Advances in Mathematics Research : Volume 25

This volume commences with an introduction to the solution attractor theory of local search systems. Here, a local search algorithm is treated as a discrete dynamical system and its search behavior is studied from the perspective of dynamical systems. Following this, this collection examines the three-year period of 1966 to 1968 when the invariant integral of fracture mechanics became popular, as well as 2015 to 2016 when the neoclassic cosmology based on the invariant integral came about. The authors go on to argue how, in the history of philosophy, the meaning of the term to be has been disputed between two research programmes: The Platonic-Aristotelian and the Pythagorean- Parmenidean-Democritean programmes through Hobbes and Boole up to Peano. The history of science and philosophy goes hand in hand with the question of the nature of mathematical objects. By implication, this was known by the Pythagoreans, even though it was not expressed in the plane of a directly named problem. The authors propose that that strict Platonism in mathematics is not possible, though may be considered in many cases. Also in this collection, perform building-scale analysis is performed, and the use of a convex map is considered. However, partitioning an architectural space is not easy due to its ambiguity. As such, an analysis method is proposed which may decompose the space with moderate granularity. One study sets out to determine the feasibility of using a hidden Markov model to assess whether goats were in estrus. Mammalian behavior has typically been studied based on observations, but direct observation requires substantial time and effort if the number of mammals observed is high or the observations are obtained over a long period of time. Thus, a machine-learning method such as a hidden Markov model may be suitable. A literature review of electric circuits and mathematical models of electric power transmission lines is provided, approaching a classification of the models regarding the nature of their parameters and frequency dependence. These models are important in predicting the voltage and current available, which aids in meeting safety and quality demands. The authors conclude with a summary of some results concerning the problem of computing a proper rational parametrization Q from P. In particular, they present an algorithm that computes a parametrization Q of V such that deg(‑Q) ≤ deg(‑P). If deg(‑Q) = 1, then Q is proper and the reparametrization problem is solved.