14,493 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 $G$ on a $K$-vector space $V$, we consider
the invariant ring $K[V \oplus V^*]^G$, where $V^*$ is the dual space. We are
particularly interested in the case where V =\gfq^n and $G$ is the group
$U_n$ of all upper unipotent matrices or the group $B_n$ of all upper
triangular matrices in \GL_n(\gfq). In fact, we determine \gfq[V \oplus
V^*]^G for $G = U_n$ and $G =B_n$. The result is a complete intersection for
all values of $n$ and $q$. 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 $G$, the number of nowhere-zero \ZZ_q-flows $\phi_G(q)$ is
known to be a polynomial in $q$. We extend the definition of nowhere-zero
\ZZ_q-flows to simplicial complexes $\Delta$ of dimension greater than one,
and prove the polynomiality of the corresponding function $\phi_{\Delta}(q)$
for certain $q$ and certain subclasses of simplicial complexes.Comment: 10 pages, to appear in Discrete Mathematics and Theoretical Computer
Science (proceedings of FPSAC'12

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