M.Ing. (Electrical and Electronic Engineering) / This dissertation deals with the mapping of an unknown environment. Mapping of an environment can be accomplished by asking the question “What is in my world?” whilst moving through the environment. Once the objects occupying the ‘world’ have been discovered, the locations of these objects are stored somewhere (for example on paper), so that the environment can be navigated at a later stage. In the context of robots, a map provides the robot with a certain degree of “intelligence”. Several different types of applications are available for robots with “intelligence”; ranging from mining applications, to search and rescue situations, to surveillance applications and recognisance applications. The research hypothesis posed by this dissertation is as follows: Produce a human readable map for an unknown defined structured environment using a single laser range finder (LRF). The focus was on mapping environments resembling mine tunnels. In mine tunnel environments sensors, such as wheel odometers, can fail. This failure makes it advantageous to be able to create a map of the environment with the data obtained solely from the LRF. For this dissertation, the following restrictions were placed on the environment being mapped. It had to be structured (i.e. the environment could be described by simple geometric primitives such as lines); it had to be static (the only entity allowed to move in the environment was the LRF to obtain data); and the environment had to be defined (i.e. have a starting and ending point). During the course of this Masters research, it was discovered that in order to create a human readable map, one has to determine the accurate localisation of the sensor in the environment whilst mapping. The described scenario is a typical problem in mapping and is referred to as the ‘simultaneous localisation and mapping (SLAM) problem’. This dissertation shows results when mapping was done with – and without – accurate localisation. The final approach used to create the human readable map consisted of determining scan matched odometry (based on a feature matching and ICP algorithm). The scan matched odometry is incorporated into a grid-based SLAM technique that utilises a particle filter to accurately determine the position of the sensor in the environment, in order to create a human readable map of the environment. The algorithm used (as described) was able to close loops (i.e. the mapping algorithm was able to handle the sensor returning to its starting point) and it produced satisfactory results for the types of environments as required by the scope of this dissertation.

Every continuous convex function defined on a separable Banach space is Gateaux differentiable on a dense G^ subset of the space E [Mazur]. Suppose we are given a sequence (xn) that Is dense in E. Can we always find a Gateaux differentiable point x such that x = z^=^anxn.for some sequence (an) with infinitely many non-zero terms so that Ση∞=1||anxn|| < co ? According to this paper, such points are called of "simple type," and shown to be dense in E. Mazur's theorem follows directly from the result and Rybakov's theorem (A countably additive vector measure F: E -* X on a cr-field is absolutely continuous with respect to |x*F] for some x* e Xs) can be shown without deep measure theoretic Involvement.

This dissertation is a study of the dynamics of one-dimensional unimodal maps and is mainly concerned with those maps which are trapezoidal. The trapezoidal function, f_e, is defined for eΣ(0,1/2) by f_e(x)=x/e for xΣ[0,e], f_e(x)=1 for xΣ(e,1-e), and f_e(x)=(1-x)/e for xΣ[1-e,1]. We study the symbolic dynamics of the kneading sequences and relate them to the analytic dynamics of these maps. Chapter one is an overview of the present theory of Metropolis, Stein, and Stein (MSS). In Chapter two a formula is given that counts the number of MSS sequences of length n. Next, the number of distinct primitive colorings of n beads with two colors, as counted by Gilbert and Riordan, is shown to equal the number of MSS sequences of length n. An algorithm is given that produces a bisection between these two quantities for each n. Lastly, the number of negative orbits of size n for the function f(z)=z^2-2, as counted by P.J. Myrberg, is shown to equal the number of MSS sequences of length n. For an MSS sequence P, let H_ϖ(P) be the unique common extension of the harmonics of P. In Chapter three it is proved that there is exactly one J(P)Σ[0,1] such that the itinerary of λ(P) under the map is λ(P)f_e is H_ϖ(P). In Chapter four it is shown that only period doubling or period halving bifurcations can occur for the family λf_e, λΣ[0,1]. Results concerning how the size of a stable orbit changes as bifurcations of the family λf_e occur are given. Let λΣ[0,1] be such that 1/2 is a periodic point of λf_e. In this case 1/2 is superstable. Chapter five investigates the boundary of the basin of attraction of this stable orbit. An algorithm is given that yields a graph directed construction such that the object constructed is the basin boundary. From this we analyze the Hausdorff dimension and measure in that dimension of the boundary. The dimension is related to the simple β-numbers, as defined by Parry.

Much of the hypermedia literature instructs developers to "Use a map to prevent users from becoming lost." However, there is very little empirical evidence that maps are effective. In addition, no one has examined how to design the maps to make them most helpful to the users. This research evaluates both issues for information retrieval tasks with a fairly small hypermedia application (about 175 nodes). This study evaluates the overall effectiveness of maps by comparing the subjects' performance using hypermedia without a map to performance with one of four maps. Then, it reveals the relative effectiveness of the different types of maps by comparing the results of the subjects' performance with four variations of a map. In addition, this research evaluates (1) the effects of the experimental conditions on the subjects' mental models of the application and (2) the effects of the subjects' spatial abilities on their performance with hypermedia. The results reveal that there is generally no difference between the subjects' performance with a map and performance without a map. In addition, users who had to navigate using the links within the application rather than selecting nodes from the map (using a "passive" map) viewed more extra nodes, but spent less time on each node and completed the tasks in less time than those who could select nodes directly from the map (using an "active" map). However, many of the subjects using the passive map would have preferred to use an active map. Also, subjects who always had a map available to them (using a "present" map) performed as well as subjects who had to call up a map to use it (a "called" map). In addition, there is no difference in the accuracy of the subjects' mental models. All the subjects understood the application fairly well. A few of the spatial abilities test results are correlated with performance, and all of significant correlations indicate that higher spatial abilities leads to improved performance with hypermedia. It is believed that the lack of differences among the conditions is due to a number of factors, including the simplicity of the application the subjects used and the tasks they performed. / Master of Science

This thesis discusses an algorithm for mapping conceptual graphs to primitive VHDL processes. The behavior of each primitive process is stored in the form of a schema. The algorithm identifies concepts in the input referring to MODAS (Modeler's Assistant) process primitives and maps their schemata to the input conceptual graph. The results of the mapping are used to modify the primitive process's VHDL and instantiate a new process. A library of schemata for the primitive processes in MODAS has been developed. This algorithm has been implemented in the CGVHDL Linker program. It has improved the capability of the CGVHDL Linker to handle more complex design specifications. The algorithm provides the CGVHDL Linker with the ability to interpret a structure in the input conceptual graph. It also eases the burden on the designer who can refer to some components without giving details of their behavior. / Master of Science

Thesis (doctoral)--Rijksuniversiteit te Utrecht, 1983. / "Stellingen": [6] p. inserted. Includes bibliographical references (p. 253-257) and index.

Orientador: Philippe Remy Bernard Devloo / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-13T10:14:35Z (GMT). No. of bitstreams: 1 Lucci_PauloCesardeAlvarenga_M.pdf: 6661587 bytes, checksum: b77bb456093ce1f153056c6b2fa89626 (MD5) Previous issue date: 2009 / Resumo: Este trabalho é dedicado ao desenvolvimento de uma metodologia específica de mapeamento curvo aplicável a qualquer tipo de elemento geométrico regular. Trata-se de uma generalização do modelo matemático de representação geométrica apresentado em 1967 por Steven Anson Coons, denominado "Bilinearly Blended Coons Patches", o qual ajusta uma superfície retangular em um contorno delimitado por quatro curvas arbitrárias. A generalização proposta permitirá a utilização deste tipo de interpolação geométrica em elementos de qualquer topologia, através de uma sistemática única e consistente. / Abstract: In this work a methodology is developed for mathematical representation of curved domains, applicable to any type of finite element geometry. This methodology is a generalization of the mathematical model of a geometric representation presented in 1967 by Steven Anson Coons, called "Bilinearly Blended Coons Patches", which patch a rectangular surface in four arbitrary boundary curves. The proposed methodology is a kind of geometric transfinite interpolation applicable to elements of any topology, using a single and consistent systematic. / Mestrado / Estruturas / Mestre em Engenharia Civil

We deal with two themes that are illustrative of the rigidity and regularity of holomorphic mappings. The first one concerns the regularity of continuous CR mappings between smooth pseudo convex, finite type hypersurfaces which is a well studied subject for it is linked with the problem of studying the boundary behaviour of proper holomorphic mappings between domains bounded by such hypersurfaces. More specifically, we study the regularity of Lipschitz CR mappings from an h-extendible(or semi-regular) hypersurface in Cn .Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A rigidity result for proper holomorphic mappings from strongly pseudo convex domains is also proved. The second theme dealt with, is the classification upto biholomorphic equivalence of model domains with abelian automorphism group in C3 .It is shown that every model domain i.e.,a hyperbolic rigid polynomial domainin C3 of finite type, with abelian automorphism group is equivalent to a domain that is balanced with respect to some weight.

We use transcendental shift-like automorphisms of Ck, k > 2 to construct two examples of non-degenerate entire mappings with prescribed ranges. The first example exhibits an entire mapping of Ck, k>2 whose range avoids a given polydisc but contains the complement of a slightly larger concentric polydisc. This generalizes a result of Dixon-Esterle in C2. The second example shows the existence of a Fatou-Bieberbach domain in Ck,k > 2 that is constrained to lie in a prescribed region. This is motivated by similar results of Buzzard and Rosay-Rudin. In the second part we compute the order and type of entire mappings that parametrize one dimensional unstable manifolds for shift-like polynomial automorphisms and show how they can be used to prove a Yoccoz type inequality for this class of automorphisms.

M.Ed. / This study is an investigation into cognitive mapping as strategy in the constructivistic approach to mathematics education to learners with a visual disability with the view to describe the change in pupils' thoughts on mathematical concepts, as well as their experiences during the process of cognitive mapping. The rationale for the investigation was derived from the shift in South African Mathematics teaching from traditional teaching to constructivistic (or problem-centered) teaching. As this implies a shift in paradigm, teachers will be in need of relevant constructivistic training to equip them with effective teaching strategies. The objective of this study is to examine cognitive mapping as a possible supportive strategy to constructivism . The study commences with a theoretical framework in which constructivism is clearly explicated. The principles of radical and social constructivism, the roots of which can be traced back to the epistemological theories of Piaget and Vygotsky, are explored. The constructivistic view of knowledge, with the relationship between public knowledge and the forming of personal knowledge, is discussed and extended to include the formation of mathematical knowledge. The focus then shifts to the concepts of instruction and learning and the role they play in the constructivistic paradigm. In the constructivistic view, learning implies cognitive restructuring, which is facilitated by assimilation and accommodation. The implications of this view of learning for instruction, and in particular mathematics instruction, is then discussed. This chapter concludes with the working definition the researcher has used to conduct the remainder of the study. The theoretical framework is structured furthermore to give background regarding cognitive mapping. According to the constructivistic approach, learning implies conceptual change. Cognitive maps externalise conceptual change by means of visual representations, and therefore it was decided to investigate them as a teaching strategy. Some definitions, as found in the literature, are given, and three types of maps are illustrated as examples. The different uses of cognitive maps, among which study strategy, lesson planning and means of evaluation, are discussed. A discussion on the different methods of constructing a map follows, with specific focus on how to include the whole class in the activity. The advantage of social interaction while constructing knowledge, is highlighted. Lastly, the advantages and disadvantages connected to cognitive mapping as teaching strategy, are discussed. The theoretical framework is complemented by a chapter on the design of the research, substantiating the choice of format and methods of data collection and analysis. The data is reported in the succeeding chapter, and examples of raw data from transcriptions, journals of the pupils and cognitive maps are presented. Finally, the consolidated data is interpreted. In the concluding chapter the findings of the study are discussed. The most significant findings of this study are: cognitive mapping, as mathematical teaching strategy, improved the understanding of grade nine learners, with a visual disability, of real numbers; the learners experienced the teaching strategy of cognitive mapping positively; the number of group members involved in the construction of a cognitive map, influenced.