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A Note on the Solution of the Von Kármán Equations Using Series and Chebyshev Spectral Methods
Makukula ZodwaG,Sibanda Precious,Motsa SandileSydney
Boundary Value Problems , 2010,
Abstract: The classical von Kármán equations governing the boundary layer flow induced by a rotating disk are solved using the spectral homotopy analysis method and a novel successive linearisation method. The methods combine nonperturbation techniques with the Chebyshev spectral collocation method, and this study seeks to show the accuracy and reliability of the two methods in finding solutions of nonlinear systems of equations. The rapid convergence of the methods is determined by comparing the current results with numerical results and previous results in the literature.
Implementation of Objective Structured Clinical Examination for Assessing Nursing Students’ Clinical Competencies: Lessons and Implications  [PDF]
Patricia Katowa-Mukwato, Lonia Mwape, Marjorie Kabinga-Makukula, Prudencia Mweemba, Margaret C. Maimbolwa
Creative Education (CE) , 2013, DOI: 10.4236/ce.2013.410A008
Abstract: Objective Structured Clinical Examination (OSCE) as a performance-based assessment method is a well established student assessment tool. Its popularity in the assessment of clinical competence is well documented and prominent in situations where reliability and content validity are fundamental. In this paper, we describe the implementation of OSCE in the Department of Nursing Sciences; University of Zambia for assessment of nursing students’ clinical competencies. The implementation process followed an eight step-approach from which several lessons were drawn and implications were generated. Major lessons included the need for adequate preparation of faculty and students, which is a fundamental ingredient to ensure reliability of the examination, and in minimizing stress and anxiety respectively. Following the implementation we acknowledged that OSCEs are suitable for testing clinical, technical and practical skills which may not be adequately assessed through traditional assessment methods as they possess the ability to improve the validity and reliability of assessments. Nevertheless, careful consideration should be taken to avoid entirely relying on OSCE as the only means of assessing clinical competencies.
On New Numerical Techniques for the MHD Flow Past a Shrinking Sheet with Heat and Mass Transfer in the Presence of a Chemical Reaction
Z. G. Makukula,P. Sibanda,S. S. Motsa,S. Shateyi
Mathematical Problems in Engineering , 2011, DOI: 10.1155/2011/489217
Abstract: We use recent innovative solution techniques to investigate the problem of MHD viscous flow due to a shrinking sheet with a chemical reaction. A comparison is made of the convergence rates, ease of use, and expensiveness (the number of iterations required to give convergent results) of three seminumerical techniques in solving systems of nonlinear boundary value problems. The results were validated using a multistep, multimethod approach comprising the use of the shooting method, the Matlab bvp4c numerical routine, and with results in the literature. 1. Introduction Boundary layer flow over a stretching surface occurs in several engineering processes such as hot rolling, wire drawing, and glass-fibre production. Materials that are manufactured by extrusion processes and heat-treated substances proceeding between a feed roll and a wind-up roll can be classified as a continuously stretching surface [1–3]. A shrinking film is useful in the packaging of bulk products since it can be unwrapped easily with adequate heat [4–7]. Shrinking problems can also be applied to the study of capillary effects in small pores and the hydraulic properties of agricultural clay soils [8]. Studies of flow due to a shrinking sheet with heat transfer and/or mass transfer have been considered by, among others, [7, 9]. In recent years, several analytical or semianalytical methods have been proposed and used to find solutions to most nonlinear equations. These methods include the Adomian decomposition method (ADM) [10, 11], differential transform method (DTM) [12], variational iteration method (VIM) [13], homotopy analysis method (HAM) [14–17], and Homotopy perturbation method (HPM) [18–23]. Motsa and Shateyi [24] obtained a numerical solution of magnetohydrodynamic (MHD) and rotating flow over a porous shrinking sheet by the new approach known as spectral homotopy analysis method (SHAM). Muhaimin et al. [5] studied magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The study found out that the shrinking of the sheet has a substantial effect on the flow field and, thus, on the heat and mass transfer rate from the sheet to the fluid. In this paper we provide a qualitative assessment of key features of three recent seminumerical techniques, namely, the successive linearisation method (SLM), the spectral-homotopy analysis method (SHAM), and the improved spectral-homotopy analysis method (ISHAM). The two methods were introduced and used by Motsa and his coworkers (see Motsa et al. [25, 26] and Makukula et al. [27–30]) to solve nonlinear boundary
A Novel Numerical Technique for Two-Dimensional Laminar Flow between Two Moving Porous Walls
Zodwa G. Makukula,Precious Sibanda,Sandile S. Motsa
Mathematical Problems in Engineering , 2010, DOI: 10.1155/2010/528956
Abstract: We investigate the steady two-dimensional flow of a viscous incompressible fluid in a rectangular domain that is bounded by two permeable surfaces. The governing fourth-order nonlinear differential equation is solved by applying the spectral-homotopy analysis method and a novel successive linearisation method. Semianalytical results are obtained and the convergence rate of the solution series was compared with numerical approximations and with earlier results where the homotopy analysis and homotopy perturbation methods were used. We show that both the spectral-homotopy analysis method and successive linearisation method are computationally efficient and accurate in finding solutions of nonlinear boundary value problems. 1. Introduction Laminar viscous flow in tubes that allow seepage across contracting or expanding permeable walls is encountered in the transport of biological fluids such as blood and filtration in kidneys and lungs. Such flows have many other practical applications such as in binary gas diffusion, chromatography, ion exchange, and ground water movement [1–6]. In addition, flow in channels with permeable walls provides a good starting point for the study of flow in multichannel filtration systems such as the wall flow monolith filter used to reduce emissions from diesel engines introduced by Oxarango et al. in [7]. Consequently, in the past four decades a considerable amount of research effort has been expended in the study of laminar flows in rectangular domains that are bounded by permeable walls [8–15]. The equations governing such flows are generally nonlinear and in the past asymptotic techniques, and numerical methods have been used to analyze such flows and to solve the equations; for example, in the pioneering study by Berman [8] asymptotic methods were used to solve the steady flow problem for small suction. In the study by Uchida and Aoki [16], numerical methods were used to solve the governing nonlinear equations and to explain the flow characteristics. Majdalani and Roh [4] and Majdalani [3] studied the oscillatory channel flow with wall injection, and the resulting governing equations were solved using asymptotic formulations (WKB and multiple-scale techniques). The multiple-scale solution was found to be advantageous over the others in that its leading-order term is simpler and more accurate than other formulations, and it displayed clearly the relationship between the physical parameters that control the final motion. It also provided means of quantifying important flow features such as corresponding vortical wave
On a linearisation method for Reiner-Rivlin swirling flow
Makukula, Zodwa G.;Sibanda, Precious;Motsa, Sandile S.;
Computational & Applied Mathematics , 2012, DOI: 10.1590/S1807-03022012000100006
Abstract: the steady flow of a reiner-rivlin fluid with joule heating and viscous dissipationis studied. we present a novel technique for accelerating the convergence of the spectral-homotopy analysis method. solutions of the nonlinear momentum and energy equations are obtained using the improved spectral homotopy analysis method. solutions were also generated using the spectral-homotopy analysis method and benchmarked against results in the literature. mathematical subject classification: primary: 76a05, 76n05; secondary: 76m25.
Stress and Coping Mechanisms Among Breast Cancer Patients and Family Caregivers: A Review of Literature
KP Mukwato, P Mweemba, MK Makukula, MM Makoleka
Medical Journal of Zambia , 2010,
Abstract: Background: Breast cancer is the most common malignancy of women worldwide accounting for 23% of all newly diagnosed cancer cases. It is also the leading cause of cancer mortality, representing 14.1%. In Zambia, it is second to cervical cancer and its incidence is steadily increasing. A diagnosis of cancer regardless of stage is a stressful event impacting on all facets of the patient’s life and that of her family caregivers. To minimize the impact, adaptive coping mechanisms are required. Aim of the review: The aim of the review was to gain an in-depth understanding of the stress and coping mechanisms used by breast cancer patients and family caregivers. Materials and methods: A comprehensive review of publications for the period 1980-2010 cited on Pub Med, Hinari, British National Index, African Journal Online was undertaken. Search terms included “stress”, “coping”, “breast cancer”, “coping mechanisms”, “coping mechanisms by breast cancer patients and family care givers”. Search Results: Of the 22 articles reviewed, 13 focused on coping with breast cancer, 5 on stress and adaptation to cancer and the last 4 on experiences of family members on care of the terminally ill. Eighteen of the 22 used solely qualitative methodology while 4 used mixed methods. Analysis of the articles revealed 4 predominant coping mechanisms for both the patient and family: (a) seeking social support, (b) reliance on God, (c) positive suggestion/attitude or re-affirmation and (d) acquisition of information and education. Conclusions: A diagnosis of breast cancer is a stressor to both the patient and the family caregivers.Coping mechanisms/strategies are therefore required in order to adapt.
Quality of Life and Adherence to Antiretroviral Drugs
P Mweemba, MK Makukula, PK Mukwato, MM Makoleka
Medical Journal of Zambia , 2010,
Abstract: Introduction: Antiretroviral therapy has led to a substantial reduction in HIV-associated morbidity and mortality. Efficacy of antiretroviral treatment in HIV/AIDS is showing inhibition of viral replication and reduction of viral load to a point where viral particles are undetectable in the blood of infected individuals. This has led to the realization that HIV/AIDS is a chronic illness and hence the quality of life of PLWHAneeds to be enhanced. Purpose: The purpose of this literature review is to analyze quality of life and adherence to antiretroviral drugs. Method: A comprehensive analysis of articles obtained from CINHAL, PUBMED, AIDSLINE, PSYCINFO, and Ohio link was conducted. Results: Quality of life has received special attention in the last decade because it has been recognized as an outcome of health care and a determinant of disease progression. Quality of life is a complex broad ranging multidimensional concept defined in terms of individual’s subjective experiences. The definition by the WHO is more appropriate because it is culturally sensitive. Studies can be undertaken to improve the understanding of quality of life concept itself and the extent to which it is individually, socially and culturally determined. Understanding the dimensions and linkages among the dimensions of quality of life will facilitate the design of optimally effective interventions and organizational structures for quality patient care and also provide information to reveal trends, suggest linkages between practice variations and patient outcomes and identify potentially problematic patterns of care. Antiretroviral regimens are demanding and difficult, with numerous possible side effects and patients need to take the pills for indefinite periods of time. Efficacy of antiretroviral drugs in HIV/AIDS is showing inhibition of viral replication and reduction of viral load to a point where viral particles are undetectable in the blood of infected individuals. Persons with HIV/AIDS that adhere to medication for at least one year are less likely to experience AIDS related mortality. Hence adherence to antiretroviral regimens is imperative not only for the health of individual patients but also for the health of the public as a whole. Determination of medication adherence leads to development of innovative, effective interventions needed to facilitate behavior change, improve quality of life and prevent resistance to antiretroviral drugs. Conclusion: The World Health Organization has developed a comprehensive culturally sensitive definition of quality of life. Generally, there is an agreement that quality of life should be measured subjectively from patient self reports and not from clinical assessments. However, there are very few interventions that have been developed to assist persons with HIV/AIDS improve their quality of life. Meanwhile studies on medication adherence have shown that there are three main ways of measuring medication adherence, pill count, self repo
A Note on the Solution of the Von Kármán Equations Using Series and Chebyshev Spectral Methods
Zodwa G. Makukula,Precious Sibanda,Sandile Sydney Motsa
Boundary Value Problems , 2010, DOI: 10.1155/2010/471793
Abstract:
Numerical Analysis for the Synthesis of Biodiesel Using Spectral Relaxation Method
Z. G. Makukula,S. S. Motsa,S. Shateyi
Mathematical Problems in Engineering , 2014, DOI: 10.1155/2014/601374
Abstract: Biodiesel is an alternative diesel fuel chemically defined as the mono-alkyl esters of long chain fatty acids derived from vegetable oils or animal fat. It is becoming more attractive as an alternative fuel due to the depleting fossil fuel resources. A mathematical model for the synthesis of biodiesel from vegetable oils and animal fats is presented in this study. Numerical solutions of the model are found using a spectral relaxation method. The method, originally developed for boundary value problems, is an iterative scheme based on the Chebyshev spectral collocation method developed by decoupling systems of equations using Gauss-Seidel type of techniques. The effects of the reaction rate constants and initial concentrations of the reactants on the amount of the final product are being investigated. The accuracy of the numerical results is validated by comparison with known analytical results and numerical results obtained using ode45, an efficient explicit 4th and 5th order Runge-Kutta method used to integrate both linear and nonlinear differential equations. 1. Introduction Due to the continuous uncertainty and increasing environmental impact associated with the utilization of petroleum-based diesel fuel, the demands for alternative fuels have increased considerably in recent years [1]. Methyl and ethyl esters derived from vegetable oil or animal fat, known as biodiesel, have good potential as alternative diesel fuel [2]. Biodiesel is synthesized through a chemical process called transesterification. During this chemical process, triglycerides in vegetable oils or animal fats react with short chain alcohols such as methanol and ethanol in the presence of homogeneous basic catalysts such as sodium hydroxide and potassium hydroxide to form fatty acid methyl esters (biodiesel) and glycerin [3, 4]. Biodiesel has many advantages over petroleum-based diesel fuels. It is biodegradable and nontoxic and produce less particles, smoke, and carbon monoxide [2]. It is also renewable and usable in a variety of diesel engines with minimum or no modification necessary [3, 5]. It burns clean, and do not form engine deposits or generate harmful pollutants which results in a significant reduction of the types of pollutants that contribute to pollution and global warming and releases up to 85% fewer cancer-causing agents [6–10]. Experiments have been carried out to investigate different aspects in the production of biodiesel [3, 4, 11–15]. In this work, we carry out a numerical study of the transesterification process for the synthesis of biodiesel from vegetable oils.
Use of Social Media to Support Nursing Students’ Learning in Zambia  [PDF]
Ruth Wahila, Lonia Mwape, Kestone Lyambai, Marjorie Kabinga-Makukula
Creative Education (CE) , 2018, DOI: 10.4236/ce.2018.98092
Abstract: This studyseeks?to explore the use of social mediato support the learning of nursing students in Zambia. Data was collected from the WhatsApp and email conversation chats involving 76 nursing students at the University of Zambia School. The content of the conversation chats was analyzed in terms of common themes, patterns and interrelationships.It was established that nursing students can take a leading role in empowering themselves by taking charge of their continued learning by using social media responsibly. Key findings that emerged from the WhatsApp and e-mail discussions are: Knowledge enhancement and sharing of best practices were?significant in the WhatsApp Group, Virtual Classroom community, was significantly stronger in the WhatsApp group, WhatsApp group had a minimally more positive placement experience, other measures (social capital/knowledge application/learning dimension community) did not differ significantly. The use of social mobile media is not only limited to professional nurses but also nursing students. As the training of nurse professionals evolves?in the midst of high technology use, more and more students may seek to prefer the use of social mobile media as a tool for continuous learning. In comparison to the email platform, students in the WhatsApp were able to maintain conversations up to the end of the allocated period of the study. The information gathered from this project can be useful to fostering a unified understanding of professional knowledge and a feeling of belongingness among nursing students.
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