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

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

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 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&apos; evolutionary concept development method. A literature search using the keywords &quot;cultural nursing competence&quot;, &quot;intercultural nursing competence&quot;, &quot;cultural nursing&quot;, &quot;cultural health nursing&quot;, and &quot;cultural competence&quot; 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

The Mechanism Underlying the Antibacterial Activity of Shikonin against Methicillin-Resistant Staphylococcus aureus

Shikonin (SKN), a highly liposoluble naphthoquinone pigment isolated from the roots of Lithospermum erythrorhizon, is known to exert antibacterial, wound-healing, anti-inflammatory, antithrombotic, and antitumor effects. The aim of this study was to examine SKN antibacterial activity against methicillin-resistant Staphylococcus aureus (MRSA). The SKN was analyzed in combination with membrane-permeabilizing agents Tris and Triton X-100, ATPase inhibitors sodium azide and N,N′-dicyclohexylcarbodiimide, and S. aureus-derived peptidoglycan; the effects on MRSA viability were evaluated by the broth microdilution method, time-kill test, and transmission electron microscopy. Addition of membrane-permeabilizing agents or ATPase inhibitors together with a low dose of SKN potentiated SKN anti-MRSA activity, as evidenced by the reduction of MRSA cell density by 75% compared to that observed when SKN was used alone; in contrast, addition of peptidoglycan blocked the antibacterial activity of SKN. The results indicate that the anti-MRSA effect of SKN is associated with its affinity to peptidoglycan, the permeability of the cytoplasmic membrane, and the activity of ATP-binding cassette (ABC) transporters. This study revealed the potential of SKN as an effective natural antibiotic and of its possible use to substantially reduce the use of existing antibiotic may also be important for understanding the mechanism underlying the antibacterial activity of natural compounds