations of this functional identity are studied, where the functions
involved are derivatives (including derivatives with respect to the modular
parameter) of the elliptic trilogarithm function introduced by Beilinson and
Levin. A differential identity satisfied by this function is also derived.
These generalized Frobenius-Stickelberger identities play a fundamental role in
the development of elliptic solutions of the Witten-Dijkgraaf-Verlinde-Verlinde
equations of associativity, with the simplest case reducing to the above
mentioned differential identity
A construction of Multidimensional Dubrovin-Novikov Brackets
A method for the construction of classes of examples of multi-dimensional,
multi-component Dubrovin-Novikov brackets of hydrodynamic type is given. This
is based on an extension of the original construction of Gelfand and Dorfman
which gave examples of Novikov algebras in terms of structures defined from
commutative, associative algebras. Given such an algebra, the construction
involves only linear algebra
Generalized Legendre transformations and symmetries of the WDVV equations
The Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations, as one would
expect from an integrable system, has many symmetries, both continuous and
discrete. One class - the so-called Legendre transformations - were introduced
by Dubrovin. They are a discrete set of symmetries between the stronger concept
of a Frobenius manifold, and are generated by certain flat vector fields. In
this paper this construction is generalized to the case where the vector field
(called here the Legendre field) is non-flat but satisfies a certain set of
defining equations. One application of this more general theory is to generate
the induced symmetry between almost-dual Frobenius manifolds whose underlying
Frobenius manifolds are related by a Legendre transformation. This also
provides a map between rational and trigonometric solutions of the WDVV
equations.Comment: 23 page
Mammalian Septins Nomenclature
There are 10 known mammalian septin genes, some of which produce multiple splice variants. The
current nomenclature for the genes and gene products is very confusing, with several different names
having been given to the same gene product and distinct names given to splice variants of the same
gene. Moreover, some names are based on those of yeast or Drosophila septins that are not the closest
homologues. Therefore, we suggest that the mammalian septin field adopt a common nomenclature
system, based on that adopted by the Mouse Genomic Nomenclature Committee and accepted by the Human Genome Organization Gene Nomenclature Committee. The human and mouse septin genes
will be named SEPT1–SEPT10 and Sept1–Sept10, respectively. Splice variants will be designated by an
underscore followed by a lowercase “v” and a number, e.g., SEPT4_v1
Compatible metrics on a manifold and non-local bi-Hamiltonian structures
Given a flat metric one may generate a local Hamiltonian structure via the
fundamental result of Dubrovin and Novikov. More generally, a flat pencil of
metrics will generate a local bi-Hamiltonian structure, and with additional
quasi-homogeneity conditions one obtains the structure of a Frobenius manifold.
With appropriate curvature conditions one may define a curved pencil of
compatible metrics and these give rise to an associated non-local
bi-Hamiltonian structure. Specific examples include the F-manifolds of Hertling
and Manin equipped with an invariant metric. In this paper the geometry
supporting such compatible metrics is studied and interpreted in terms of a
multiplication on the cotangent bundle. With additional quasi-homogeneity
assumptions one arrives at a so-called weak \F-manifold - a curved version of
a Frobenius manifold (which is not, in general, an F-manifold). A submanifold
theory is also developed.Comment: 17 page
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