The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. In this thesis, the development of a symbolic computer algebra toolbox to compute two dimensional Fourier transforms in polar coordinates is discussed. Among the many operations implemented in this toolbox are different types of convolutions and procedures that allow for managing the toolbox effectively. The implementation of the two dimensional Fourier transform in polar coordinates within the toolbox is shown to be a combination of two significantly simpler transforms. The toolbox is also tested throughout the thesis to verify its capabilities.

The purpose of this thesis is the creation of documentation of the St. Michael the Archangel church in Dolní Věstonice village, which includes topographic situation of the object, drawing of the first floor, vertical and longitudinal sections and outdoor views of the façades. The church, it’s location and chronological description of all activities is included in the text of the thesis. Chapter named Preparatory work describes reconnaissance of current point field, creation of network of extra points for measuring and sketches preparation. The next section describes the methods used for positional and height measurement of detailed and assist points. The following chapter entitled Office work includes description of all the calculations and the making of individual drawings. The summary of results and the possibility of future use of the created documentation is described in the end of this thesis. All drawings, calculations reports and the accuracy testing of detailed points are found in the annexes.

Aircraft industry is constantly facing the need to increase security not only in the case of large machines, but also in the small aircraft. Many systems were established in order to inform the pilot of the impending hazard, where appropriate, about the location of the other aircraft. The main objective is to establish a facility which uses global position system for determining the position and imparts coordinates using wireless networks for subsequent determination of collision. The functions of satellites and GPS receivers, sending wireless data and collision calculation and synchronization of individual modules is described in detail.

No description available.

<p> The theory of canonical correlation analysis has been combined with that of trend surface analysis in order to construct a multivariate trend surface which is called a canonical trend surface. </p> <p> A canonical trend surface is a parsimonious summarization of areal variations of a set of geological variates. This trend has a property of maximum correlation between variates and geographic coordinates. It does not show the absolute value of each variate, but it shows the nature of the variation of a linear combination of the variates. The Permian system in western Kansas and eastern Colorado was studied as a numerical example to illustrate the general procedures in solving practical problems and also to demonstrate the validity of this technique. By use of this type of trend it is possible to reveal the underlying pattern of geographic variation common to a set of variates. </p> <p> Other applications of canonical correlation analysis in geology have been explained with illustrative geological examples, namely: the relationships between two sets of variates, matching two factor patterns, Q-technique canonical correlation, and discriminatory analysis. </p> <p> Comparison of canonical correlation analysis and principal factor solution in factor analysis suggests that factor analysis may be more appropriate for suggesting interrelationships among variables, while canonical correlation analysis may be a suitable tool for prediction problems. </p> <p> FORTRAN IV programs for these computations are listed in appendices with instructions for using them. </p> / Thesis / Doctor of Philosophy (PhD)

The existence of a coordinate system can often improve the routing in a wireless sensor network. While most coordinate systems correspond to the geometrical or geographical coordinates, in recent years researchers had proposed the use of virtual coordinates. Virtual coordinates depend only on the topology of the network as defined by the connectivity of the nodes, without requiring geographical information. The work in this thesis extends the use of virtual coordinates to scenarios where the wireless sensor network has a mobile sink. One reason to use a mobile sink is to distribute the energy consumption more evenly among the sensor nodes and thus extend the life-time of the network. We developed two algorithms, MS-DVCR and CU-DVCR which perform routing towards a mobile sink using virtual coordinates. In contrast to the baseline virtual coordinate routing MS-DVCR limits routing updates triggered by the sink movement to a local area around the sink. In contrast, CU-DVCR limits the route updates to a circular area on the boundary of the local area. We describe the design justification and the implementation of these algorithms. Using a set of experimental studies, we show that MS-DVCR and CU-DVCR achieve a lower energy consumption compared to the baseline virtual coordinate routing without any noticeable impact on routing performance. In addition, CU-DVCR provides a lower energy consumption than MS-DVCR for the case of a fast moving sink.

Triangle is the mostly used primitive in computer graphics. Calculation of its intersection with a ray has many applications and is often a bottleneck of a program. This work focuses on its usage and various methods of calculation. It tries to combine these techniques to achieve high performance on modern processors.

Thesis: B.S., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 1978 / Bibliography: leaf 55. / by Kenneth Church. / B.S. / B.S. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science

Physics education research found that graphs in kinematics have been a problem to students, even at university level. The study hence investigates what deficiencies first-year Physics students at the Central University of Technology, Bloemfontein, South Africa have in terms of transferring mathematics knowledge and understanding when solving kinematics problems. According to the National Department of Education (DoE, 2003), mathematics enables learners to have creative and logical reasoning about problems in the physical and social worlds. Graphs in kinematics are one of the domains that need that skill in mathematics. DoE (2011) further emphasises that learners should be able to collect, analyze, organize and critically evaluate information at the end of their FET sector and that include graphing in kinematics. The study started by exploring graph sense and comprehension from literature. The study further explored from a literature review students‘ problems and possible solutions in transferring their mathematics understanding and knowledge to solve physics problems. The literature study served as conceptual framework for the empirical study, i.e. the design and interpretation of questionnaires, and interview questions. The mathematics and kinematics questions of the questionnaire were divided into four constructs, namely area, gradient, reading coordinates and form/expression of graphs. The participants undertook the questionnaire and interviews voluntarily according to the research ethics. Hundred and fifty two (152) out of 234 students registered for first-year physics from the faculties of humanities (natural science), health and environmental science and engineering and information technology undertook the questionnaire. The researcher interviewed 14 students of these participants as a follow up to the responses of the questionnaire. The responses of the participants were analysed statistically to conclude this study. The average percentages of the questionnaire showed that the majority (62.7% participants) have the mathematics knowledge compared to the low percentage of 34.7 % on physics knowledge. With regard to the constructs the participants generally performed similarly on gradient, reading coordinates and form/expression, i.e. they could either answer both the corresponding mathematics and physics questions and neither of them. In the area construct, most participants with the mathematics knowledge did not transfer it to the physics context. The study further revealed that the majority of interviewees do not have an understanding of the basic physics concepts such as average velocity and acceleration. The researcher therefore recommends that physical science teachers in the FET schools should also undergo constant training in data handling and graphs by subject specialists and academic professionals from Higher Education Institutions. Other remedial actions are also proposed in the dissertation. / MSc (Natural Science Education), North-West University, Potchefstroom Campus, 2015

Physics education research found that graphs in kinematics have been a problem to students, even at university level. The study hence investigates what deficiencies first-year Physics students at the Central University of Technology, Bloemfontein, South Africa have in terms of transferring mathematics knowledge and understanding when solving kinematics problems. According to the National Department of Education (DoE, 2003), mathematics enables learners to have creative and logical reasoning about problems in the physical and social worlds. Graphs in kinematics are one of the domains that need that skill in mathematics. DoE (2011) further emphasises that learners should be able to collect, analyze, organize and critically evaluate information at the end of their FET sector and that include graphing in kinematics. The study started by exploring graph sense and comprehension from literature. The study further explored from a literature review students‘ problems and possible solutions in transferring their mathematics understanding and knowledge to solve physics problems. The literature study served as conceptual framework for the empirical study, i.e. the design and interpretation of questionnaires, and interview questions. The mathematics and kinematics questions of the questionnaire were divided into four constructs, namely area, gradient, reading coordinates and form/expression of graphs. The participants undertook the questionnaire and interviews voluntarily according to the research ethics. Hundred and fifty two (152) out of 234 students registered for first-year physics from the faculties of humanities (natural science), health and environmental science and engineering and information technology undertook the questionnaire. The researcher interviewed 14 students of these participants as a follow up to the responses of the questionnaire. The responses of the participants were analysed statistically to conclude this study. The average percentages of the questionnaire showed that the majority (62.7% participants) have the mathematics knowledge compared to the low percentage of 34.7 % on physics knowledge. With regard to the constructs the participants generally performed similarly on gradient, reading coordinates and form/expression, i.e. they could either answer both the corresponding mathematics and physics questions and neither of them. In the area construct, most participants with the mathematics knowledge did not transfer it to the physics context. The study further revealed that the majority of interviewees do not have an understanding of the basic physics concepts such as average velocity and acceleration. The researcher therefore recommends that physical science teachers in the FET schools should also undergo constant training in data handling and graphs by subject specialists and academic professionals from Higher Education Institutions. Other remedial actions are also proposed in the dissertation. / MSc (Natural Science Education), North-West University, Potchefstroom Campus, 2015