Positive Numbers Divisible by their Iterative Digit Sum Revisited

This paper is about the existence of numbers divisible by their iterative digit sum (NDIDS). Three conjectures were proposed, firstly, 9 multiply a NDIDS produces a multiple NDIDS. Secondly, there are no 15 or more consecutive NDIDS in the sequence of positive integers. Lastly, all Niven numbers are also NDIDS but the converse is not true. The detailed composition, properties, sequences and comparison with Niven numbers of NDIDS are discusse

On Some Notes on the Engel Expansion of Ratios of Sequences Obtained from the Sum of Digits of Squared Positive Integers

Objective: To introduce a new novel approach to the understanding of Engel expansions of ratios of number sequences. Methodology: Let C be the ratios of consecutive elements of sequence obtained from the sum of digits of squared positive integers and D be the ratios of consecutive elements of sequence that is the complement of C but the domain is the positive integer. Engel series expansions and Pierce expansion were obtained for C while only Engel series expansions were obtained for D. Findings: The distance between the respective Engel series and their means for the two sequences are neither unique nor uniformly distributed. The finite Engel series elements of the mean may not be the member of the series. The research will help in examining the amount of variance or divergence or how different rational numbers varies in a given sequenc

Global age-sex-specific mortality, life expectancy, and population estimates in 204 countries and territories and 811 subnational locations, 1950–2021, and the impact of the COVID-19 pandemic: a comprehensive demographic analysis for the Global Burden of Disease Study 2021

Background: Estimates of demographic metrics are crucial to assess levels and trends of population health outcomes. The profound impact of the COVID-19 pandemic on populations worldwide has underscored the need for timely estimates to understand this unprecedented event within the context of long-term population health trends. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 provides new demographic estimates for 204 countries and territories and 811 additional subnational locations from 1950 to 2021, with a particular emphasis on changes in mortality and life expectancy that occurred during the 2020–21 COVID-19 pandemic period. Methods: 22 223 data sources from vital registration, sample registration, surveys, censuses, and other sources were used to estimate mortality, with a subset of these sources used exclusively to estimate excess mortality due to the COVID-19 pandemic. 2026 data sources were used for population estimation. Additional sources were used to estimate migration; the effects of the HIV epidemic; and demographic discontinuities due to conflicts, famines, natural disasters, and pandemics, which are used as inputs for estimating mortality and population. Spatiotemporal Gaussian process regression (ST-GPR) was used to generate under-5 mortality rates, which synthesised 30 763 location-years of vital registration and sample registration data, 1365 surveys and censuses, and 80 other sources. ST-GPR was also used to estimate adult mortality (between ages 15 and 59 years) based on information from 31 642 location-years of vital registration and sample registration data, 355 surveys and censuses, and 24 other sources. Estimates of child and adult mortality rates were then used to generate life tables with a relational model life table system. For countries with large HIV epidemics, life tables were adjusted using independent estimates of HIV-specific mortality generated via an epidemiological analysis of HIV prevalence surveys, antenatal clinic serosurveillance, and other data sources. Excess mortality due to the COVID-19 pandemic in 2020 and 2021 was determined by subtracting observed all-cause mortality (adjusted for late registration and mortality anomalies) from the mortality expected in the absence of the pandemic. Expected mortality was calculated based on historical trends using an ensemble of models. In location-years where all-cause mortality data were unavailable, we estimated excess mortality rates using a regression model with covariates pertaining to the pandemic. Population size was computed using a Bayesian hierarchical cohort component model. Life expectancy was calculated using age-specific mortality rates and standard demographic methods. Uncertainty intervals (UIs) were calculated for every metric using the 25th and 975th ordered values from a 1000-draw posterior distribution. Findings: Global all-cause mortality followed two distinct patterns over the study period: age-standardised mortality rates declined between 1950 and 2019 (a 62·8% [95% UI 60·5–65·1] decline), and increased during the COVID-19 pandemic period (2020–21; 5·1% [0·9–9·6] increase). In contrast with the overall reverse in mortality trends during the pandemic period, child mortality continued to decline, with 4·66 million (3·98–5·50) global deaths in children younger than 5 years in 2021 compared with 5·21 million (4·50–6·01) in 2019. An estimated 131 million (126–137) people died globally from all causes in 2020 and 2021 combined, of which 15·9 million (14·7–17·2) were due to the COVID-19 pandemic (measured by excess mortality, which includes deaths directly due to SARS-CoV-2 infection and those indirectly due to other social, economic, or behavioural changes associated with the pandemic). Excess mortality rates exceeded 150 deaths per 100 000 population during at least one year of the pandemic in 80 countries and territories, whereas 20 nations had a negative excess mortality rate in 2020 or 2021, indicating that all-cause mortality in these countries was lower during the pandemic than expected based on historical trends. Between 1950 and 2021, global life expectancy at birth increased by 22·7 years (20·8–24·8), from 49·0 years (46·7–51·3) to 71·7 years (70·9–72·5). Global life expectancy at birth declined by 1·6 years (1·0–2·2) between 2019 and 2021, reversing historical trends. An increase in life expectancy was only observed in 32 (15·7%) of 204 countries and territories between 2019 and 2021. The global population reached 7·89 billion (7·67–8·13) people in 2021, by which time 56 of 204 countries and territories had peaked and subsequently populations have declined. The largest proportion of population growth between 2020 and 2021 was in sub-Saharan Africa (39·5% [28·4–52·7]) and south Asia (26·3% [9·0–44·7]). From 2000 to 2021, the ratio of the population aged 65 years and older to the population aged younger than 15 years increased in 188 (92·2%) of 204 nations. Interpretation: Global adult mortality rates markedly increased during the COVID-19 pandemic in 2020 and 2021, reversing past decreasing trends, while child mortality rates continued to decline, albeit more slowly than in earlier years. Although COVID-19 had a substantial impact on many demographic indicators during the first 2 years of the pandemic, overall global health progress over the 72 years evaluated has been profound, with considerable improvements in mortality and life expectancy. Additionally, we observed a deceleration of global population growth since 2017, despite steady or increasing growth in lower-income countries, combined with a continued global shift of population age structures towards older ages. These demographic changes will likely present future challenges to health systems, economies, and societies. The comprehensive demographic estimates reported here will enable researchers, policy makers, health practitioners, and other key stakeholders to better understand and address the profound changes that have occurred in the global health landscape following the first 2 years of the COVID-19 pandemic, and longer-term trends beyond the pandemic

Adaptive vector precoding for multiuser MIMO OFDM

This paper presents an adaptive vector precoding schemes for the downlink multiuser multiple input multiple-output orthogonal frequency division multiplexing systems (MIMO OFDM) with multiple data streams per user. The zf precoder requires pseudo inversion of the channel matrix, where this operation is only optimum when the transmitter power is unconstrained. This paper presents efficient methods to reduce the computational load of the algorithm by interpolating the precoding and decoding matrices corresponding to different OFDM subcarriers. In the feedback scenario, the precoder matrix has to be designed for all subcarriers and can get positively large. The precoded MIMO OFDM systems will adapt to change in channel characteristics due to the automatic updating. This approach yields an improvement to the bit error rate probability by approximately an order of magnitude as compared to the ZF approach, utilizing other channel decomposition techniques. In comparison to Moore-Penrose pseudo inverse an increase in the capacity of the MIMO OFDM, with less computational complexity is achieved

A Prospective Study of Spectrum, Risk Factors and Immediate Outcome of Congenital Anomalies in Bida, North Central Nigeria

Background: Congenital disorders are structural, metabolic, behavioral and functional disorders that are present at birth. Their manifestations are protean ranging from mild anomalies to life‑threatening conditions. Aim: The objectives of this study were to describe the congenital anomalies in children seen at Federal Medical Center, Bida over a 12 month period, determine possible factors associated with these anomalies; and their short term outcome. Subjects and Methods: Children with clinically recognized congenital malformations were recruited consecutively over a 12 month period and socio‑demographic, etiologic and other relevant clinical data were obtained. A detailed examination was also performed and abnormalities documented. The data was analyzed using Epi‑info version 6 (Atlanta, USA). The Chi‑square was used to identify significant differences for categorical variables. Mid‑P and Fisher’s exact tests were utilized as appropriate. A P < 0.05 was considered to be significant.Results: A total of 46 children with congenital anomalies were seen during the study period, all which were recruited into the study. The hospital based prevalence amongst neonates was 111/1000 neonates. The most common system affected was the digestive system (50.0%) followed by the central nervous system and head and neck anomalies. There was no significant difference in distribution of anomalies amongst the various ethnic groups. About 22% of families were consanguineous, all being first cousins and 8.7% of mothers were greater than 35 years of age. The case fatality rate for congenital malformations was 2.2%, while 60.9% were referred to other hospitals for further care. Conclusion: The study has demonstrated a wide variety of congenital anomalies in Bida, North‑Central Nigeria with the digestive system anomalies being the most frequent. The findings of this study strengthen the need for empowerment of the institution in appropriate management of these disorders.Keywords: Anomalies, Bida, Congenital malformation

Personal name in Igbo Culture: A dataset on randomly selected personal names and their statistical analysis

This data article contains the statistical analysis of Igbo personal names and a sample of randomly selected of such names. This was presented as the following: 1). A simple random sampling of some Igbo personal names and their respective gender associated with each name. 2). The distribution of the vowels, consonants and letters of alphabets of the personal names. 3). The distribution of name length. 4). The distribution of initial and terminal letters of Igbo personal names. The significance of the data was discussed. Keywords: Igbo name, Personal name, Statistics, Distribution, Linguistics, Onomastic

Fixed‐dose combination therapy‐based protocol compared with free pill combination protocol: Results of a cluster randomized trial

Abstract Fixed‐dose combination (FDC) therapy is recommended for hypertension management in Nigeria based on randomized trials at the individual level. This cluster‐randomized trial evaluates effectiveness and safety of a treatment protocol that used two‐drug FDC therapy as the second and third steps for hypertension control compared with a protocol that used free pill combinations. From January 2021 to June 2021, 60 primary healthcare centers in the Federal Capital Territory of Nigeria were randomized to a protocol using FDC therapy as second and third steps compared with a protocol that used the same medications in free pill combination therapy for these steps. Eligible patients were adults (≥18 years) with hypertension. The primary outcome was the odds of a patient being controlled at their last visit between baseline to 6‐month follow‐up in the FDC group compared to the free pill group. 4427 patients (mean [SD] age: 49.0 [12.4] years, 70.5% female) were registered with mean (SD) baseline systolic/diastolic blood pressure 155 (20.6)/96 (13.1) mm Hg. Baseline characteristics of groups were similar. After 6‐months, hypertension control rate improved in the two treatment protocols, but there were no differences between the groups after adjustment (FDC = 53.9% versus free pill combination = 47.9%, cluster‐adjusted p = .29). Adverse events were similarly low (<1%) in both groups. Both protocols improved hypertension control rates at 6‐months in comparison to baseline, though no differences were observed between groups. Further work is needed to determine if upfront FDC therapy is more effective and efficient to improve hypertension control rates

Changes in body mass index and hemoglobin concentration in breastfeeding women living with HIV with a CD4 count over 350: Results from 4 African countries (The ANRS 12174 trial)

Introduction: Breastfeeding is recommended for infants born to HIV-infected women in low-income settings. Both breastfeeding and HIV-infection are energy demanding. Our objective was to explore how exclusive and predominant breastfeeding changes body mass index (BMI) among breastfeeding HIV1-positive women participating in the ANRS12174 trial (clinical trial no NCT0064026). Methods: HIV-positive women (n = 1 267) with CD4 count >350, intending to breastfeed HIV-negative infants were enrolled from Burkina Faso, South Africa, Uganda and Zambia and counselled on breastfeeding. N = 1 216 were included in the analysis. The trial compared Lamivudine and Lopinavir/Ritonavir as a peri-exposure prophylaxis. We ran a linear mixed-effect model with BMI as the dependent variable and exclusive or predominant breastfeeding duration as the key explanatory variable. Results: Any breastfeeding or exclusive/predominant) breastfeeding was initiated by 99.6% and 98.6% of the mothers respectively in the first week after birth. The median (interquartile range: IQR) duration of the group that did any breastfeeding or the group that did exclusive /predominant breastfeeding were 9.5 (7.5; 10.6) and 5.8 (5.6; 5.9)) months, respectively. The median (IQR) age, BMI, CD4 count, and HIV viral load at baseline (day 7) were 27 (23.3; 31) years, 23.7 (21.3; 27.0) kg/m2, 530 (432.5; 668.5) cells/μl and 0.1 (0.8; 13.7)1000 copies/mL, respectively. No major change in mean BMI was seen in this cohort over a 50-week period during lactation. The mean change between 26 and 50 weeks after birth was 0.7 kg/m2. Baseline mean BMI (measured on day 7 postpartum) and CD4 count were positively associated with maternal BMI change, with a mean increase of 1.0 kg/m2 (0.9; 1.0) per each additional baseline-BMI kilogram and 0.3 kg/m2 (0.2; 0.5) for each additional CD4 cell/μl, respectively. Conclusion: Breastfeeding was not negatively correlated with the BMI of HIV-1 infected Sub-Saharan African mothers. However, a higher baseline BMI and a CD4 count >500 cells/μl were associated with maternal BMI during the exclusive/ predominant breastfeeding period. Considering the benefits of breast milk for the infants and the recurrent results from different studies that breastfeeding is not harmful to the HIV-1-infected mothers, this study also supports the WHO 2016 guidelines on infant feeding that mothers living with HIV should breastfeed where formula is not safe for at least 12 months and up to 24 months, given that the right treatment or prophylaxis for the infection is administered. These findings and conclusions cannot be extrapolated to women who are immune-compromised or have AIDS

Adaptation of the Wound Healing Questionnaire universal-reporter outcome measure for use in global surgery trials (TALON-1 study): mixed-methods study and Rasch analysis

BackgroundThe Bluebelle Wound Healing Questionnaire (WHQ) is a universal-reporter outcome measure developed in the UK for remote detection of surgical-site infection after abdominal surgery. This study aimed to explore cross-cultural equivalence, acceptability, and content validity of the WHQ for use across low- and middle-income countries, and to make recommendations for its adaptation.MethodsThis was a mixed-methods study within a trial (SWAT) embedded in an international randomized trial, conducted according to best practice guidelines, and co-produced with community and patient partners (TALON-1). Structured interviews and focus groups were used to gather data regarding cross-cultural, cross-contextual equivalence of the individual items and scale, and conduct a translatability assessment. Translation was completed into five languages in accordance with Mapi recommendations. Next, data from a prospective cohort (SWAT) were interpreted using Rasch analysis to explore scaling and measurement properties of the WHQ. Finally, qualitative and quantitative data were triangulated using a modified, exploratory, instrumental design model.ResultsIn the qualitative phase, 10 structured interviews and six focus groups took place with a total of 47 investigators across six countries. Themes related to comprehension, response mapping, retrieval, and judgement were identified with rich cross-cultural insights. In the quantitative phase, an exploratory Rasch model was fitted to data from 537 patients (369 excluding extremes). Owing to the number of extreme (floor) values, the overall level of power was low. The single WHQ scale satisfied tests of unidimensionality, indicating validity of the ordinal total WHQ score. There was significant overall model misfit of five items (5, 9, 14, 15, 16) and local dependency in 11 item pairs. The person separation index was estimated as 0.48 suggesting weak discrimination between classes, whereas Cronbach's α was high at 0.86. Triangulation of qualitative data with the Rasch analysis supported recommendations for cross-cultural adaptation of the WHQ items 1 (redness), 3 (clear fluid), 7 (deep wound opening), 10 (pain), 11 (fever), 15 (antibiotics), 16 (debridement), 18 (drainage), and 19 (reoperation). Changes to three item response categories (1, not at all; 2, a little; 3, a lot) were adopted for symptom items 1 to 10, and two categories (0, no; 1, yes) for item 11 (fever).ConclusionThis study made recommendations for cross-cultural adaptation of the WHQ for use in global surgical research and practice, using co-produced mixed-methods data from three continents. Translations are now available for implementation into remote wound assessment pathways