Results and conjectures on simultaneous core partitions

An n-core partition is an integer partition whose Young diagram contains no hook lengths equal to n. We consider partitions that are simultaneously a-core and b-core for two relatively prime integers a and b. These are related to abacus diagrams and the combinatorics of the affine symmetric group (type A). We observe that self-conjugate simultaneous core partitions correspond to the combinatorics of type C, and use abacus diagrams to unite the discussion of these two sets of objects. In particular, we prove that (2n)- and (2mn+1)-core partitions correspond naturally to dominant alcoves in the m-Shi arrangement of type C_n, generalizing a result of Fishel--Vazirani for type A. We also introduce a major statistic on simultaneous n- and (n+1)-core partitions and on self-conjugate simultaneous (2n)- and (2n+1)-core partitions that yield q-analogues of the Coxeter-Catalan numbers of type A and type C. We present related conjectures and open questions on the average size of a simultaneous core partition, q-analogs of generalized Catalan numbers, and generalizations to other Coxeter groups. We also discuss connections with the cyclic sieving phenomenon and q,t-Catalan numbers.Comment: 17 pages; to appear in the European Journal of Combinatoric

Completion Report: Arkansas State Pesticides in Ground Water Monitoring Project Phase V: Vulnerable areas in Jackson, Monroe, Lawrence and Lonoke Counties

In 1996, sixty-seven water samples were drawn from 65 wells, including 62 new wells and 3 wells sampled previously . One Woodruff County well and two Pulaski County wells were resampled. Thirty-two samples were drawn from 30 wells in Monroe County (well #1 was sampled 3 times during this phase) . Ten wells in Jackson County, 12 wells in Lawrence County and 10 wells in Lonoke were also tested (Figures 1-5) . With the completion of Phase V, the number of wells tested has risen to 231 with a total of 258 samples analyzed . Initially, the wells were tested for 13 pesticides and ni~rate. Two more pesticides, aldicarb and carbofuran were added to the analyte list during Phase V. The analyte list is shown in Table 3 . All results from all the wells are listed in Appendix A. Quality control information for these data follow the results. The Phase V Quality Assurance Report is included in this document as Part II

Development and selection of operational management strategies to achieve policy objectives

Since the reform of the EU Common Fisheries Policy in 2002, effort has been devoted to addressing the governance, scientific, social and economic issues required to introduce an ecosystem approach to fisheries management (EAFM) in Europe. Fisheries management needs to support the three pillars of sustainability (ecological, social and economic) and Fisheries Ecosystem Plans (FEPs) have been developed as a tool to assist managers considering the ecological, social and economic implications of their decision. Building upon previous studies (e.g. the FP5-funded European Fisheries Ecosystem Plan project), the core concept of the Making the European Fisheries Ecosystem Plan Operational (MEFEPO) project is to deliver operational frameworks (FEPs) for three regional seas. The project focus is on how best to make current institutional frameworks responsive to an EAFM at regional and pan-European levels in accordance with the principles of good governance. The regional seas selected for the project are the North Sea (NS), North Western Waters (NWW) and South Western Waters (SWW) RAC regions. The aim of this work package (WP5) was to develop operational objectives to achieve the ecological objectives identified for the 3 regional seas in WP2. This report describes the development and implementation of a transparent and formal process that should lead to identification of the “best” operational management strategies for an EAFM, based on sound scientific information and stakeholder involvement (e.g. regional industry groups, citizen groups, managers and other interest groups)

Experiences and perceptions of Spring Lane Sure Start Children's Centre

Spring Lane Sure Start Children’s Centre was designated in September 2007, and ‘officially opened’ in February 2009. The Centre is housed in refurbished premises within a nursery/school complex in the heart of Northampton and offers diverse health, childcare, early education and support services delivered by a multi-professional team. These services and activities are available to children aged 0-5 years old, and their parents/carers, residing within a catchment area comprising eight ‘Super Output Areas’ in the Castle and St. James ward of Northampton. In April 2009, the Centre for Children and Youth (CCY) – a research centre based at The University of Northampton – was commissioned by Spring Lane Sure Start Children’s Centre to collate and gather evaluative data regarding experiences and perceptions of the Children’s Centre during its first year of activitie

Flexible copper-indium-diselenide films and devices for space applications

With the ever increasing demands on space power systems, it is imperative that low cost, lightweight, reliable photovoltaics be developed. One avenue of pursuit for future space power applications is the use of low cost, lightweight flexible PV cells and arrays. Most work in this area assumes the use of flexible amorphous silicon (a-Si), despite its inherent instability and low efficiencies. However, polycrystalline thin film PV such as copper-indium-diselenide (CIS) are inherently more stable and exhibit better performance than a-Si. Furthermore, preliminary data indicate that CIS also offers exciting properties with respect to space applications. However, CIS has only heretofore only produced on rigid substrates. The implications of flexible CIS upon present and future space power platforms was explored. Results indicate that space qualified CIS can dramatically reduce the cost of PV, and in most cases, can be substituted for silicon (Si) based on end-of-life (EOL) estimations. Furthermore, where cost is a prime consideration, CIS can become cost effective than gallium arsenide (GaAs) in some applications. Second, investigations into thin film deposition on flexible substrates were made, and data from these tests indicate that fabrication of flexible CIS devices is feasible. Finally, data is also presented on preliminary TCO/CdS/CuInSe2/Mo devices

Measurement of the hyperfine structure of the S1/2-D5/2 transition in 43Ca+

The hyperfine structure of the S1/2-D5/2 quadrupole transition at 729 nm in 43Ca+ has been investigated by laser spectroscopy using a single trapped 43Ca+ ion. We determine the hyperfine structure constants of the metastable level as A=-3.8931(2) MHz and B=-4.241(4) MHz. The isotope shift of the transition with respect to 40Ca+ was measured to be 4134.713(5) MHz. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at non-zero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known 'clock transitions' between m=0 levels at zero magnetic field.Comment: corrected for sign errors in the hyperfine constants. No corrections to were made to the data analysi

Microstructural Rearrangements and their Rheological Implications in a Model Thixotropic Elastoviscoplastic Fluid

We identify the sequence of microstructural changes that characterize the evolution of an attractive particulate gel under flow and discuss their implications on macroscopic rheology. Dissipative particle dynamics is used to monitor shear-driven evolution of a fabric tensor constructed from the ensemble spatial configuration of individual attractive constituents within the gel. By decomposing this tensor into isotropic and nonisotropic components we show that the average coordination number correlates directly with the flow curve of the shear stress versus shear rate, consistent with theoretical predictions for attractive systems. We show that the evolution in nonisotropic local particle rearrangements are primarily responsible for stress overshoots (strain-hardening) at the inception of steady shear flow and also lead, at larger times and longer scales, to microstructural localization phenomena such as shear banding flow-induced structure formation in the vorticity direction

Telescopic actions

A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1] spaces, in particular on 3 and 4-dimensional hyperbolic spaces. As applications we give new proofs of the following statements: (1) Aitchison's theorem: Every finitely presented group G can appear as the fundamental group of M/J, where M is a compact 3-manifold and J is an involution which has only isolated fixed points; (2) Taubes' theorem: Every finitely presented group G can appear as the fundamental group of a compact complex 3-manifold.Comment: +higher dimension