Submanifolds in five-dimensional pseudo-Euclidean spaces and four-dimensional FRW universes

Equations for submanifolds, which correspond to embeddings of the four-dimensional FRW universes in five-dimensional pseudo-Euclidean spaces, are presented in convenient form in general case. Several specific examples are considered.Comment: 7 pages, LaTeX, the mathematical part of this paper is based on the withdrawn preprint arXiv:1012.0320 [gr-qc

Spatial, temporal, and demographic patterns in prevalence of smoking tobacco use and attributable disease burden in 204 countries and territories, 1990-2019 : a systematic analysis from the Global Burden of Disease Study 2019

Background Ending the global tobacco epidemic is a defining challenge in global health. Timely and comprehensive estimates of the prevalence of smoking tobacco use and attributable disease burden are needed to guide tobacco control efforts nationally and globally. Methods We estimated the prevalence of smoking tobacco use and attributable disease burden for 204 countries and territories, by age and sex, from 1990 to 2019 as part of the Global Burden of Diseases, Injuries, and Risk Factors Study. We modelled multiple smoking-related indicators from 3625 nationally representative surveys. We completed systematic reviews and did Bayesian meta-regressions for 36 causally linked health outcomes to estimate non-linear dose-response risk curves for current and former smokers. We used a direct estimation approach to estimate attributable burden, providing more comprehensive estimates of the health effects of smoking than previously available. Findings Globally in 2019, 1.14 billion (95% uncertainty interval 1.13-1.16) individuals were current smokers, who consumed 7.41 trillion (7.11-7.74) cigarette-equivalents of tobacco in 2019. Although prevalence of smoking had decreased significantly since 1990 among both males (27.5% [26. 5-28.5] reduction) and females (37.7% [35.4-39.9] reduction) aged 15 years and older, population growth has led to a significant increase in the total number of smokers from 0.99 billion (0.98-1.00) in 1990. Globally in 2019, smoking tobacco use accounted for 7.69 million (7.16-8.20) deaths and 200 million (185-214) disability-adjusted life-years, and was the leading risk factor for death among males (20.2% [19.3-21.1] of male deaths). 6.68 million [86.9%] of 7.69 million deaths attributable to smoking tobacco use were among current smokers. Interpretation In the absence of intervention, the annual toll of 7.69 million deaths and 200 million disability-adjusted life-years attributable to smoking will increase over the coming decades. Substantial progress in reducing the prevalence of smoking tobacco use has been observed in countries from all regions and at all stages of development, but a large implementation gap remains for tobacco control. Countries have a dear and urgent opportunity to pass strong, evidence-based policies to accelerate reductions in the prevalence of smoking and reap massive health benefits for their citizens. Copyright (C) 2021 The Author(s). Published by Elsevier Ltd.Peer reviewe

Causes of blindness and vision impairment in 2020 and trends over 30 years, and prevalence of avoidable blindness in relation to VISION 2020: The Right to Sight: An analysis for the Global Burden of Disease Study

Background: Many causes of vision impairment can be prevented or treated. With an ageing global population, the demands for eye health services are increasing. We estimated the prevalence and relative contribution of avoidable causes of blindness and vision impairment globally from 1990 to 2020. We aimed to compare the results with the World Health Assembly Global Action Plan (WHA GAP) target of a 25% global reduction from 2010 to 2019 in avoidable vision impairment, defined as cataract and undercorrected refractive error. Methods: We did a systematic review and meta-analysis of population-based surveys of eye disease from January, 1980, to October, 2018. We fitted hierarchical models to estimate prevalence (with 95% uncertainty intervals [UIs]) of moderate and severe vision impairment (MSVI; presenting visual acuity from \u3c6/18 to 3/60) and blindness (\u3c3/60 or less than 10° visual field around central fixation) by cause, age, region, and year. Because of data sparsity at younger ages, our analysis focused on adults aged 50 years and older. Findings: Global crude prevalence of avoidable vision impairment and blindness in adults aged 50 years and older did not change between 2010 and 2019 (percentage change −0·2% [95% UI −1·5 to 1·0]; 2019 prevalence 9·58 cases per 1000 people [95% IU 8·51 to 10·8], 2010 prevalence 96·0 cases per 1000 people [86·0 to 107·0]). Age-standardised prevalence of avoidable blindness decreased by −15·4% [–16·8 to −14·3], while avoidable MSVI showed no change (0·5% [–0·8 to 1·6]). However, the number of cases increased for both avoidable blindness (10·8% [8·9 to 12·4]) and MSVI (31·5% [30·0 to 33·1]). The leading global causes of blindness in those aged 50 years and older in 2020 were cataract (15·2 million cases [9% IU 12·7–18·0]), followed by glaucoma (3·6 million cases [2·8–4·4]), undercorrected refractive error (2·3 million cases [1·8–2·8]), age-related macular degeneration (1·8 million cases [1·3–2·4]), and diabetic retinopathy (0·86 million cases [0·59–1·23]). Leading causes of MSVI were undercorrected refractive error (86·1 million cases [74·2–101·0]) and cataract (78·8 million cases [67·2–91·4]). Interpretation: Results suggest eye care services contributed to the observed reduction of age-standardised rates of avoidable blindness but not of MSVI, and that the target in an ageing global population was not reached. Funding: Brien Holden Vision Institute, Fondation Théa, The Fred Hollows Foundation, Bill & Melinda Gates Foundation, Lions Clubs International Foundation, Sightsavers International, and University of Heidelberg