Decomposition of the unitary representation of SU(1,1) on the unit disk into irreducible components

In this thesis, we decompose the representation of SU(1,1) on the unit disk into ir reducible components. We start with the decomposition over the maximal compact subgroup K, we identify the modules of eigenfunctions which are square integrable with respect to the quasi invariant measure on the unit disk. These modules rep resent the discrete series representations. Then, we use the induction in stages method to find the principal series representation. The matrix coefficient with the principal series and a K-invariant vector turns to be an important function which is called a spherical function. There is a nice function (Harish Chandra’s function) controlling the decay of the spherical function at infinity. Finally, we use a new approach to find the inversion formula which is equivalent to decomposition into irreducible representations using the geometry of cycles with dual numbers and the covariant transform

Content Analysis of Essential Economic Values in the Vocational Textbook as Compared to the Saudi Arabian Education Policy Document

This study explores the extent to which five essential economic values related to the themes of production, savings, moderation in expenditure, labor, and economic development were included in the Saudi Arabian Educational Policy Document and their reflection in a high school vocational textbook. A systematic quantitative descriptive approach was used to analyze the contents of the two documents. Results showed that the Education Policy Document only included the production domain value. The vocational textbook did not significantly include all economic values, except the theme related to respecting and the value of time. This means that the two documents should be revised to include these important economic values, as they are important for students’ future

SARS-CoV-2 vaccination modelling for safe surgery to save lives: data from an international prospective cohort study

Background: Preoperative SARS-CoV-2 vaccination could support safer elective surgery. Vaccine numbers are limited so this study aimed to inform their prioritization by modelling. Methods: The primary outcome was the number needed to vaccinate (NNV) to prevent one COVID-19-related death in 1 year. NNVs were based on postoperative SARS-CoV-2 rates and mortality in an international cohort study (surgical patients), and community SARS-CoV-2 incidence and case fatality data (general population). NNV estimates were stratified by age (18-49, 50-69, 70 or more years) and type of surgery. Best- and worst-case scenarios were used to describe uncertainty. Results: NNVs were more favourable in surgical patients than the general population. The most favourable NNVs were in patients aged 70 years or more needing cancer surgery (351; best case 196, worst case 816) or non-cancer surgery (733; best case 407, worst case 1664). Both exceeded the NNV in the general population (1840; best case 1196, worst case 3066). NNVs for surgical patients remained favourable at a range of SARS-CoV-2 incidence rates in sensitivity analysis modelling. Globally, prioritizing preoperative vaccination of patients needing elective surgery ahead of the general population could prevent an additional 58 687 (best case 115 007, worst case 20 177) COVID-19-related deaths in 1 year. Conclusion: As global roll out of SARS-CoV-2 vaccination proceeds, patients needing elective surgery should be prioritized ahead of the general population