This study examines the residential subdivision of land in rural areas within the context of Community Planning Area Number 14 in the Regional District of Comox-Strathcona, British Columbia. Two separate elements comprise the major portion of the study. Interviews with a select sample of developers who practise within the Community Planning Area provide information about the extent and practise of residential land development in the study area. The interview schedule is designed to elicit both facts and opinions. The analysis of these interviews supplies the necessary background for the study. A random sample of residential subdivisions provides the basis for subdivision case studies. Each sample subdivision is subjected to a physical evaluation in terms of commonly accepted planning standards and principles for location and design. The extent to which the sample subdivisions meet the needs of the residents is discovered through interviews with the residents. These interviews are designed to elicit facts, opinions and levels of satisfaction pertaining to the subdivisions. The background to the problem and the methodology of the study are described. Concepts of residential subdivision location and design are discussed. The results of the comparative physical evaluation of the sample subdivisions and the results of the interviews with residents are also discussed. Conclusions are made about the location and design of the subdivisions and about the level of satisfaction which the residents express. It is shown in the study that "rural area residential subdivisions" in Community Planning Area Number 14 do not conform with accepted planning standards and principles. However, it is also shown that the needs of residents who have chosen to live in these subdivisions are satisfied despite those deficiencies. / Applied Science, Faculty of / Community and Regional Planning (SCARP), School of / Graduate

A set S of vertices in a graph G is a total dominating set of G if every vertex is adjacent to a vertex in S. The total domination number yγ t (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt (G) of a graph G is the minimum number of edges that must be subdivided (where each edge in G can be subdivided at most once) in order to increase the total domination number. Haynes et al. (J. Combin. Math. Combin. Comput. 44 (2003) 115) showed that for any tree T of order at least 3, 1 ≤sdγt (T)≤3. In this paper, we give a constructive characterization of trees whose total domination subdivision number is 3.

Introduction: The purpose of this study is to compare dental and skeletal differences between Class I and Class II sides and their contributions to the degree of asymmetric molar relationship in Class II subdivision malocclusions using CBCT. Methods: One hundred and eight patients presenting with Angle Class II subdivision malocclusions (mean age =21.05 years) were assessed with 3-dimensional cone-beam computed tomography scans. Paired t-tests were used to compare linear skeletal, angular and dental measurement differences between Class I and Class II sides. Correlations of linear skeletal, angular and dental measurement differences between Class I and Class II sides were made against the Asymmetric Molar Relationship measurement. Differences between Class I and Class II sides were correlated to the degree of skeletal asymmetry, as defined by defined as menton deviation from mid-sagittal plane. Results: Maxillary first molar position was more mesially positioned on the Class II side and the mandibular first molar position was more distally positioned on the Class II side. No significant skeletal differences were found between Class I and Class II sides. Asymmetric Molar Relationship was correlated with a more mesially positioned maxillary first molar position and distally positioned mandibular first molar position on the Class II side. There were no significant skeletal differences that were correlated significantly with the Asymmetric Molar Relationship. Conclusion: In a sample of one hundred and eight patients exhibiting Class II subdivision malocclusion with and without skeletal asymmetry, the Class I and Class II sides display differences that are mainly dentoalveolar in nature. The degree of molar relationship asymmetry was correlated with a more a mesially positioned maxillary molar and a more distally positioned mandibular molar on the Class II side. There were no significant skeletal differences between Class I and Class II sides and no significant skeletal contributions to molar asymmetry.

The emerging seasonal subdivisions in the rural mountainous regions of Kane County was the focus of this study . A native of Kanab, county seat, the author has been in a position to witness the development of these projects. The desired purpose of the study was to ascertain the degree of involvement of local government and to indicate problems, their solutions and consequences. The problems encountered in analyzing these developments are basically those that must be faced by any new emerging community. No individual study was discovered that dealt with the specific locality under consideration. Of very recent origin, the developments have provided little time for in depth analysis. The absence of related studies has offered the author more personal contact with involved individuals than might otherwise have been the case. The author attempted to view the subdivisions as seen by both subdivider and governing official. Written questionnaires, personal interviews and informal discussions, on-site inspection of subdivisions , vis its to county offices, letters, and telephone interviews have provided the background material for this thesis. The study resulted in the following observations: 1. Local government must engage in long-range planning to effectively deal with the problems of the subdivisions. 2. Failure to adequately prepare now will necessitate far greater expenditures in future county operations. 3. As the problems continue to grow, so, too , will the cost of their eradication or containment. 4. Intergovernmental cooperative studies appear to be a logical method of determining overall effect of the problems. 5. Restructuring of local government may become necessary.

The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every nonsingular, prime alternating link and all torus links, and explore some of their properties and applications. Several examples are exhibited with color coding of tiles.

No / Wounds arising from various conditions are painful, embarrassing and often requires treatment plans which are costly. A crucial task, during the treatment of wounds is the measurement of the size, area and volume of the wounds. This enables to provide appropriate objective means of measuring changes in the size or shape of wounds, in order to evaluate the efficiency of the available therapies in an appropriate fashion. Conventional techniques for measuring physical properties of a wound require making some form of physical contact with it. We present a method to model a wide variety of geometries of wound shapes. The shape modelling is based on formulating mathematical boundary-value problems relating to solutions of Partial Differential Equations (PDEs). In order to model a given geometric shape of the wound a series of boundary functions which correspond to the main features of the wound are selected. These boundary functions are then utilised to solve an elliptic PDE whose solution results in the geometry of the wound shape. Thus, here we show how low order elliptic PDEs, such as the Biharmonic equation subject to suitable boundary conditions can be used to model complex wound geometry. We also utilise the solution of the chosen PDE to automatically compute various physical properties of the wound such as the surface area, volume and mass. To demonstrate the methodology a series of examples are discussed demonstrating the capability of the method to produce good representative shapes of wounds.

Combinatorial methods are utilized to examine preimage iterations of topologically glued polynomials. In particular, this paper addresses using finite subdivision rules and Hubbard trees as tools to model the dynamic behavior of mated quadratic functions. Several methods of construction of invariant structures on modified degenerate matings are detailed, and examples of parameter-based families of matings for which these methods succeed (and fail) are given. / Ph. D.

Nearly Euclidean Thurston maps are simple generalizations of rational Lattes maps. A Thurston map is called nearly Euclidean if its local degree at each critical point is 2 and it has exactly four postcritical points. We investigate when such a map has the property that the associated pullback map on Teichmuller space is constant. We also show that no Thurston map of degree 2 has constant pullback map. / Ph. D.

Nous nous intéressons à la modélisation de formes complexes de type structures arborescences, formes lacunaires ou surfaces rugueuses. Ces formes sont intéressantes de par leurs propriétés physiques particulières :objets légers, économie de matière, résistance mécanique, absorption acoustique importante. Les modèles basés sur le concept de la géométrie fractale permettent de générer de telles formes et notamment les formes auto-similaires. A partir des travaux de Barnsley sur les systèmes itérés de fonctions, Tosan et al, ont proposé une extension, Boundary Controled Iterated Funcions Systems (BCIFS) pour contrôler plus facilement les formes et faciliter leur description. Nous nous intéressons aux propriétés différentielles des formes décrites par BCIFS. Nous proposons une définition plus générale d'espace tangent qui permet de caractériser le comportement de cas non-classiquement différentiables.Nous montrons que l'étude du comportement différentiel peut alors se faire simplement par analyse des valeurs propres et vecteurs propres généralisés des opérateurs de subdivision. Il devient alors possible de contrôler ces propriétés différentielles. Nous présentons une application de nos résultats, en proposant une méthode pour construire des raccords entre deux structures définies par des processus de subdivision différents. Cette méthode est appliquée pour la construction d'un raccord entre une surface de subdivision de Doo-Sabin(schéma dual) et une surface de subdivision de Catmull-Clark (schéma primal) / The fractal geometry is a relatively new branch of mathematics that studies complex objects of non-integer dimensions. It finds applications in many branches of science as objects of such complex structure often poses interesting properties. In 1988 Barnsley presented the Iterative Func-tion System (IFS) model that allows modelling complex fractal shapes with only a limited set of contractive transformations. Later many other models were based on the IFS model such as Language-Restricted IFS,Projective IFS, Controlled IFS and Boundary Controlled IFS. The lastto allow modelling complex shapes with control points and specific topol-ogy. These models cover classical geometric models such as B-splines and subdivision surfaces as well as fractal shapes.This thesis focuses on the analysis of the differential behaviour of the shapes described with Controlled IFS and Boundary Controlled IFS. Wederive the necessary and sufficient conditions for differentiability for ev-erywhere dense set of points. Our study is based on the study of the eigenvalues and eigenvectors of the transformations composing the IFS. We apply the obtained conditions to modelling curves in surfaces. We describe different examples of differential behaviour presented in shapes modelled with Controlled IFS and Boundary Controlled IFS. We also use the Boundary Controlled IFS to solve the problem of connecting different subdivision schemes. We construct a junction between Doo-Sabin and Catmull-Clark subdivision surfaces and analyse the differential behaviour of the intermediate surface

Les schémas de subdivision et les schémas de subdivision inverse sont largement utilisés en informatiquegraphique; les uns pour lisser des objets 3D, et les autres pour minimiser le coût d'encodagede l'information. Ce sont les deux aspects abordés dans cette thèse.Les travaux présentés dans le cadre de la subdivision décrivent l'études et la construction d'un nouveautype de schémas de subdivision. Celui-ci unifie deux schémas de subdivision de type géométriquesdifférents. Cela permet de modéliser des objets 3D composés de zones issues de l'applicationd'un schéma approximant et de zones issues de l'application d'un schéma interpolant. Dans le cadrede la subdivision inverse, Nous présentons une méthode de construction des schémas de subdivisionbi-réguliers inverses (quadrilatères et triangles)