In this paper Euclidean and hyperbolic discontinuous isometries* are discussed and compared. The graphic artist M.C. Escher (1898-1972) produced works which have for the structure points, lines, and angles, which repeat in the plane (Euclidean and...
“Was mathematics invented or discovered?” This is an age old question that has yet to be definitively answered. Some people believe that the human mind is the creator of mathematics, like a painter or poet, is a maker of patterns. [N, p. 2027] ...
Multivariate analysis; Stratified sets; Bayesian statistical decision theory
Data mining, at times, involves applying cluster analysis to large databases
containing multivariate normal parameters. Most finite mixture clustering methods use
the expectation-maximum (EM) algorithm to find solutions to the unknown parameters,...
The goal of this thesis is to trace the development in mathematical theory that led to the proof of the insolvability of the quintic. That is, there does not exist a general formula in radicals for equations of the form [not reproducible-see full...
Let X and Z be topological spaces and Y be a subspace of X. A con-
tinuous function f : Y ! Z is extendable to X if there exists a continuous
function f : X ! Z such that f(x) = f(x) for all x 2 Y . If every continuous
function f : Y ! Z is...