Remarks on the rings of functions which have a finite numb er of di scontinuities

[EN] Let X be an arbitrary topological space. F(X) denotes the set of all real-valued functions on X and C(X)F denotes the set of all f ∈ F(X) such that f is discontinuous at most on a finite set. It is proved that if r is a positive real number, then for any f ∈ C(X)F which is not a unit of C(X)F there exists g ∈ C(X)F such that g ≠ 1 and f = gr f. We show that every member of C(X)F is continuous on a dense open subset of X if and only if every non-isolated point of X is nowhere dense. It is shown that C(X)F is an Artinian ring if and only if the space X is finite. We also provide examples to illustrate the results presented herein.Department of pure Mathematics Yazd university. We record our pleasure to the anonymous referee for his or her constructive report and many helpful suggestions on the main results of the earlier version of the manuscript which improved the presentation of the paper.Ahmadi Zand, MR.; Khosravi, Z. (2021). Remarks on the rings of functions which have a finite numb er of di scontinuities. Applied General Topology. 22(1):139-147. https://doi.org/10.4995/agt.2021.14332OJS139147221M. R. Ahmadi Zand, An algebraic characterization of Blumberg spaces, Quaest. Math. 33, no. 2 (2010), 223-230. https://doi.org/10.2989/16073606.2010.491188A. J. Berrick and M. E. Keating, An Introduction to Rings and Modules, Cambridge University Press, 2000. https://doi.org/10.1017/9780511608674W. Dunham, T1/2 -spaces, Kyungpook Math. J. 17, no. 2 (1977), 161-169.R. Engelking, General Topology, Sigma Ser. Pure Math. 6, Heldermann-Verlag, Berlin, 1989.Z. Gharabaghi, M. Ghirati. and A. Taherifar, On the rings of functions which are discontinuous on a finite set, Houston J. Math. 44, no. 2 (2018), 721-739.L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, New York-Heidelberg, 1976.N. Levine, Generalized closed sets in topology. Rend. Circ. Mat. Palermo. 19, no. 2 (1970), 89-96. https://doi.org/10.1007/BF0284388

Mandibular second premolars with three root canals: A review and 3 case reports

ABSTRACT: Before initiating any endodontic therapy, probability of extra canals should be considered. The Incidence of three canals in mandibular second premolar has been reported to be 0.46-0.5%. The present report describes nonsurgical endodontic treatment of three mandibular second premolars with three canals. In these cases, three orifices were located in mesiobuccal, distobuccal and lingual. Mesiobuccal orifices were found after removing dentinal shelves. Even in teeth with extremely complex root canal morphologies, conventional endodontic treatment without surgical intervention can result in adequate healing, as in these cases. Clinicians should be aware of unusual root canal anatomy in mandibular premolars. Very careful examination of the pulpal space, preferably with an optical device is recommended to locate any unusual orifices

The Immediate Pain-Relieving Effects of Non-Thermal CO2 Laser Therapy on Genital Ulcers of Behcet’s Disease: A Case Report

Behçet’s disease (BD) is a chronic, relapsing, systemic vasculitis of unknown etiology. Oral and genital aphthous ulcers are considered as the hallmarks of BD. The genital ulcers of BD may be extremely painful and often refractory to multiple treatments. In addition, they exert a negative impact on the patient’s quality of life. Some investigations have demonstrated the significant and immediate pain-relieving effects of NTCLT (non-thermal CO2 laser therapy) on some oral lesions with no visible adverse effects. In this paper, we report a case of BD whose painful genital ulcers were irradiated with NTCLT and the patient’s pain caused by the ulcers relieved immediately and significantly with no visible complications

Role of decomposition products in the oxidation of cyclohexene using a manganese(III) complex

Metal complexes are extensively explored as catalysts for oxidation reactions; molecular-based mechanisms are usually proposed for such reactions. However, the roles of the decomposition products of these materials in the catalytic process have yet to be considered for these reactions. Herein, the cyclohexene oxidation in the presence of manganese(III) 5,10,15,20-tetra(4-pyridyl)-21H,23H-porphine chloride tetrakis(methochloride) (1) in a heterogeneous system via loading the complex on an SBA-15 substrate is performed as a study case. A molecular-based mechanism is usually suggested for such a metal complex. Herein, 1 was selected and investigated under the oxidation reaction by iodosylbenzene or (diacetoxyiodo)benzene (PhI(OAc)2). In addition to 1, at least one of the decomposition products of 1 formed during the oxidation reaction could be considered a candidate to catalyze the reaction. First-principles calculations show that Mn dissolution is energetically feasible in the presence of iodosylbenzene and trace amounts of water

Covalent modification of reduced graphene oxide with piperazine as a novel nanoadsorbent for removal of H2S gas

In the present research, piperazine grafted-reduced graphene oxide RGO-N-(piperazine) was synthesized through a three-step reaction and employed as a highly efficient nanoadsorbent for H2S gas removal. Temperature optimization within the range of 30–90 °C was set which significantly improved the adsorption capacity of the nanoadsorbent. The operational conditions including the initial concentration of H2S (60,000 ppm) with CH4 (15 vol%), H2O (10 vol%), O2 (3 vol%) and the rest by helium gas and gas hour space velocity (GHSV) 4000–6000 h−1 were examined on adsorption capacity. The results of the removal of H2S after 180 min by RGO-N-(piperazine), reduced graphene oxide (RGO), and graphene oxide (GO) were reported as 99.71, 99.18, and 99.38, respectively. Also, the output concentration of H2S after 180 min by RGO-N-(piperazine), RGO, and GO was found to be 170, 488, and 369 ppm, respectively. Both chemisorption and physisorption are suggested as mechanism in which the chemisorption is based on an acid–base reaction between H2S and amine, epoxy, hydroxyl functional groups on the surface of RGO-N-(piperazine), GO, and RGO. The piperazine augmentation of removal percentage can be attributed to the presence of amine functional groups in the case of RGO-N-(piperazine) versus RGO and GO. Finally, analyses of the equilibrium models used to describe the experimental data showed that the three-parameter isotherm equations Toth and Sips provided slightly better fits compared to the three-parameter isotherms

Global, regional, and national burden of stroke and its risk factors, 1990–2019: a systematic analysis for the Global Burden of Disease Study 2019

Background Regularly updated data on stroke and its pathological types, including data on their incidence, prevalence, mortality, disability, risk factors, and epidemiological trends, are important for evidence-based stroke care planning and resource allocation. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) aims to provide a standardised and comprehensive measurement of these metrics at global, regional, and national levels. Methods We applied GBD 2019 analytical tools to calculate stroke incidence, prevalence, mortality, disability-adjusted life-years (DALYs), and the population attributable fraction (PAF) of DALYs (with corresponding 95% uncertainty intervals [UIs]) associated with 19 risk factors, for 204 countries and territories from 1990 to 2019. These estimates were provided for ischaemic stroke, intracerebral haemorrhage, subarachnoid haemorrhage, and all strokes combined, and stratified by sex, age group, and World Bank country income level. Findings In 2019, there were 12·2 million (95% UI 11·0–13·6) incident cases of stroke, 101 million (93·2–111) prevalent cases of stroke, 143 million (133–153) DALYs due to stroke, and 6·55 million (6·00–7·02) deaths from stroke. Globally, stroke remained the second-leading cause of death (11·6% [10·8–12·2] of total deaths) and the third-leading cause of death and disability combined (5·7% [5·1–6·2] of total DALYs) in 2019. From 1990 to 2019, the absolute number of incident strokes increased by 70·0% (67·0–73·0), prevalent strokes increased by 85·0% (83·0–88·0), deaths from stroke increased by 43·0% (31·0–55·0), and DALYs due to stroke increased by 32·0% (22·0–42·0). During the same period, age-standardised rates of stroke incidence decreased by 17·0% (15·0–18·0), mortality decreased by 36·0% (31·0–42·0), prevalence decreased by 6·0% (5·0–7·0), and DALYs decreased by 36·0% (31·0–42·0). However, among people younger than 70 years, prevalence rates increased by 22·0% (21·0–24·0) and incidence rates increased by 15·0% (12·0–18·0). In 2019, the age-standardised stroke-related mortality rate was 3·6 (3·5–3·8) times higher in the World Bank low-income group than in the World Bank high-income group, and the age-standardised stroke-related DALY rate was 3·7 (3·5–3·9) times higher in the low-income group than the high-income group. Ischaemic stroke constituted 62·4% of all incident strokes in 2019 (7·63 million [6·57–8·96]), while intracerebral haemorrhage constituted 27·9% (3·41 million [2·97–3·91]) and subarachnoid haemorrhage constituted 9·7% (1·18 million [1·01–1·39]). In 2019, the five leading risk factors for stroke were high systolic blood pressure (contributing to 79·6 million [67·7–90·8] DALYs or 55·5% [48·2–62·0] of total stroke DALYs), high body-mass index (34·9 million [22·3–48·6] DALYs or 24·3% [15·7–33·2]), high fasting plasma glucose (28·9 million [19·8–41·5] DALYs or 20·2% [13·8–29·1]), ambient particulate matter pollution (28·7 million [23·4–33·4] DALYs or 20·1% [16·6–23·0]), and smoking (25·3 million [22·6–28·2] DALYs or 17·6% [16·4–19·0]). Interpretation The annual number of strokes and deaths due to stroke increased substantially from 1990 to 2019, despite substantial reductions in age-standardised rates, particularly among people older than 70 years. The highest age-standardised stroke-related mortality and DALY rates were in the World Bank low-income group. The fastest-growing risk factor for stroke between 1990 and 2019 was high body-mass index. Without urgent implementation of effective primary prevention strategies, the stroke burden will probably continue to grow across the world, particularly in low-income countries.publishedVersio

Global, regional, and national burden of stroke and its risk factors, 1990-2019: a systematic analysis for the Global Burden of Disease Study 2019

Background Regularly updated data on stroke and its pathological types, including data on their incidence, prevalence, mortality, disability, risk factors, and epidemiological trends, are important for evidence-based stroke care planning and resource allocation. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) aims to provide a standardised and comprehensive measurement of these metrics at global, regional, and national levels. Methods We applied GBD 2019 analytical tools to calculate stroke incidence, prevalence, mortality, disability-adjusted life-years (DALYs), and the population attributable fraction (PAF) of DALYs (with corresponding 95% uncertainty intervals UIs]) associated with 19 risk factors, for 204 countries and territories from 1990 to 2019. These estimates were provided for ischaemic stroke, intracerebral haemorrhage, subarachnoid haemorrhage, and all strokes combined, and stratified by sex, age group, and World Bank country income level. Findings In 2019, there were 12.2 million (95% UI 11.0-13.6) incident cases of stroke, 101 million (93.2-111) prevalent cases of stroke, 143 million (133-153) DALYs due to stroke, and 6.55 million (6.00-7.02) deaths from stroke. Globally, stroke remained the second-leading cause of death (11.6% 10.8-12.2] of total deaths) and the third-leading cause of death and disability combined (5.7% 5.1-6.2] of total DALYs) in 2019. From 1990 to 2019, the absolute number of incident strokes increased by 70.0% (67.0-73.0), prevalent strokes increased by 85.0% (83.0-88.0), deaths from stroke increased by 43.0% (31.0-55.0), and DALYs due to stroke increased by 32.0% (22.0-42.0). During the same period, age-standardised rates of stroke incidence decreased by 17.0% (15.0-18.0), mortality decreased by 36.0% (31.0-42.0), prevalence decreased by 6.0% (5.0-7.0), and DALYs decreased by 36.0% (31.0-42.0). However, among people younger than 70 years, prevalence rates increased by 22.0% (21.0-24.0) and incidence rates increased by 15.0% (12.0-18.0). In 2019, the age-standardised stroke-related mortality rate was 3.6 (3.5-3.8) times higher in the World Bank low-income group than in the World Bank high-income group, and the age-standardised stroke-related DALY rate was 3.7 (3.5-3.9) times higher in the low-income group than the high-income group. Ischaemic stroke constituted 62.4% of all incident strokes in 2019 (7.63 million 6.57-8.96]), while intracerebral haemorrhage constituted 27.9% (3.41 million 2.97-3.91]) and subarachnoid haemorrhage constituted 9.7% (1.18 million 1.01-1.39]). In 2019, the five leading risk factors for stroke were high systolic blood pressure (contributing to 79.6 million 67.7-90.8] DALYs or 55.5% 48.2-62.0] of total stroke DALYs), high body-mass index (34.9 million 22.3-48.6] DALYs or 24.3% 15.7-33.2]), high fasting plasma glucose (28.9 million 19.8-41.5] DALYs or 20.2% 13.8-29.1]), ambient particulate matter pollution (28.7 million 23.4-33.4] DALYs or 20.1% 16.6-23.0]), and smoking (25.3 million 22.6-28.2] DALYs or 17.6% 16.4-19.0]). Interpretation The annual number of strokes and deaths due to stroke increased substantially from 1990 to 2019, despite substantial reductions in age-standardised rates, particularly among people older than 70 years. The highest age-standardised stroke-related mortality and DALY rates were in the World Bank low-income group. The fastest-growing risk factor for stroke between 1990 and 2019 was high body-mass index. Without urgent implementation of effective primary prevention strategies, the stroke burden will probably continue to grow across the world, particularly in low-income countries

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BACKGROUND Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. METHODS The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model-a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates-with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality-which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. FINDINGS The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2-100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1-290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1-211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4-48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3-37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7-9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. INTERPRETATION Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. FUNDING Bill & Melinda Gates Foundation

Global, regional, and national burden of disorders affecting the nervous system, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BackgroundDisorders affecting the nervous system are diverse and include neurodevelopmental disorders, late-life neurodegeneration, and newly emergent conditions, such as cognitive impairment following COVID-19. Previous publications from the Global Burden of Disease, Injuries, and Risk Factor Study estimated the burden of 15 neurological conditions in 2015 and 2016, but these analyses did not include neurodevelopmental disorders, as defined by the International Classification of Diseases (ICD)-11, or a subset of cases of congenital, neonatal, and infectious conditions that cause neurological damage. Here, we estimate nervous system health loss caused by 37 unique conditions and their associated risk factors globally, regionally, and nationally from 1990 to 2021.MethodsWe estimated mortality, prevalence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs), with corresponding 95% uncertainty intervals (UIs), by age and sex in 204 countries and territories, from 1990 to 2021. We included morbidity and deaths due to neurological conditions, for which health loss is directly due to damage to the CNS or peripheral nervous system. We also isolated neurological health loss from conditions for which nervous system morbidity is a consequence, but not the primary feature, including a subset of congenital conditions (ie, chromosomal anomalies and congenital birth defects), neonatal conditions (ie, jaundice, preterm birth, and sepsis), infectious diseases (ie, COVID-19, cystic echinococcosis, malaria, syphilis, and Zika virus disease), and diabetic neuropathy. By conducting a sequela-level analysis of the health outcomes for these conditions, only cases where nervous system damage occurred were included, and YLDs were recalculated to isolate the non-fatal burden directly attributable to nervous system health loss. A comorbidity correction was used to calculate total prevalence of all conditions that affect the nervous system combined.FindingsGlobally, the 37 conditions affecting the nervous system were collectively ranked as the leading group cause of DALYs in 2021 (443 million, 95% UI 378–521), affecting 3·40 billion (3·20–3·62) individuals (43·1%, 40·5–45·9 of the global population); global DALY counts attributed to these conditions increased by 18·2% (8·7–26·7) between 1990 and 2021. Age-standardised rates of deaths per 100 000 people attributed to these conditions decreased from 1990 to 2021 by 33·6% (27·6–38·8), and age-standardised rates of DALYs attributed to these conditions decreased by 27·0% (21·5–32·4). Age-standardised prevalence was almost stable, with a change of 1·5% (0·7–2·4). The ten conditions with the highest age-standardised DALYs in 2021 were stroke, neonatal encephalopathy, migraine, Alzheimer's disease and other dementias, diabetic neuropathy, meningitis, epilepsy, neurological complications due to preterm birth, autism spectrum disorder, and nervous system cancer.InterpretationAs the leading cause of overall disease burden in the world, with increasing global DALY counts, effective prevention, treatment, and rehabilitation strategies for disorders affecting the nervous system are needed

Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

Funder: European Society of Intensive Care Medicine; doi: http://dx.doi.org/10.13039/501100013347Funder: Flemish Society for Critical Care NursesAbstract: Purpose: Intensive care unit (ICU) patients are particularly susceptible to developing pressure injuries. Epidemiologic data is however unavailable. We aimed to provide an international picture of the extent of pressure injuries and factors associated with ICU-acquired pressure injuries in adult ICU patients. Methods: International 1-day point-prevalence study; follow-up for outcome assessment until hospital discharge (maximum 12 weeks). Factors associated with ICU-acquired pressure injury and hospital mortality were assessed by generalised linear mixed-effects regression analysis. Results: Data from 13,254 patients in 1117 ICUs (90 countries) revealed 6747 pressure injuries; 3997 (59.2%) were ICU-acquired. Overall prevalence was 26.6% (95% confidence interval [CI] 25.9–27.3). ICU-acquired prevalence was 16.2% (95% CI 15.6–16.8). Sacrum (37%) and heels (19.5%) were most affected. Factors independently associated with ICU-acquired pressure injuries were older age, male sex, being underweight, emergency surgery, higher Simplified Acute Physiology Score II, Braden score 3 days, comorbidities (chronic obstructive pulmonary disease, immunodeficiency), organ support (renal replacement, mechanical ventilation on ICU admission), and being in a low or lower-middle income-economy. Gradually increasing associations with mortality were identified for increasing severity of pressure injury: stage I (odds ratio [OR] 1.5; 95% CI 1.2–1.8), stage II (OR 1.6; 95% CI 1.4–1.9), and stage III or worse (OR 2.8; 95% CI 2.3–3.3). Conclusion: Pressure injuries are common in adult ICU patients. ICU-acquired pressure injuries are associated with mainly intrinsic factors and mortality. Optimal care standards, increased awareness, appropriate resource allocation, and further research into optimal prevention are pivotal to tackle this important patient safety threat