The amalgamated duplication of a ring along a multiplicative-canonical ideal

After recalling briefly the main properties of the amalgamated duplication of a ring $R$ along an ideal $I$, denoted by R\JoinI, we restrict our attention to the study of the properties of R\JoinI, when $I$ is a multiplicative canonical ideal of $R$ \cite{hhp}. In particular, we study when every regular fractional ideal of $R\Join I$ is divisorial

Epidemiology and health related quality of life in hypoparathyroidism in Norway.

OBJECTIVE: The epidemiology of hypoparathyroidism (HP) is largely unknown. We aimed to determine prevalence, etiologies, health related quality of life (HRQoL) and treatment pattern of HP. METHODS: Patients with HP and 22q11 deletion syndrome (DiGeorge syndrome) were identified in electronic hospital registries. All identified patients were invited to participate in a survey. Among patients who responded, HRQoL was determined by Short Form 36 (SF-36) and Hospital Anxiety and Depression scale (HADS). Autoantibodies were measured and candidate genes (CaSR, AIRE, GATA3 and 22q11-deletion) were sequenced for classification of etiology. RESULTS: We identified 522 patients (511 alive) and estimated overall prevalence at 102 per million divided among post-surgical HP (64 per million), non-surgical HP (30 per million) and pseudo-HP (8 per million). Non-surgical HP comprised autosomal dominant hypocalcemia (21%), autoimmune polyendocrine syndrome type 1 (17%), DiGeorge/22q11 deletion syndrome (15%), idiopathic HP (44%), and others, 4%. Among the 283 respondents (median age 53 years (range 9-89), 75% females), seven formerly classified as idiopathic were reclassified after genetic and immunological analyses, whereas 26 (17% of non-surgical HP) remained idiopathic. Most were treated with vitamin D (94%) and calcium (70%), and 10 received parathyroid hormone. HP patients scored significantly worse than the normative population on SF-36 and HADS; patients with post-surgical scored worse than those with non-surgical HP and pseudo-HP, especially on physical health. CONCLUSIONS: We found higher prevalence of non-surgical HP in Norway than reported elsewhere. Genetic testing and autoimmunity screening of idiopathic HP identified a specific cause in 21%. Further research is necessary to unravel the causes of idiopathic HP and to improve the reduced HRQoL reported by HP patients

Multiwavelength studies of MHD waves in the solar chromosphere: An overview of recent results

The chromosphere is a thin layer of the solar atmosphere that bridges the relatively cool photosphere and the intensely heated transition region and corona. Compressible and incompressible waves propagating through the chromosphere can supply significant amounts of energy to the interface region and corona. In recent years an abundance of high-resolution observations from state-of-the-art facilities have provided new and exciting ways of disentangling the characteristics of oscillatory phenomena propagating through the dynamic chromosphere. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate the role waves play in supplying energy to sustain chromospheric and coronal heating. Here, we review the recent progress made in characterising, categorising and interpreting oscillations manifesting in the solar chromosphere, with an impetus placed on their intrinsic energetics.Comment: 48 pages, 25 figures, accepted into Space Science Review