17,410 research outputs found
The Transcendence Degree over a Ring
For a finitely generated algebra over a field, the transcendence degree is
known to be equal to the Krull dimension. The aim of this paper is to
generalize this result to algebras over rings. A new definition of the
transcendence degree of an algebra A over a ring R is given by calling elements
of A algebraically dependent if they satisfy an algebraic equation over R whose
trailing coefficient, with respect to some monomial ordering, is 1. The main
result is that for a finitely generated algebra over a Noetherian Jacobson
ring, the transcendence degree is equal to the Krull dimension
Stellar dust production and composition in the Magellanic Clouds
The dust reservoir in the interstellar medium of a galaxy is constantly being
replenished by dust formed in the stellar winds of evolved stars. Due to their
vicinity, nearby irregular dwarf galaxies the Magellanic Clouds provide an
opportunity to obtain a global picture of the dust production in galaxies. The
Small and Large Magellanic Clouds have been mapped with the Spitzer Space
Telescope from 3.6 to 160 {\mu}m, and these wavelengths are especially suitable
to study thermal dust emission. In addition, a large number of individual
evolved stars have been targeted for 5-40 {\mu}m spectroscopy, revealing the
mineralogy of these sources. Here I present an overview on the work done on
determining the total dust production rate in the Large and Small Magellanic
Clouds, as well as a first attempt at revealing the global composition of the
freshly produced stardust.Comment: accepted for publication by Earth, Planets & Spac
On reconstructing n-point configurations from the distribution of distances or areas
One way to characterize configurations of points up to congruence is by
considering the distribution of all mutual distances between points. This paper
deals with the question if point configurations are uniquely determined by this
distribution. After giving some counterexamples, we prove that this is the case
for the vast majority of configurations. In the second part of the paper, the
distribution of areas of sub-triangles is used for characterizing point
configurations. Again it turns out that most configurations are reconstructible
from the distribution of areas, though there are counterexamples.Comment: 21 pages, late
Some complete intersection symplectic quotients in positive characteristic: invariants of a vector and a covector
Given a linear action of a group on a -vector space , we consider
the invariant ring , where is the dual space. We are
particularly interested in the case where V =\gfq^n and is the group
of all upper unipotent matrices or the group of all upper
triangular matrices in \GL_n(\gfq). In fact, we determine \gfq[V \oplus
V^*]^G for and . The result is a complete intersection for
all values of and . We present explicit lists of generating invariants
and their relations. This makes an addition to the rather short list of "doubly
parametrized" series of group actions whose invariant rings are known to have a
uniform description.Comment: 16 page
Flows on Simplicial Complexes
Given a graph , the number of nowhere-zero \ZZ_q-flows is
known to be a polynomial in . We extend the definition of nowhere-zero
\ZZ_q-flows to simplicial complexes of dimension greater than one,
and prove the polynomiality of the corresponding function
for certain and certain subclasses of simplicial complexes.Comment: 10 pages, to appear in Discrete Mathematics and Theoretical Computer
Science (proceedings of FPSAC'12
Lossless Representation of Graphs using Distributions
We consider complete graphs with edge weights and/or node weights taking
values in some set. In the first part of this paper, we show that a large
number of graphs are completely determined, up to isomorphism, by the
distribution of their sub-triangles. In the second part, we propose graph
representations in terms of one-dimensional distributions (e.g., distribution
of the node weights, sum of adjacent weights, etc.). For the case when the
weights of the graph are real-valued vectors, we show that all graphs, except
for a set of measure zero, are uniquely determined, up to isomorphism, from
these distributions. The motivating application for this paper is the problem
of browsing through large sets of graphs.Comment: 19 page
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