Explore the vast range of titles available.

Uprooted and living with an aunt in 1960s Oklahoma, thirteen-year-old Garnet and her older sister Opal brave their mother's desertion and their father's recovery from an accident, learning that \"the best home of all is the one you make inside yourself.\"

This paper generalises the work done in Currie and Love (2010), where we studied the effect of applying two Crum-type transformations to a weighted second-order difference equation with various combinations of Dirichlet, non-Dirichlet, and affine -dependent boundary conditions at the end points, where is the eigenparameter. We now consider general -dependent boundary conditions. In particular we show, using one of the Crum-type transformations, that it is possible to go up and down a hierarchy of boundary value problems keeping the form of the second-order difference equation constant but possibly increasing or decreasing the dependence on of the boundary conditions at each step. In addition, we show that the transformed boundary value problem either gains or loses an eigenvalue, or the number of eigenvalues remains the same as we step up or down the hierarchy.

When her mother leaves her family suddenly to take a new job, fourteen-year-old Phoebe tries to deal with her own confused feelings and, in the process, learns some things about love and the complicated ties that bind families together.

We consider a general weighted second-order difference equation. Two transformations are studied which transform the given equation into another weighted second order difference equation of the same type, these are based on the Crum transformation. We also show how Dirichlet and non-Dirichlet boundary conditions transform as well as how the spectra and norming constants are affected.

A medieval orphan girl called Mouse gains the courage she needs to follow her dreams of becoming a puppeteer's apprentice.

This is an extension of the work done by Currie and Love (2010) where we studied the effect of applying two Crum-type transformations to a weighted second-order difference equation with non-eigenparameter-dependent boundary conditions at the end points. In particular, we now consider boundary conditions which depend affinely on the eigenparameter together with various combinations of Dirichlet and non-Dirichlet boundary conditions. The spectra of the resulting transformed boundary value problems are then compared to the spectra of the original boundary value problems.

This paper uses the forward transformation defined in Currie and Love (Adv. Differ. Equ. 2010:947058, 2010) to develop a hierarchy for difference boundary value problems with eigenparameter-dependent boundary conditions. In particular, we show how various sets of these boundary conditions transform under this forward transformation. The resulting hierarchy is then illustrated in a tabular form where the number of eigenvalues for each of the problems is also given. In addition, we point out certain analogies to the work done in Currie and Love (Bound. Value Probl. 2011:743135, 2011) where the reverse Crum-type transformation was used to establish a hierarchy of difference boundary value problems. MSC: 39A05, 34K10, 65Q10, 65Q30.

This paper uses the forward transformation defined in Currie and Love (Adv. Differ. Equ. 2010:947058, 2010) to develop a hierarchy for difference boundary value problems with eigenparameter-dependent boundary conditions. In particular, we show how various sets of these boundary conditions transform under this forward transformation. The resulting hierarchy is then illustrated in a tabular form where the number of eigenvalues for each of the problems is also given. In addition, we point out certain analogies to the work done in Currie and Love (Bound. Value Probl. 2011:743135, 2011) where the reverse Crum-type transformation was used to establish a hierarchy of difference boundary value problems. MSC: 39A05, 34K10, 65Q10, 65Q30.[PUBLICATION ABSTRACT]

Oesophageal adenocarcinoma represents one of the fastest rising cancers in high-income countries. Barrett's oesophagus is the premalignant precursor of oesophageal adenocarcinoma. However, only a few patients with Barrett's oesophagus develop adenocarcinoma, which complicates clinical management in the absence of valid predictors. Within an international consortium investigating the genetics of Barrett's oesophagus and oesophageal adenocarcinoma, we aimed to identify novel genetic risk variants for the development of Barrett's oesophagus and oesophageal adenocarcinoma. We did a meta-analysis of all genome-wide association studies of Barrett's oesophagus and oesophageal adenocarcinoma available in PubMed up to Feb 29, 2016; all patients were of European ancestry and disease was confirmed histopathologically. All participants were from four separate studies within Europe, North America, and Australia and were genotyped on high-density single nucleotide polymorphism (SNP) arrays. Meta-analysis was done with a fixed-effects inverse variance-weighting approach and with a standard genome-wide significance threshold (p<5 × 10−8). We also did an association analysis after reweighting of loci with an approach that investigates annotation enrichment among genome-wide significant loci. Furthermore, the entire dataset was analysed with bioinformatics approaches—including functional annotation databases and gene-based and pathway-based methods—to identify pathophysiologically relevant cellular mechanisms. Our sample comprised 6167 patients with Barrett's oesophagus and 4112 individuals with oesophageal adenocarcinoma, in addition to 17 159 representative controls from four genome-wide association studies in Europe, North America, and Australia. We identified eight new risk loci associated with either Barrett's oesophagus or oesophageal adenocarcinoma, within or near the genes CFTR (rs17451754; p=4·8 × 10−10), MSRA (rs17749155; p=5·2 × 10−10), LINC00208 and BLK (rs10108511; p=2·1 × 10−9), KHDRBS2 (rs62423175; p=3·0 × 10−9), TPPP and CEP72 (rs9918259; p=3·2 × 10−9), TMOD1 (rs7852462; p=1·5 × 10−8), SATB2 (rs139606545; p=2·0 × 10−8), and HTR3C and ABCC5 (rs9823696; p=1·6 × 10−8). The locus identified near HTR3C and ABCC5 (rs9823696) was associated specifically with oesophageal adenocarcinoma (p=1·6 × 10−8) and was independent of Barrett's oesophagus development (p=0·45). A ninth novel risk locus was identified within the gene LPA (rs12207195; posterior probability 0·925) after reweighting with significantly enriched annotations. The strongest disease pathways identified (p<10−6) belonged to muscle cell differentiation and to mesenchyme development and differentiation. Our meta-analysis of genome-wide association studies doubled the number of known risk loci for Barrett's oesophagus and oesophageal adenocarcinoma and revealed new insights into causes of these diseases. Furthermore, the specific association between oesophageal adenocarcinoma and the locus near HTR3C and ABCC5 might constitute a novel genetic marker for prediction of the transition from Barrett's oesophagus to oesophageal adenocarcinoma. Fine-mapping and functional studies of new risk loci could lead to identification of key molecules in the development of Barrett's oesophagus and oesophageal adenocarcinoma, which might encourage development of advanced prevention and intervention strategies. US National Cancer Institute, US National Institutes of Health, National Health and Medical Research Council of Australia, Swedish Cancer Society, Medical Research Council UK, Cambridge NIHR Biomedical Research Centre, Cambridge Experimental Cancer Medicine Centre, Else Kröner Fresenius Stiftung, Wellcome Trust, Cancer Research UK, AstraZeneca UK, University Hospitals of Leicester, University of Oxford, Australian Research Council.