Dobrowolski, Edward

The main achievement of the thesis is the proof that 1+√17 is not a Mahler measure of an algebraic number. This answers a question of A. Schinzel posted in [6] in 2004. We also show that, theoretically, there exists an algorithm to reduce the shortness of a polynomial without changing its Mahler measure, a problem considered in [5] by J. McKee and C. Smyth. However the number of computations required makes this algorithm infeasible.

Archaeological Predictive modelling is a tool that predicts the location of archaeological sites and materials in a region, based on the observed pattern in a sample data or on assumptions about human behavior. This project examines the combination of variables to produce a model with high predictability and the application of inductive predictive modelling method in locating areas of high archaeological potential in Prince George using Binary Logistic Regression. Results from the analysis have shown that terrain variables: slope, ruggedness, elevation, solar incidence and proximity to water, jointly explains the predictive model and that the model successfully predicts areas of high and low potentials in Prince George municipal. The results from the Kvamme’s gain statistic shows that the predictive model is moderately efficient. The study recommends that by incorporating more terrain variables, the model performance will be higher and probably be more efficient.

The aim and objective of the thesis entitled “Interval-valued Pythagorean Fuzzy Decision-Making Models for Evaluating Challenges of Digital Transformation” are as follows: The first objective is to develop new entropy and divergence measures to handle the uncertainty under interval-valued Pythagorean fuzzy environment to determine the significance degree/weight DT challenges of the manufacturing systems. The second objective is to develop a hybrid decision-making models to evaluate the DT challenges of the manufacturing systems from interval-valued Pythagorean fuzzy perspective. And the last objective is to propose a comprehensive framework to evaluate digital transformation challenges in sustainable financial service systems of the banking sector.

The ideal class group problem is one of the very interesting problems in algebraic number theory. In this thesis we focused on quadratic fields. We studied the group of units of the rings of algebraic integers and calculated fundamental units in several quadratic fields. We also studied a detailed proof of the analytic Dirichlet class number formula with numerical examples and its relation to binary quadratic forms. In addition, we also presented a detailed proof of Carlitz's theorem with numerical examples.

Complexity poses a pervasive challenge in understanding formal and natural systems which can arise from a combination of a system's state and state transition rules. In situations in which many aspects of a system are changing together, it is desirable to quantify how much they do so. We motivate and define five mathematical functions that can be used to quantify coordinated changes in structure. We also developed ConAction, a Python package which implements these novel mathematical tools in a way that is performant, easy to install, and easy to use. These new tools can be applied to real research problems, which we exemplified by evaluating a classic isolation by distance model for Dendroctonus ponderosae populations in western North America

No abstract available.

The design of efficient control strategies is a well studied problem. Due to recent technological advancements and applications in the field of robotics, exploring novel ways to design optimal control for multi-robot systems has gained interest. In this respect, the concept of ergodicity has successfully been applied as an effective control technique for tracking and area coverage. The generation of flocking behaviour is a problem that involves both tracking and coverage, and as such is also suited for the use of ergodicity. The main contribution of this thesis is the application of ergodicity to emulate flocking behaviour. This approach is appealing because control and communication is assumed to be local, self-organized, and does not require separate algorithms in order to generate different behaviour. Simulation results show that the proposed approach is effective and a prototype provides evidence that flocking behaviour is possible using ergodicity in a real-life setting.