It is our purpose here to investigate the method of solving equations for real roots by Newton's Method and to indicate a generalization arising from this method.

Quantile is a basic and an important quantity of a random variable. In some distributions, their quantiles have closed-form expressions. However, for many continuous distributions, the closed-form expressions of their quantiles do not exist. Yu and Zelterman (2011) and Chang (2004) have proposed an approximation of quantiles. In this paper, we propose an improved method which is combined the Taylor expansion with Newton¡¦s method. Some examples are given to compare the computing time of the method we proposed with the methods in Yu and Zelterman (2011) and Chang (2004).

In this study, the use of robotics was explored in a Grade 12 Technical Sciences class, to further understand it as an emerging pedagogy that allows learners to apply creative thinking and produce innovative solutions to problems in Newton’s Second law of motion. The study's conceptual framework was underpinned by constructivism, constructionism and the Cognitive Refinement Instructional Approach (CRIA), which supports the notion that through assimilation and accommodation, Lego Mindstorms robotics tools can be used as manipulatives to develop new knowledge. The learners participating in this mixed-method procedure of enquiry were randomly assigned to an experimental group (n = 21) that took part in the robotics intervention and a control group (n = 21) that continued with conventional extra classes. It was evident in the qualitative results that learner’s knowledge improved regarding the concepts of acceleration and net force, but misconceptions persisted in the concepts of frictional force and tension force. In the analysis of the quantitative results, the independent-samples t-test showed that there was a significant difference in the post-test scores between the control group (M= 3.19, SD= 1.16) and experimental group (M=4.57, SD= 1.43); t(40)= 3.42, p = 0.001. The study found that robotics does have a significant effect on the academic test scores of Technical Sciences learners than the traditional intervention in Newton’s Second Law. The scientific merit and significance of this study will contribute to teaching methods and learning of science in the technical-academic schooling stream. / Dissertation (MEd)--University of Pretoria, 2021. / Science, Mathematics and Technology Education / MEd / Unrestricted

ABSTRACT The aim of this study was to investigate the effect of an active learning approach (ALA) on the achievement of 11 th grade learners in Newton’s laws of motion, The case study was done in one school by comparing the achievement of learners in Newton’s laws of motion through an Active Learning Approach (ALA) with that of learners taught through Traditional Direct I nstruction (TDI) and to determine whether learners taught with ALA retained the material better than those taught with TDI. Two grade 11 classes in one school in the Queenstown District of the Eastern Cape were selected on their performance in two differen t tests and used as case study . The Force Concept Inventory was used to determine the achievements and retention of knowledge of the two groups. The effect of the active lear ning approach on the treatment group was also measured by ask ing each learner in t he group to complete a learner assessment of instruction form. The treatment group was also subjected to a classroom group interview. T he following information emerged from the study: i) Learners taught using the ALA achieved significantly better in FCI pos t - test than those taught with traditional direct instruction. ii) In the retention of knowledge test, the mean score of the learners taught using the ALA was 4.8% higher than those taught with TDI although insignificant. iii) Learners subjected to the ALA liked the instructional approach and as such put in extra time to learn. The findings suggest that the active learning approach had positive effect on the achievement of the Grade 11 learners and thus, can be adapted to enhance learning in the classroom. / Physics

Charles University in Prague, Faculty of Pharmacy in Hradec Kralove Department of biophysics and physical chemistry Candidate: Bc. Jana Palátová Supervisor: Mgr. Monika Kuchařová, Ph.D. Title of thesis: The effect of natural cosmetics on chase the mechanical properties of the skin This thesis in theoretical part deals with the structure of skin, its biochemistry and functions. Discusses the changes that the skin undergoes during development and aging. It describes the mechanical properties of the skin and the discipline that deals with these characteristics. The practical part deals with the measurement of mechanical parameters of human skin after application of a natural cream. The trial involved a total of ten women were about the same age. Measurements were performed on a dynamic elastomers being developed at the Department of Biophysics and Physical Chemistry of the Faculty of Pharmacy at Charles University in Hradec Kralove. The investigated parameters were Hooke and Newton factor. Hooke's coefficient indicates the elasticity of the skin, Newton coefficient of its viscosity. The results show that the test cream affected as skin elasticity, and its viscosity. In 90 % of the test persons there was a significant increase in the values of the Hooke and Newton coefficient and the resulting effect...

Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of convergence. Different acceleration techniques are discussed with analysis of the asymptotic behavior of the iterates. Analogies between single variable and multivariable problems are detailed. We also explore some interesting phenomena while analyzing Newton's method for complex variables.

We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points al,...,am C Rn . This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structure makes it particularly amenable to solution by interior-point methods, and it has been the subject of much theoretical complexity analysis. Here we focus on computation. We present a combined interior-point and active-set method for solving this problem. Our computational results demonstrate that our method solves very large problem instances (m = 30, 000 and n = 30) to a high degree of accuracy in under 30 seconds on a personal computer.

Führungsgetriebe die durch Servomotoren angetrieben werden, benötigen für definierte Stellungen des Abtriebsglieds eine programmierte Funktion (elektronische Kurvenscheibe). Diese leitet sich aus dem möglicherweise fehlerbehafteten kinematischen Modell des Getriebes ab (inverse Kinematik). Zur Verbesserung der Genauigkeit der Führungsbewegung wird ein Verfahren zur Justierung der Übertragungsfunktion auf Basis des Newton-Verfahrens unter Nutzung der Singulärwertzerlegung vorgestellt. Dabei werden die realen Getriebeabmessungen anhand einer Messung berechnet und werden anschließend korrigiert zur Anpassung der Übertragungsfunktion verwendet.

Nonlinear algebraic equations (NAEs) occur in many areas of science and engineering. The process of solving these NAEs is generally difficult, from finding a good initial guess that leads to a desired solution to deciding on convergence criteria for the approximate solution. In practice, Newton's method is the only robust general-purpose method for solving a system of NAEs. Many variants of Newton's method exist. However, it is generally impossible to know a priori which variant of Newton's method will be effective for a given problem.<p>Many high-quality software libraries are available for the numerical solution of NAEs. However, the user usually has little control over many aspects of what the library does. For example, the user may not be able to easily switch between direct and indirect methods for the linear algebra. This thesis describes a problem-solving environment (PSE) called pythNon for studying the effects (e.g., performance) of different strategies for solving systems of NAEs. It provides the researcher, teacher, or student with a flexible environment for rapid prototyping and numerical experiments. In pythNon, users can directly influence the solution process on many levels, e.g., investigation of the effects of termination criteria and/or globalization strategies. In particular, to show the power, flexibility, and ease of use of the pythNon PSE, this thesis also describes the development of a novel forcing-term strategy for approximating the Newton direction efficiently in the pythNon PSE.

Nonlinear algebraic equations (NAEs) occur in many areas of science and engineering. The process of solving these NAEs is generally difficult, from finding a good initial guess that leads to a desired solution to deciding on convergence criteria for the approximate solution. In practice, Newton's method is the only robust general-purpose method for solving a system of NAEs. Many variants of Newton's method exist. However, it is generally impossible to know a priori which variant of Newton's method will be effective for a given problem.<p>Many high-quality software libraries are available for the numerical solution of NAEs. However, the user usually has little control over many aspects of what the library does. For example, the user may not be able to easily switch between direct and indirect methods for the linear algebra. This thesis describes a problem-solving environment (PSE) called pythNon for studying the effects (e.g., performance) of different strategies for solving systems of NAEs. It provides the researcher, teacher, or student with a flexible environment for rapid prototyping and numerical experiments. In pythNon, users can directly influence the solution process on many levels, e.g., investigation of the effects of termination criteria and/or globalization strategies. In particular, to show the power, flexibility, and ease of use of the pythNon PSE, this thesis also describes the development of a novel forcing-term strategy for approximating the Newton direction efficiently in the pythNon PSE.