49,621 research outputs found
On the Olson and the Strong Davenport constants
A subset of a finite abelian group, written additively, is called
zero-sumfree if the sum of the elements of each non-empty subset of is
non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e.,
the (small) Olson constant. We determine the maximal cardinality of such sets
for several new types of groups; in particular, -groups with large rank
relative to the exponent, including all groups with exponent at most five.
These results are derived as consequences of more general results, establishing
new lower bounds for the cardinality of zero-sumfree sets for various types of
groups. The quality of these bounds is explored via the treatment, which is
computer-aided, of selected explicit examples. Moreover, we investigate a
closely related notion, namely the maximal cardinality of minimal zero-sum
sets, i.e., the Strong Davenport constant. In particular, we determine its
value for elementary -groups of rank at most , paralleling and building
on recent results on this problem for the Olson constant
Remarks on the plus-minus weighted Davenport constant
For a finite abelian group the plus-minus weighted Davenport
constant, denoted , is the smallest such that each
sequence over has a weighted zero-subsum with weights +1
and -1, i.e., there is a non-empty subset such that
for . We present new bounds for
this constant, mainly lower bounds, and also obtain the exact value of this
constant for various additional types of groups
Vertical Coherence of Turbulence in the Atmospheric Surface Layer: Connecting the Hypotheses of Townsend and Davenport
Statistical descriptions of coherent flow motions in the atmospheric boundary
layer have many applications in the wind engineering community. For instance,
the dynamical characteristics of large-scale motions in wall-turbulence play an
important role in predicting the dynamical loads on buildings, or the
fluctuations in the power distribution across wind farms. Davenport (Quarterly
Journal of the Royal Meteorological Society, 1961, Vol. 372, 194-211) performed
a seminal study on the subject and proposed a hypothesis that is still widely
used to date. Here, we demonstrate how the empirical formulation of Davenport
is consistent with the analysis of Baars et al. (Journal of Fluid Mechanics,
2017, Vol. 823, R2) in the spirit of Townsend's attached-eddy hypothesis in
wall turbulence. We further study stratification effects based on two-point
measurements of atmospheric boundary-layer flow over the Utah salt flats. No
self-similar scaling is observed in stable conditions, putting the application
of Davenport's framework, as well as the attached eddy hypothesis, in question
for this case. Data obtained under unstable conditions exhibit clear
self-similar scaling and our analysis reveals a strong sensitivity of the
statistical aspect ratio of coherent structures (defined as the ratio of
streamwise and wall-normal extent) to the magnitude of the stability parameter
ON P-ADIC FIELDS AND P-GROUPS
The dissertation is divided into two parts. The first part mainly treats a conjecture of Emil Artin from the 1930s. Namely, if f = a_1x_1^d + a_2x_2^d +...+ a_{d^2+1}x^d where the coefficients a_i lie in a finite unramified extension of a rational p-adic field, where p is an odd prime, then f is isotropic. We also deal with systems of quadratic forms over finite fields and study the isotropicity of the system relative to the number of variables. We also study a variant of the classical Davenport constant of finite abelian groups and relate it to the isotropicity of diagonal forms. The second part deals with the theory of finite groups. We treat computations of Chermak-Delgado lattices of p-groups. We compute the Chermak-Delgado lattices for all p-groups of order p^3 and p^4 and give results on p-groups of order p^5
Adjusting the melting point of a model system via Gibbs-Duhem integration: application to a model of Aluminum
Model interaction potentials for real materials are generally optimized with
respect to only those experimental properties that are easily evaluated as
mechanical averages (e.g., elastic constants (at T=0 K), static lattice
energies and liquid structure). For such potentials, agreement with experiment
for the non-mechanical properties, such as the melting point, is not guaranteed
and such values can deviate significantly from experiment. We present a method
for re-parameterizing any model interaction potential of a real material to
adjust its melting temperature to a value that is closer to its experimental
melting temperature. This is done without significantly affecting the
mechanical properties for which the potential was modeled. This method is an
application of Gibbs-Duhem integration [D. Kofke, Mol. Phys.78, 1331 (1993)].
As a test we apply the method to an embedded atom model of aluminum [J. Mei and
J.W. Davenport, Phys. Rev. B 46, 21 (1992)] for which the melting temperature
for the thermodynamic limit is 826.4 +/- 1.3K - somewhat below the experimental
value of 933K. After re-parameterization, the melting temperature of the
modified potential is found to be 931.5K +/- 1.5K.Comment: 9 pages, 5 figures, 4 table
Formulating problems for real algebraic geometry
We discuss issues of problem formulation for algorithms in real algebraic
geometry, focussing on quantifier elimination by cylindrical algebraic
decomposition. We recall how the variable ordering used can have a profound
effect on both performance and output and summarise what may be done to assist
with this choice. We then survey other questions of problem formulation and
algorithm optimisation that have become pertinent following advances in CAD
theory, including both work that is already published and work that is
currently underway. With implementations now in reach of real world
applications and new theory meaning algorithms are far more sensitive to the
input, our thesis is that intelligently formulating problems for algorithms,
and indeed choosing the correct algorithm variant for a problem, is key to
improving the practical use of both quantifier elimination and symbolic real
algebraic geometry in general.Comment: To be presented at The "Encuentros de \'Algebra Computacional y
Aplicaciones, EACA 2014" (Meetings on Computer Algebra and Applications) in
Barcelon
Cauchy-Davenport type theorems for semigroups
Let be a (possibly non-commutative) semigroup. For we define , where is the set of the units of , and The paper
investigates some properties of and shows the following
extension of the Cauchy-Davenport theorem: If is cancellative and
, then This
implies a generalization of Kemperman's inequality for torsion-free groups and
strengthens another extension of the Cauchy-Davenport theorem, where
is a group and in the above is replaced by the
infimum of as ranges over the non-trivial subgroups of
(Hamidoune-K\'arolyi theorem).Comment: To appear in Mathematika (12 pages, no figures; the paper is a sequel
of arXiv:1210.4203v4; shortened comments and proofs in Sections 3 and 4;
refined the statement of Conjecture 6 and added a note in proof at the end of
Section 6 to mention that the conjecture is true at least in another
non-trivial case
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