A biparametric family of four-step sixteenth-order root-finding methods with the optimal efficiency index

AbstractA biparametric family of four-step multipoint iterative methods of order sixteen to solve nonlinear equations are developed and their convergence properties are established. The optimal efficiency indices are all found to be 161/5≈1.741101. Numerical examples as well as comparison with existing methods are demonstrated to verify the developed theory

Numerical Sensitivity Tests of Volatile Organic Compounds Emission to PM2.5 Formation during Heat Wave Period in 2018 in Two Southeast Korean Cities

A record-breaking severe heat wave was recorded in southeast Korea from 11 July to 15 August 2018, and the numerical sensitivity simulations of volatile organic compound (VOC) to secondarily generated particulate matter with diameter of less than 2.5 mu m (PM2.5) concentrations were studied in the Busan and Ulsan metropolitan areas in southeast Korea. A weather research and forecasting (WRF) model coupled with chemistry (WRF-Chem) was employed, and we carried out VOC emission sensitivity simulations to investigate variations in PM2.5 concentrations during the heat wave period that occurred from 11 July to 15 August 2018. In our study, when anthropogenic VOC emissions from the Comprehensive Regional Emissions Inventory for Atmospheric Transport Experiment-2015 (CREATE-2015) inventory were increased by approximately a factor of five in southeast Korea, a better agreement with observations of PM2.5 mass concentrations was simulated, implying an underestimation of anthropogenic VOC emissions over southeast Korea. The simulated secondary organic aerosol (SOA) fraction, in particular, showed greater dominance during high temperature periods such as 19-21 July, 2018, with the SOA fractions of 42.3% (in Busan) and 34.3% (in Ulsan) among a sub-total of seven inorganic and organic components. This is considerably higher than observed annual mean organic carbon (OC) fraction (28.4 +/- 4%) among seven components, indicating the enhancement of secondary organic aerosols induced by photochemical reactions during the heat wave period in both metropolitan areas. The PM2.5 to PM10 ratios were 0.69 and 0.74, on average, during the study period in the two cities. These were also significantly higher than the typical range in those cities, which was 0.5-0.6 in 2018. Our simulations implied that extremely high temperatures with no precipitation are significantly important to the secondary generation of PM2.5 with higher secondary organic aerosol fraction via photochemical reactions in southeastern Korean cities. Other possible relationships between anthropogenic VOC emissions and temperature during the heat wave episode are also discussed in this study

A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics

The article of record as published may be found at http://dx.doi.org/10.1016/j.amc.2015.08.039Under the assumption of the known multiplicity of zeros of nonlinear equations, a class of two-point sextic-order multiple-zero finders and their dynamics are investigated in this paper by means of extensive analysis of modified double-Newton type of methods. Wit the introduction of a bivariate weight function dependent on function-to-function and derivative-to-derivative ratios, higher-order convergence is obtained. Additional investigation is carried out for extraneous fixed points of the iterative maps associated with the proposed methods along with a comparison with typically selected cases. Through a variety of test equations, numerical experiments strongly support the theory developed in this paper. In addition, relevant dynamics of the proposed methods is successfully explored for various polynomials with a number of illustrative basins of attraction.National Research Foundation of KoreaMinistry of Education, Science and Technology under the research grant (Project Number: 2015-R1D1A3A-0102080

On developing a higher-order family of double-Newton methods with a bivariate weighting function

The article of record as published may be found at http://dx.doi.org/10.1016/j.amc.2014.12.130A high-order family of two-point methods costing two derivatives and two functions are developed by introducing a two-variable weighting function in the second step of the classical double-Newton method. Their theoretical and computational properties are fully investigated along with a main theorem describing the order of convergence and the asymptotic error constant as well as proper choices of special cases. A variety of concrete numerical examples and relevant results are extensively treated to verify the underlying theoretical development. In addition, this paper investigates the dynamics of rational iterative maps associated with the proposed method and an existing method based on illustrated description of basins of attraction for various polynomials

A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points

The article of record as published may be found at http://dx.doi.org/10.1016/j.amc.2016.02.029A class of three-point sixth-order multiple-root finders and the dynamics behind their extraneous fixed points are investigated by extending modified Newton-like methods with the introduction of the multivariate weight functions in the intermediate steps. The multivariate weight functions dependent on function-to-function ratios play a key role in constructing higher-order iterative methods. Extensive investigation of extraneous fixed points of the proposed iterative methods is carried out for the study of the dynamics associated with corresponding basins of attraction. Numerical experiments applied to a number of test equations strongly support the underlying theory pursued in this paper. Relevant dynamics of the proposed methods is well presented with a variety of illustrative basins of attraction applied to various test polynomials.Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education under the research grant (Project Number: 2015-R1D1A3A-01020808)Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education under the research grant (Project Number: 2015-R1D1A3A-01020808

On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics

With an error corrector via principal branch of the mth root of a function-to-function ratio, we propose optimal quartic-order multiple-root finders for nonlinear equations. The relevant optimal order satisfies Kung-Traub conjecture made in 1974. Numerical experiments performed for various test equations demonstrate convergence behavior agreeing with theory and the basins of attractions for several examples are presented

Development and Evaluation of Multilingual Education Materials to Promote Immigrant Women's Adaptation to Pregnancy

PURPOSE: This study was done to develop and evaluate multilingual education materials to promote health and adaptation to pregnancy for immigrant women in Korea. METHODS: This study had three procedures: First, contents of the education materials were developed according to pregnant women's needs, literature reviews, and group discussion. Details in contents were constructed based on Roy's adaptation model; Second, validity verification and translation of education materials were accomplished; Third, evaluation of the education materials was done through a survey of immigrant women. RESULTS: The education materials were developed in six languages (Korean, English, Chinese, Vietnamese, Filipino, and Cambodian). The title is "Healthy mother, happy family: eight-step guide to a healthy pregnancy". It was composed of an eight-step guide to healthy pregnancy, self-examination check list, websites for childbirth education and information, and guidelines on education materials in a brochure. In the evaluation, the average response score for the questionnaire items was high (3.23 on a four-point Likert scale). The average score for Cambodian immigrants was the highest of all immigrant women. CONCLUSION: Multilingual education materials developed in this research will help community health nurses to manage pregnancies for immigrant women and will be useful for health education for these women

A Concept Analysis of Cultural Nursing Competence

PURPOSE: The aim of this study was to conduct a concept analysis of cultural nursing competence. METHODS: Cultural nursing competence was analyzed using Rodgers' evolutionary concept development method. A literature search using the keywords "cultural nursing competence", "intercultural nursing competence", "cultural nursing", "cultural health nursing", and "cultural competence" was conducted in PubMed, CINAHL, ERIC, and RISS on material published before 2015. Database and bibliographic searches yielded 35 records. RESULTS: Cultural nursing competence comprised cognitive, affective, and behavioral domains. The critical attributes of the concept were sensitivity, equality, and activity. The analysis identified the following dimensions: awareness, openness, and coherence. The consequences of cultural nursing competence were personal satisfaction and social justice. The definition contained competence on both an individual and social level. CONCLUSION: Cultural competency enhances quality of care by narrowing health disparities and increasing client satisfaction. The concept analysis of cultural nursing competence may offer an acceptable framework which can be used to develop psychometric tools of this concept and provide guidelines in nursing practice

Effects of anxiety, depression, social support, and physical health status on the health-related quality of life of pregnant women in post-pandemic Korea: a cross-sectional study

Purpose This study aimed to examine the effects of anxiety, depression, social support, and physical health status on the health-related quality of life of Korean pregnant women using Spilker’s quality of life model. Methods This was a cross-sectional study with a correlational design. The participants included 166 pregnant women who were recruited via convenience sampling at two healthcare centers in South Korea. Questionnaires were collected from April 22 to May 29, 2023, in two cities in South Korea. The EuroQol-5D-3L, General Anxiety Disorder-7, Patient Health Questionnaire-2, Perceived Social Support through Others Scale-8, and EuroQol visual analog scale were used to assess the study variables. The t-test, Pearson correlation coefficients, and multiple regression tests were conducted using IBM SPSS ver. 26.0. Results Statistically significant correlations were identified between the health-related quality of life of pregnant women and anxiety (r=.29, p<.001), depression (r=.31, p<.001), social support (r=–.34, p<.001), and physical health status (r=–.44, p<.001). Physical health status (β=–.31, p<.001) and social support (β=–.21, p=.003) had the greatest effect on health-related quality of life (F=15.50, p<.001), with an explanatory power of 26.0%. Conclusion The health-related quality of life of pregnant women was affected by social support and physical health status. This study demonstrated that physical health and social support promotion can improve the health-related quality of life of pregnant women. Healthcare providers should consider integrating physical health into social support interventions for pregnant women in the post-pandemic era

A Survey on the Educational Needs and Competence of Nurses in Maternal Fetal Intensive Care Unit

PURPOSE: Maternal Fetal Intensive Care Unit (MFICU), which provides intensive care to high-risk mothers with increasing maternal age and high-risk newborns, has become a new field of nursing work in South Korea. The present study was conducted to identify the educational needs and self-assessing clinical competence of nurses in MFICU. METHODS: The education needs and competencies of MFICU nurses were measured through prepared questionnaires by researchers based on the previous studies on job analysis of nurses in MFICU. Data were collected from January 2019 to March 2019. The study involved 168 nurses working in MFICUs at 12 hospitals nationwide as study subjects. The data were analyzed using the SPSS WIN 23.0 program. RESULTS: The education needs of nurses in MFICU had an average of 4.21 points (±0.50) and their nursing competence was average 3.38 points (±0.60). The items reported as high education needs but low competency by nurses in MFICU were as following: ‘postpartum hemorrhage and shock,’ ‘cardiopulmonary resuscitation (CPR) for neonate,’ ‘CPR during pregnancy,’ ‘disseminated intravascular coagulation,’ ‘sepsis,’ and ‘mechanical ventilation during pregnancy.’ CONCLUSION: Based on these results, it is proposed that a comprehensive education program for nurses in MFICU should be developed by considering low capabilities among MFICU nurses as a priority factor