3,921 research outputs found
Finitely generated abelian groups of units
In 1960 Fuchs posed the problem of characterizing the groups which are the
groups of units of commutative rings. In the following years, some partial
answers have been given to this question in particular cases. In this paper we
address Fuchs' question for {\it finitely generated abelian} groups and we
consider the problem of characterizing those groups which arise in some fixed
classes of rings , namely the integral domains, the torsion free
rings and the reduced rings. To determine the realizable groups we have to
establish what finite abelian groups (up to isomorphism) occur as torsion
subgroup of when varies in , and on the other hand, we
have to determine what are the possible values of the rank of when
. Most of the paper is devoted to the study of the class
of torsion-free rings, which needs a substantially deeper study.Comment: 28 page
Finite groups of units of finite characteristic rings
In \cite[Problem 72]{Fuchs60} Fuchs asked the following question: which
groups can be the group of units of a commutative ring? In the following years,
some partial answers have been given to this question in particular cases. The
aim of the present paper is to address Fuchs' question when is a {\it
finite characteristic ring}. The result is a pretty good description of the
groups which can occur as group of units in this case, equipped with examples
showing that there are obstacles to a "short" complete classification. As a
byproduct, we are able to classify all possible cardinalities of the group of
units of a finite characteristic ring, so to answer Ditor's question
\cite{ditor}
Upper ramification jumps in abelian extensions of exponent p
In this paper we present a classification of the possible upper ramification
jumps for an elementary abelian p-extension of a p-adic field. The fundamental
step for the proof of the main result is the computation of the ramification
filtration for the maximal elementary abelian p-extension of the base field K.
This is a generalization of a previous work of the second author and Dvornicich
where the same result is proved under the assumption that K contains a
primitive p-th root of unity. Using the class field theory and the explicit
relations between the normic group of an extension and its ramification jumps,
it is fairly simple to recover necessary and sufficient conditions for the
upper ramification jumps of an elementary abelian p-extension of K.Comment: 9 page
A multi-class approach for ranking graph nodes: models and experiments with incomplete data
After the phenomenal success of the PageRank algorithm, many researchers have
extended the PageRank approach to ranking graphs with richer structures beside
the simple linkage structure. In some scenarios we have to deal with
multi-parameters data where each node has additional features and there are
relationships between such features.
This paper stems from the need of a systematic approach when dealing with
multi-parameter data. We propose models and ranking algorithms which can be
used with little adjustments for a large variety of networks (bibliographic
data, patent data, twitter and social data, healthcare data). In this paper we
focus on several aspects which have not been addressed in the literature: (1)
we propose different models for ranking multi-parameters data and a class of
numerical algorithms for efficiently computing the ranking score of such
models, (2) by analyzing the stability and convergence properties of the
numerical schemes we tune a fast and stable technique for the ranking problem,
(3) we consider the issue of the robustness of our models when data are
incomplete. The comparison of the rank on the incomplete data with the rank on
the full structure shows that our models compute consistent rankings whose
correlation is up to 60% when just 10% of the links of the attributes are
maintained suggesting the suitability of our model also when the data are
incomplete
On wild extensions of a p-adic field
In this paper we consider the problem of classifying the isomorphism classes
of extensions of degree pk of a p-adic field, restricting to the case of
extensions without intermediate fields. We establish a correspondence between
the isomorphism classes of these extensions and some Kummer extensions of a
suitable field F containing K. We then describe such classes in terms of the
representations of Gal(F/K). Finally, for k = 2 and for each possible Galois
group G, we count the number of isomorphism classes of the extensions whose
normal closure has a Galois group isomorphic to G. As a byproduct, we get the
total number of isomorphism classes
Block Tridiagonal Reduction of Perturbed Normal and Rank Structured Matrices
It is well known that if a matrix solves the
matrix equation , where is a linear bivariate polynomial,
then is normal; and can be simultaneously reduced in a finite
number of operations to tridiagonal form by a unitary congruence and, moreover,
the spectrum of is located on a straight line in the complex plane. In this
paper we present some generalizations of these properties for almost normal
matrices which satisfy certain quadratic matrix equations arising in the study
of structured eigenvalue problems for perturbed Hermitian and unitary matrices.Comment: 13 pages, 3 figure
Compression of unitary rank--structured matrices to CMV-like shape with an application to polynomial rootfinding
This paper is concerned with the reduction of a unitary matrix U to CMV-like
shape. A Lanczos--type algorithm is presented which carries out the reduction
by computing the block tridiagonal form of the Hermitian part of U, i.e., of
the matrix U+U^H. By elaborating on the Lanczos approach we also propose an
alternative algorithm using elementary matrices which is numerically stable. If
U is rank--structured then the same property holds for its Hermitian part and,
therefore, the block tridiagonalization process can be performed using the
rank--structured matrix technology with reduced complexity. Our interest in the
CMV-like reduction is motivated by the unitary and almost unitary eigenvalue
problem. In this respect, finally, we discuss the application of the CMV-like
reduction for the design of fast companion eigensolvers based on the customary
QR iteration
A CMV--based eigensolver for companion matrices
In this paper we present a novel matrix method for polynomial rootfinding. By
exploiting the properties of the QR eigenvalue algorithm applied to a suitable
CMV-like form of a companion matrix we design a fast and computationally simple
structured QR iteration.Comment: 14 pages, 4 figure
Warmer Temperatures on American Kestrel (Falco sparverius) Breeding Grounds Associated with Earlier Laying and Successful Reproduction
The American Kestrel (Falco sparverius) recently has been discovered to be in decline and the reason is still unknown. Many studies have shown climate’s effect on migratory birds, but the relationship between climate and kestrel ecology has received little attention. This study sought to determine whether the climate in northwestern New Jersey and kestrel reproductive efforts have changed over the course of 20 years as well as determining whether these two factors are related. Monthly temperature, rainfall, and snowfall data were obtained from online databases. Breeding variables, including percentage of nest boxes used, clutch and brood size, percentage of successful attempts, and mean number of fledglings per successful attempt (MFPSA), were obtained from a nest box program established in 1995. Correlative statistics and a principal component analysis were conducted. Weather variables changed little through the study period. Regarding breeding variables, earlier laying dates were strongly correlated with larger clutch sizes. Of the climate variables, temperature exhibited the most variability and had the strongest relationships with breeding variables, warmer temperatures being associated with higher reproductive success. Weather did not seem to influence how many kestrels reached the breeding grounds, but once the birds arrived, temperature may have had a significant impact on when the birds lay their eggs, which has a positive relationship to clutch size, brood size, and therefore the number of fledglings that live to banding age, the standard measure of reproductive success
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