Ball convergence for Steffensen-type fourth-order methods

We present a local convergence analysis for a family of Steffensen-type fourth-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as [1], [5]-[28] using hypotheses up to the fifth derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study

Unified Ball Convergence of Inexact Methods For Finding Zeros with Multiplicity

We present an extended ball convergence of inexact methods for approximating a zero of a nonlinear equation with multiplicity m; where m is a natural number. Many popular methods are special cases of the inexact method

Extending the Applicability of an Efficient Fifth Order Method Under Weak Conditions in Banach Space

We extend the applicability of an efficient fifth order method for solving Banach space valued equations. To achieve this we use weaker Lipschitz-type conditions in combination with our idea of the restricted convergence region. Numerical examples are used to compare our results favorably to the ones in earlier works

Fine structure in the {\alpha}-decay of odd-even nuclei

Systematic study on {\alpha}-decay fine structure is presented for the first time in the case of odd-even nuclei in the range 83 \leq Z \leq 101. The model used for the study is the recently proposed Coulomb and proximity potential model for deformed nuclei (CPPMDN), which employs deformed Coulomb potential, deformed two term proximity potential and centrifugal potential. The computed partial half lives, total half lives and branching ratios are compared with experimental data and are in good agreement. The standard deviation of partial half-life is 1.08 and that for branching ratio is 1.21. Our formalism is also successful in predicting angular momentum hindered and structure hindered transitions. The present study reveals that CPPMDN is a unified theory which is successful in explaining alpha decay from ground and isomeric state; and alpha fine structure of even-even, even-odd and odd-even nuclei. Our study relights that the differences in the parent and daughter surfaces or the changes in the deformation parameters as well as the shell structure of the parent and daughter nuclei, influences the alpha decay probability.Comment: 35 pages, 5 figure

THE EFFECTS OF PARENTING STYLES ON ACADEMIC ACHIEVEMENT AND SCHOOL ADJUSTMENT AMONG HIGH SCHOOL STUDENTS IN NAGALAND, INDIA: THE MEDIATING EFFECTS OF ATTACHMENT DIMENSIONS, ACADEMIC SELF-EFFICACY AND EMOTIONAL REGULATION

The present study attempted to examine the mediating effects of adolescent attachment, emotional regulation and academic self-efficacy between parenting styles, academic achievement, and school adjustment among high school students in Nagaland, India. Furthermore, it investigated whether the structure of direct and indirect structural relationships hypothesized varies as a function of their parents’ genders. The participants of this study were high school students from Nagaland, India. The questionnaire consisted of the following scales: Parenting Authority Scale, Adolescent Attachment Questionnaire, Academic Self-efficacy Scale, Difficulties in Emotion Regulation Scale, College Adjustment Test and GPA. In order to meet the study's objectives, three studies were designed and conducted via SEM and AMOS with the purpose to investigate the direct and indirect effects of parenting styles on academic achievement and school adjustment among high school students in Nagaland, India: the mediating effects of attachment dimensions, academic self-efficacy, and emotional regulation. The results revealed that authoritarian parenting style had direct correlation with academic achievement and that authoritarian and permissive parenting styles had indirectly effect on school adjustment mediated by adolescent attachment and emotional regulation. The pattern of structural relationships hypothesized for the proposed model parenting styles the result found it operate differently for fathers and mothers. There were neither direct nor indirect correlation between the predictor and the outcome in the case of the fathers parenting style in this sample group. But in the case of the mother, authoritarian parenting style had direct significant correlation with academic achievement and significant correlation between school adjustment and lack of angry distress, goal-corrected partnership, and emotional regulation. The study's limitations, implications, and future avenues were also discussed

ROLE OF ANTIDEPRESSANT ON THE GLYCAEMIC CONTROL OF UNCONTROLLED TYPE 2 DIABETES MELLITUS PATIENTS

Background: Depression incidence is higher in diabetic patients when compared to the non-diabetic individuals and there exist a two-directional relationship between depression and the development of type 2 diabetes mellitus. Objectives: This study aimed to estimate the frequency of depression and the effect of antidepressant on glycemic control in type 2 diabetes mellitus patients. Methods: This prospective interventional study was conducted in type 2 diabetes mellitus patients with a sample size of 100. These patients were diagnosed with depression using WHO-ICD10 criteria. All study patients had uncontrolled blood glucose levels and were on an optimized maximal dose of combination oral hypoglycemic agents with stable glycoregulation (HbA1c 8.4 ±0.5) were taken up for the intervention with antidepressant. These patients were started on with antidepressant after enrollment and followed up for fasting blood sugar (FBS), post-prandial blood sugar (PPBS), and HbA1c at the end of 3 months and 6 months. And also Hamilton depression rating scale scores were estimated at the beginning of the study and at the end of 6 months. Results: The frequency of depression among the type 2 diabetes mellitus patients was found to be 42%. There were reduction of mean FBS levels from baseline value of 177 mg/dl to follow-up value of 160 mg/dl (p<0.001), mean PPBS levels from 251.16 mg/dl to 217.84 mg/dl (p<0.001), and mean HbA1c dropped from 8.41 to 7.57 (p<0.001) after the treatment with antidepressant. Conclusion: Our study concluded that patient started on antidepressant showed a reduction in the blood sugar levels and HbA1c levels from their baseline values, which was clinically and statistically significant

On Newton's method for subanalytic equations

We present local and semilocal convergence results for Newton’s method in order to approximate solutions of subanalytic equations. The local convergence results are given under weaker conditions than in earlier studies such as [9], [10], [14], [15], [24], [25], [26], resulting to a larger convergence ball and a smaller ratio of convergence. In the semilocal convergence case contravariant conditions not used before are employed to show the convergence of Newton’s method. Numerical examples illustrating the advantages of our approach are also presented in this study

Expanding the applicability of Newton-Tikhonov method for ill-posed equations

We present a new semilocal convergence analysis of Newton- Tikhonov methods for solving ill-posed operator equations in a Hilbert space setting. Using more precise majorizing sequences and under the same computational cost as in earlier studies such as [13]-[20], we provide: weaker sufficient convergence criteria; tighter error estimates on the distances involved and an at least as precise information on the location of the solution. Applications include Hammertein nonlinear integral equations

Local convergence analysis of two competing two-step iterative methods free of derivatives for solving equations and systems of equations

We present the local convergence analysis of two-step iterative methods free of derivatives for solving equations and systems of equations under similar hypotheses based on Lipschitz-type conditions. The methods are in particular useful for solving equations or systems involving non-differentiable terms. A comparison is also provided using suitable numerical example

Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence

We present a local convergence analysis Potra-Ptak-type method with optimal fourth order of convergence in order to approximate a solution of a nonlinear equation. In earlier studies such as [1], [5]-[28] hypotheses up to the fourth derivative are used. In this paper we use hypotheses up to the first derivative only, so that the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study