This thesis investigates problems in hierarchical games. Mathematical models are used in tennis to determine when players should alter their effort in a game, set or match to optimize their available energy resources. By representing warfare, as a hierarchical scoring system, the results obtained in tennis are used to solve defence strategy problems. Forecasting in tennis is also considered in this thesis. A computer program is written in Visual Basic for Applications (VBA), to estimate the probabilities of players winning for a match in progress. A Bayesian updating rule is formulated to update the initial estimates with the actual match statistics as the match is progressing. It is shown how the whole process can be implemented in real-time. The estimates would provide commentators and spectators with an objective view on who is likely to win the match. Forecasting in tennis has applications to gambling and it is demonstrated how mathematical models can assist both punters and bookmakers. Investigation is carried out on how the court surface affects a player�s performance. Results indicate that each player is best suited to a particular surface, and how a player performs on a surface is directly related to the court speed of the surfaces. Recursion formulas and generating functions are used for the modelling techniques. Backward recursion formulas are used to calculate conditional probabilities and mean lengths remaining with the associated variance for points within a game, games within a set and sets within a match. Forward recursion formulas are used to calculate the probabilities of reaching score lines for points within a game, games within a set and sets within a match. Generating functions are used to calculate the parameters of distributions of the number of points, games and sets in a match.

Human disturbance as the main factor influencing the habitat of brown bear (Ursus arctos) has occurred frequently with the development of human society. How to reduce and prevent the conflict between human and brown bears is considered as an important question for brown bear conservation, management and public safety. Sånfjället National Park has one of the densest bear populations in Sweden. Many tourists are attracted to visit bears each year. Through this study, the most possibility brown bear denning habitat in Sånfjället National Park was determined by using Multi-Criteria Analysis. A customized habitat distribution map generator was programmed within the Microsoft Visual Basic® for Applications (VBA) in ArcGIS. Three themes were designed in the map generator, i.e., the human impact emphasis weighted, neutral weighted themes and customized weighted theme. Customized weighted theme was produced for user discovering denning habitat results with user-defined weights. Comparing the final maps generated from the human impact emphasis weighted and neutral weighted themes, human influence concentrated in the south area of the National Park. The trails near Sveduterget should be changed to avoid human disturbance in the bear denning period.