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Long-range dependence in discrete and continuous time Markov chains over a countable state space is defined via embedded renewal processes brought about by visits to a fixed state. In the discrete time chain, solidarity properties are obtained and long-range dependence of functionals are examined. On the other hand, the study of LRD of continuous time chains is defined via the number of visits in a given time interval. Long-range dependence of Markov chains over a non-countable state space is also carried out through positive Harris chains. Examples of these chains are...

This work presents procedures for generating solutions to the n-Queens problem using 2-circulant matrices, maximal cliques of graphs and 0-1 integer programming. Some constructions on matrices to prove that a solution exists for n > 3 are also presented. The use of maximal cliques is an application from the field of graph theory; the use of 0-1 integer programming is an application from the field of operations research.

One of the many problems encountered in coming up with a multiple linear regression model is the presence of severe multicollinearity in the data set. In this work, the focus is on the mathematics of multicollinearity -- what it is, what it does to the model, how it can be detected and combated. Aside from the classical methods, artificial neural networks were also employed to combat multicollinearity. Softwares such as Statistical Package for the Social Science (SPPS) Release 7.0 and 10.0 for Windows, MATLAB version 5.3 and Stuttgart Neural Network Simulator (SNNS) version 4.1 were used to...