Geometrical interpretations of Bäcklund transformations and certain types of partial differential equations : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University

Page 37 is missing from the original copy.Gauss' Theorema Egregium contains a partial differential equation relating the Gaussian curvature K to components of the metric tensor and its derivatives. Well known partial differential equations such as the Schrödinger equation and the sine-Gordon equation correspond to this PDE for special choices of K and special coördinate systems. The sine-Gordon equation, for example, can be derived via Gauss' equation for K = –1 using the Tchebychef net as a coördinate system. In this thesis we consider a special class of Bäcklund Transformations which correspond to coördinate transformations on surfaces having a specified Gaussian curvature. These transformations lead to Gauss' PDE in different forms and provide a method for solving certain classes of non-linear second order partial differential equations. In addition, we develop a more systematic way to obtain a coordinate system for a more general class of PDE, such that this PDE corresponds to the Gauss equation

The limiting equivalent conductances of acid anions at 25�C

Imperial Users onl

Higher education in the Republic of Yemen : the University of Sana'a

Enrollment in the University of Sana'a grew gradually from fewer than 100 students in 1970, shortly after it opened, to about 4,500 in 1979. Government policy at first tried to balance the university enrollment with the capacity of the marketplace to absorb university graduates. University enrollment began to increase at an outstanding rate after 1985, following the heavy expansion of secondary education in the country in the late 1970s. From 1987 to 1991, total enrollment expanded from about 17,000 to 44,000 students. If the present rate of intake continues, total enrollment is projected to reach 79,000 students by the year 2000. This explosive growth has created numerous problems, including overcrowded classrooms, insufficient staff resources, deteriorating physical plant and equipment, inadequate educational materials and equipment, and a low level of absorption of graduates into the labor force. These developments threaten the quality of degree programs in several disciplines. The government should act immediately to develop a strategy to protect its investment in higher education. The policy should consider the country's medium and long-term needs, the constraints on its resources, and the growing social aspirations of its people. The goal of this assessment should be to design a strategy that will make higher education a more effective investment to serve the needs of the country and to protect itsresources.Gender and Education,Health Monitoring&Evaluation,Teaching and Learning,Curriculum&Instruction,Tertiary Education

The link between learning spaces and employability outcomes

Universities are investing considerable funds in designing and building innovative learning spaces without knowing the positive impact on student learning and their achievement of employability skills for the 21st century. There is a possibility of designing these new generation learning spaces to enable active and deep learning approaches to be employed to improve student learning outcomes and their achievement of employability skills.  This paper proposes that an evaluative framework for innovative learning spaces and tools to measure the impact of these learning spaces on students’ achievement of employability skills is a worthy endeavour.  Best practice innovative active learning strategies can then be identified and incorporated into a professional learning module for academics teaching in higher education. The outcomes can guide universities in developing learning spaces that maximise student learning consistent with 21st century employability skills

Chemistry Students’ Competence throughout their BSc Course in some Problem-Solving Strategies

The main objective of the study was to test chemistry students’ competence, in the first, second and final years of their BSc course, in some basic problem-solving strategies. Five strategies were tested: clarification and clear representation of problems; focusing sharply on the goal; identification and use of relevant principles; use of equations for calculations and deductions and use of a step-by-step procedure. The study method used was the analysis of students’ solutions to questions that were carefully designed to test competence in problem-solving strategies. The study showed that performance was poor in all the problem-solving strategies tested and that there was no improvement in performance as students progressed from year to year. About a half of the students tested (average performance in all of the 11 questions used for testing) had difficulty in answering the questions. Possible reasons for students’ difficulties are identified and suggestions are made for rectifying the difficulties. It is suggested that difficulties with the use of cognitive strategies are often not due to students’ inability to understand and use them but to insufficient emphasis being placed on them in their courses. Since an increase in competence in cognitive strategies and cognitive skills can be expected to lead to more efficient learning and problem-solving, not only in education courses but also throughout their lives, there is a need for training students in them until they become automatic and spontaneous mental operations. Such training should be integrated, throughout any course, with the teaching of content knowledge.Keywords: Cognitive strategies, thinking, problem solving, students’ difficulties with problem solvin

Students’ Competence in some Problem Solving Skills throughout their B.Sc. Course

The main objective of the study was to test students’ competence, throughout all their years (first, second and final years) of a B.Sc. course, in five important types of problem solving skills: information processing skills; skills concerning equations; graphical skills; three-dimensional visualization skills and inverse proportion reasoning skills. The study method used was the analysis of students’ solutions to carefully designed questions. Students’ performance was found to be poor for most of the skills tested. For example, more than half of all the students tested could not deduce information organized in equations, transform quantitative information in statements into equations and use inverse-proportion reasoning to do a calculation; and about a quarter of the students could not combine two equations and also could not visualize three-dimensionally the drawing of a cube. The study also showed that there wasn’t much improvement in cognitive skills as students progressed from year to year. This suggests insufficient emphasis being placed on training students in cognitive skills in their courses. Since the development of students’ competence in cognitive abilities should be an important objective of education courses, there is a need for explicitly identifying important cognitive skills and strategies and training students in them. Such training should be integrated with the teaching of content knowledge.Keywords: Cognitive skills, thinking skills, problem solving, students’ difficulties with cognitive skill

High School Physical Sciences Teachers’ Competence in Some Basic Cognitive Skills

The successful implementation of the national high school Physical Sciences curriculum in South Africa, which places strong emphasis on critical thinking and reasoning abilities of students, would need teachers who are competent in cognitive skills and strategies. The main objectives of this study were to test South African high school Physical Sciences teachers’ competence in the cognitive skills and strategies needed for studying Physical Sciences effectively and also to identify possible reasons for their difficulties and suggest methods for overcoming them. The study method used was the analysis of teachers’ answers to questions that were carefully designed to test competence in explanation skills, mathematical skills, graphical skills, three-dimensional visualization skills, information-processing skills and reasoning skills. Seventy-three teachers from about 50 Dinaledi schools in the North West and Kwazulu-Natal provinces were tested. Teachers’ competence was found to be poor in most of the skills tested. About 40 % (average performance in all 14 test questions) of them had difficulty in answering the questions. Teachers’ lack of competence in cognitive skills and strategies would be an important limiting factor in the successful implementation of the Physical Sciences curriculum. An urgent need therefore exists for training teachers to increase their competence in the cognitive skills and strategies that are needed for studying science effectively.Keywords: Cognitive skills, thinking skills, questions testing skills, problem solving, teacher training, high school physical scienc

THE MECHANISM OF CADMIUM-INDUCED FETAL GROWTH RESTRICTION: ROLE OF PLACENTAL 11 ß - HYDROXY STEROID DEHYDROGENASE 2 (llß-HSD2) AND METALLOTHIONEIN PROTEINS I & H.

Maternal cadmium exposure induces fetal growth restriction (FGR), but the underlying mechanisms remain largely unknown. Placental llß-hydroxysteroid dehydrogenase type 2 (llß-HSD2) has been implicated as a potential molecular target by which cadmium induces FGR. Furthermore, metallothionein-I and II (MT-I/II) sequester cadmium in the placenta, thereby reducing its toxicity on the developing fetus. The present study was undertaken to examine the role of MT- I/II in cadmium-induced FGR using the MT-I/IIA mouse model. Maternal cadmium administration led to FGR and reductions in placental llß- HSD2 activity in MT-I/II1\u27 but not MT-I/lf/+ mice. Although it did not alter placental weight or structure, maternal cadmium administration increased placental cell death in MT-I/lf/+ and MT-I/lf\u27 mice. Together, these results demonstrate that MT-I/II/_ mice are vulnerable to cadmium-induced FGR and reductions in placental llß-HSD2 activity, suggesting that MT-I/II proteins protect the fetus from adverse effects of cadmium on fetal growth and development