Double Sawi Transform: Theory and Applications to Boundary Values Problems

Symmetry can play an important role in the study of boundary value problems, which are a type of problem in mathematics that involves finding the solutions to differential equations subject to given boundary conditions. Integral transforms play a crucial role in solving ordinary differential equations (ODEs), partial differential equations (PDEs), and integral equations. This article focuses on extending a single-valued Sawi transform to a double-valued ST, which we call the double Sawi (DS) transform. We derive some fundamental features and theorems for the proposed transform. Finally, we study the applications of the proposed transform by solving some boundary value problems such as the Fourier heat equation and the D’Alembert wave equation.The APC is supported by the Basque Government, Grant IT1555-22

Some new exact solutions of (4+1)-dimensional Davey–Stewartson-Kadomtsev–Petviashvili equation

Exact solutions of nonlinear equations have got formidable attraction of researchers because these solutions demonstrate the physical behaviour of a model. In this paper, we focus on extracting some new exact solutions of a (4+1)-dimensional Davey–Stewartson-Kadomtsev–Petviashvili (DSKP) equation. To find new travelling wave solutions of the DSKP equation, we use ()-expansion technique. The obtained solutions are in the form of the exponential and trigonometric functions. We obtain different kinds of waves solutions for specific values of parameters. We simulate the achieved solutions in 3D and 2D plots.The authors are grateful to the Basque Government, Spain for its support through Grant IT1555-22 and to MCIN/AEI 269.10.13039/5011 00011033 for Grant PID2021-1235430B-C21/C22. All authors approved the version of the manuscript to be published

Thermodynamic Geometry: Evolution, Correlation and Phase Transition

Under the fluctuation of the electric charge and atomic mass, this paper considers the theory of the thin film depletion layer formation of an ensemble of finitely excited, non-empty $d/f$-orbital heavy materials, from the thermodynamic geometric perspective. At each state of the local adiabatic evolutions, we examine the nature of the thermodynamic parameters, \textit{viz.}, electric charge and mass, changing at each respective embeddings. The definition of the intrinsic Riemannian geometry and differential topology offers the properties of (i) local heat capacities, (ii) global stability criterion and (iv) global correlation length. Under the Gaussian fluctuations, such an intrinsic geometric consideration is anticipated to be useful in the statistical coating of the thin film layer of a desired quality-fine high cost material on a low cost durable coatant. From the perspective of the daily-life applications, the thermodynamic geometry is thus intrinsically self-consistent with the theory of the local and global economic optimizations. Following the above procedure, the quality of the thin layer depletion could self-consistently be examined to produce an economic, quality products at a desired economic value.Comment: 22 pages, 5 figures, Keywords: Thermodynamic Geometry, Metal Depletion, Nano-science, Thin Film Technology, Quality Economic Characterization; added 1 figure and 1 section (n.10), and edited bibliograph

Behaviour change in perinatal care practices among rural women exposed to a women's group intervention in Nepal [ISRCTN31137309]

BACKGROUND: A randomised controlled trial of participatory women's groups in rural Nepal previously showed reductions in maternal and newborn mortality. In addition to the outcome data we also collected previously unreported information from the subgroup of women who had been pregnant prior to study commencement and conceived during the trial period. To determine the mechanisms via which the intervention worked we here examine the changes in perinatal care of these women. In particular we use the information to study factors affecting positive behaviour change in pregnancy, childbirth and newborn care. METHODS: Women's groups focusing on perinatal care were introduced into 12 of 24 study clusters (average cluster population 7000). A total of 5400 women of reproductive age enrolled in the trial had previously been pregnant and conceived during the trial period. For each of four outcomes (attendance at antenatal care; use of a boiled blade to cut the cord; appropriate dressing of the cord; not discarding colostrum) each of these women was classified as BETTER, GOOD, BAD or WORSE to describe whether and how she changed her pre-trial practice. Multilevel multinomial models were used to identify women most responsive to intervention. RESULTS: Among those not initially following good practice, women in intervention areas were significantly more likely to do so later for all four outcomes (OR 1.92 to 3.13). Within intervention clusters, women who attended groups were more likely to show a positive change than non-group members with regard to antenatal care utilisation and not discarding colostrum, but non-group members also benefited. CONCLUSION: Women's groups promoted significant behaviour change for perinatal care amongst women not previously following good practice. Positive changes attributable to intervention were not restricted to specific demographic subgroups

The association of maternal nutrition and children's pre-primary experience with over-age attendance in secondary school: evidence from lowland Nepal.

•Over-age attendance is increasing but remains under-studied in South Asia.•Children fall behind by entering pre-primary or primary late, and by repeating a grade during/after primary school.•Rural location, thin and uneducated mothers predicted late pre-primary entry.•Educational research and interventions need to focus on the earlier time-point of pre-primary.•Improving maternal nutrition and education may ensure timely progression of children in school

State-space Manifold and Rotating Black Holes

We study a class of fluctuating higher dimensional black hole configurations obtained in string theory/ $M$-theory compactifications. We explore the intrinsic Riemannian geometric nature of Gaussian fluctuations arising from the Hessian of the coarse graining entropy, defined over an ensemble of brane microstates. It has been shown that the state-space geometry spanned by the set of invariant parameters is non-degenerate, regular and has a negative scalar curvature for the rotating Myers-Perry black holes, Kaluza-Klein black holes, supersymmetric $AdS_5$ black holes, $D_1$-$D_5$ configurations and the associated BMPV black holes. Interestingly, these solutions demonstrate that the principal components of the state-space metric tensor admit a positive definite form, while the off diagonal components do not. Furthermore, the ratio of diagonal components weakens relatively faster than the off diagonal components, and thus they swiftly come into an equilibrium statistical configuration. Novel aspects of the scaling property suggest that the brane-brane statistical pair correlation functions divulge an asymmetric nature, in comparison with the others. This approach indicates that all above configurations are effectively attractive and stable, on an arbitrary hyper-surface of the state-space manifolds. It is nevertheless noticed that there exists an intriguing relationship between non-ideal inter-brane statistical interactions and phase transitions. The ramifications thus described are consistent with the existing picture of the microscopic CFTs. We conclude with an extended discussion of the implications of this work for the physics of black holes in string theory.Comment: 44 pages, Keywords: Rotating Black Holes; State-space Geometry; Statistical Configurations, String Theory, M-Theory. PACS numbers: 04.70.-s Physics of black holes; 04.70.Bw Classical black holes; 04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics; 04.50.Gh Higher-dimensional black holes, black strings, and related objects. Edited the bibliograph

Prevalence and determinants of caesarean section in private and public health facilities in underserved South Asian communities: cross-sectional analysis of data from Bangladesh, India and Nepal.

OBJECTIVES: To describe the prevalence and determinants of births by caesarean section in private and public health facilities in underserved communities in South Asia. DESIGN: Cross-sectional study. SETTING: 81 community-based geographical clusters in four locations in Bangladesh, India and Nepal (three rural, one urban). PARTICIPANTS: 45,327 births occurring in the study areas between 2005 and 2012. OUTCOME MEASURES: Proportion of caesarean section deliveries by location and type of facility; determinants of caesarean section delivery by location. RESULTS: Institutional delivery rates varied widely between settings, from 21% in rural India to 90% in urban India. The proportion of private and charitable facility births delivered by caesarean section was 73% in Bangladesh, 30% in rural Nepal, 18% in urban India and 5% in rural India. The odds of caesarean section were greater in private and charitable health facilities than in public facilities in three of four study locations, even when adjusted for pregnancy and delivery characteristics, maternal characteristics and year of delivery (Bangladesh: adjusted OR (AOR) 5.91, 95% CI 5.15 to 6.78; Nepal: AOR 2.37, 95% CI 1.62 to 3.44; urban India: AOR 1.22, 95% CI 1.09 to 1.38). We found that highly educated women were particularly likely to deliver by caesarean in private facilities in urban India (AOR 2.10; 95% CI 1.61 to 2.75) and also in rural Bangladesh (AOR 11.09, 95% CI 6.28 to 19.57). CONCLUSIONS: Our results lend support to the hypothesis that increased caesarean section rates in these South Asian countries may be driven in part by the private sector. They also suggest that preferences for caesarean delivery may be higher among highly educated women, and that individual-level and provider-level factors interact in driving caesarean rates higher. Rates of caesarean section in the private sector, and their maternal and neonatal health outcomes, require close monitoring

The Equity Impact of Community Women's Groups to Reduce Neonatal Mortality: A Meta-analysis of Four Cluster Randomized Trials

Socioeconomic inequalities in neonatal mortality are substantial in many developing countries. Little is known about how to address this problem. Trials in Asia and Africa have shown strong impacts on neonatal mortality of a participatory learning and action intervention with women’s groups. Whether this intervention also reduces mortality inequalities remains unknown. We describe the equity impact of this women’s groups intervention on the neonatal mortality rate (NMR) across socioeconomic strata. We conducted a meta-analysis of all four participatory women’s group interventions that were shown to be highly effective in cluster randomized trials in India, Nepal, Bangladesh and Malawi. We estimated intervention effects on NMR and health behaviours for lower and higher socioeconomic strata using random effects logistic regression analysis. Differences in effect between strata were tested. Analysis of 69120 live births and 2505 neonatal deaths shows that the intervention strongly reduced the NMR in lower (50–63% reduction depending on the measure of socioeconomic position used) and higher (35–44%) socioeconomic strata. The intervention did not show evidence of ‘elite-capture’: among the most marginalized populations, the NMR in intervention areas was 63% lower [95% confidence interval (CI) 48–74%] than in control areas, compared with 35% (95% CI: 15–50%) lower among the less marginalized in the last trial year (P-value for difference between most/less marginalized: 0.009). The intervention strongly improved home care practices, with no systematic socioeconomic differences in effect. Participatory women’s groups with high population coverage benefit the survival chances of newborns from all socioeconomic strata, and perhaps especially those born into the most deprived households

Cause-specific neonatal mortality: analysis of 3772 neonatal deaths in Nepal, Bangladesh, Malawi and India.

OBJECTIVE: Understanding the causes of death is key to tackling the burden of three million annual neonatal deaths. Resource-poor settings lack effective vital registration systems for births, deaths and causes of death. We set out to describe cause-specific neonatal mortality in rural areas of Malawi, Bangladesh, Nepal and rural and urban India using verbal autopsy (VA) data. DESIGN: We prospectively recorded births, neonatal deaths and stillbirths in seven population surveillance sites. VAs were carried out to ascertain cause of death. We applied descriptive epidemiological techniques and the InterVA method to characterise the burden, timing and causes of neonatal mortality at each site. RESULTS: Analysis included 3772 neonatal deaths and 3256 stillbirths. Between 63% and 82% of neonatal deaths occurred in the first week of life, and males were more likely to die than females. Prematurity, birth asphyxia and infections accounted for most neonatal deaths, but important subnational and regional differences were observed. More than one-third of deaths in urban India were attributed to asphyxia, making it the leading cause of death in this setting. CONCLUSIONS: Population-based VA methods can fill information gaps on the burden and causes of neonatal mortality in resource-poor and data-poor settings. Local data should be used to inform and monitor the implementation of interventions to improve newborn health. High rates of home births demand a particular focus on community interventions to improve hygienic delivery and essential newborn care