579 research outputs found
When is the Bloch-Okounkov q-bracket modular?
We obtain a condition describing when the quasimodular forms given by the
Bloch-Okounkov theorem as -brackets of certain functions on partitions are
actually modular. This condition involves the kernel of an operator {\Delta}.
We describe an explicit basis for this kernel, which is very similar to the
space of classical harmonic polynomials.Comment: 12 pages; corrected typo
Quantitative Results on Diophantine Equations in Many Variables
We consider a system of integer polynomials of the same degree with
non-singular local zeros and in many variables. Generalising the work of Birch
(1962) we find quantitative asymptotics (in terms of the maximum of the
absolute value of the coefficients of these polynomials) for the number of
integer zeros of this system within a growing box. Using a quantitative version
of the Nullstellensatz, we obtain a quantitative strong approximation result,
i.e. an upper bound on the smallest integer zero provided the system of
polynomials is non-singular.Comment: Accepted for publication in Acta Arithmetica. Added a few pages so
that familiarity with Birch's work is no longer assumed; 24 page
Triply mixed coverings of arbitrary base curves: Quasimodularity, quantum curves and a mysterious topological recursions
Simple Hurwitz numbers enumerate branched morphisms between Riemann surfaces
with fixed ramification data. In recent years, several variants of this notion
for genus base curves have appeared in the literature. Among them are
so-called monotone Hurwitz numbers, which are related to the HCIZ integral in
random matrix theory and strictly monotone Hurwitz numbers which count certain
Grothendieck dessins d'enfants. We generalise the notion of Hurwitz numbers to
interpolations between simple, monotone and strictly monotone Hurwitz numbers
to any genus and any number of arbitrary but fixed ramification profiles. This
yields generalisations of several results known for Hurwitz numbers. When the
target surface is of genus one, we show that the generating series of these
interpolated Hurwitz numbers are quasimodular forms. In the case that all
ramification is simple, we refine this result by writing this series as a sum
of quasimodular forms corresonding to tropical covers weighted by Gromov-Witten
invariants. Moreover, we derive a quantum curve for monotone and Grothendieck
dessins d'enfants Hurwitz numbers for arbitrary genera and one arbitrary but
fixed ramification profile. Thus, we obtain spectral curves via the
semiclassical limit as input data for the CEO topological recursion.
Astonishingly, we find that the CEO topological recursion for the genus
spectral curve of the strictly monotone Hurwitz numbers compute the monotone
Hurwitz numbers in genus . Thus, we give a new proof that monotone Hurwitz
numbers satisfy CEO topological recursion. This points to an unknown relation
between those enumerants. Finally, specializing to target surface
, we find recursions for monotone and Grothendieck dessins
d'enfants double Hurwitz numbers, which enables the computation of the
respective Hurwitz numbers for any genera with one arbitrary but fixed
ramification profile.Comment: 41 page
Fear of exercise and health-related quality of life in patients with an implantable cardioverter defibrillator
Several studies have reported improved survival rates thanks to the use of an implantable cardioverter defibrillator (ICD) in the treatment of patients with life-threatening arrhythmia. However, the effects of the ICD on health-related quality of life (HR-QoL) of these patients are not clear. The aim of this study is to describe HR-QoL and fear of exercise in ICD patients. Eighty-nine ICD patients from the University Hospital in Groningen, the Netherlands, participated in this study. HR-QoL was measured using the Rand-36 and the Quality of Life After Myocardial Infarction Dutch language version questionnaires. Fear of exercise was measured using the Tampa Scale for Kinesiophobia, Dutch version and the Fear Avoidance Beliefs Questionnaire, Dutch version. Association between outcome variables was analysed by linear regression analyses. Study results show that the HR-QoL of patients with ICDs in our study population is significantly worse than that of normal healthy people. Furthermore, fear of exercise is negatively associated with HR-QoL corrected for sex, age and number of years living with an ICD. After implantation of the ICD, patients with a clear fear of exercise should be identified and interventions should be considered in order to increase their HR-QoL
Assessing the adaptation of arable farmers to climate change using DEA and bio-economic modelling
The objective of this article is to assess the impact of climate change on arable farming systems in Flevoland (the Netherlands) and to explore the adoption of different adaptation strategies. Data Envelopment Analysis (DEA) is applied that uses empirical data from individual farms to identify “best” current farm practices and derive relationships regarding current farm managemen
Triply mixed coverings of arbitrary base curves : quasimodularity, quantum curves and a mysterious topological recursions
Simple Hurwitz numbers are classical invariants in enumerative geometry counting branched morphisms between Riemann surfaces with fixed ramification data. In recent years, several modifications of this notion for genus 0 base curves have appeared in the literature. Among them are so-called monotone Hurwitz numbers, which are related to the Harish–Chandra–Itzykson–Zuber integral in random matrix theory and strictly monotone Hurwitz numbers which enumerate certain Grothendieck dessins d’enfants. We generalise the notion of Hurwitz numbers to interpolations between simple, monotone and strictly monotone Hurwitz numbers for arbitrary genera and any number of arbitrary but fixed ramification profiles. This yields generalisations of several results known for Hurwitz numbers. When the target surface is of genus one, we show that the generating series of these interpolated Hurwitz numbers are quasimodular forms. In the case that all ramification is simple, we refine this result by writing this series as a sum of quasimodular forms corresponding to tropical covers weighted by Gromov–Witten invariants. Moreover, we derive a quantum curve for monotone and Grothendieck dessins d’enfants Hurwitz numbers for arbitrary genera and one arbitrary but fixed ramification profile. Thus, we obtain spectral curves via the semi-classical limit as input data for the Chekhov–Eynard–Orantin (CEO) topological recursion. Astonishingly, we find that the CEO topological recursion for the genus 1 spectral curve of the strictly monotone Hurwitz numbers computes the monotone Hurwitz numbers in genus 0. Thus, we give a new proof that monotone Hurwitz numbers satisfy CEO topological recursion. This points to an unknown relation between those enumerative invariants. Finally, specializing to target surface ℙ1, we find recursions for monotone and Grothendieck dessins d’enfants double Hurwitz numbers, which enables the computation of the respective Hurwitz numbers for any genera with one arbitrary but fixed ramification profile
Adapting agriculture in 2050 in Flevoland; perspectives from stakeholders
Although recently more research has gone into farm level studies, little attention has been given to the variety of responses of farmers, considering their characteristics, objectives and the socio-economic, technological and political contexts (Reidsma et al, 2010). In the Agri-Adapt project we focus on farm level adaptation within an agricultural region considering the socio-economic context of 2050
Climate change adaptation in agriculture; the use of multi-scale modelling and stakeholder participation in the Netherlands
Abstract about a research project to develop a methodology to assess adaptation of agriculture to climatic and socio-economic changes at multiple scales, with a first application in the Province of Flevoland, the Netherlands
- …