In the study of uniform convergence, one is led naturally to
the question of how uniform convergence on subsets relates to uniform convergence on the whole space. This paper develops theorems on how pointwise convergence relates to uniform convergence
on finite sets, how uniform convergence on finite subsets relates to...
A construct is developed which is useful in the
investigation of the global convergence properties of
Newton's method.
This construct is used to study the application of
Newton's method to polynomials. A proof that Newton's
method converges almost globally for polynomials with
only real zeroes is extended to a larger...
This study undertakes to determine the existence or nonexistence
of an implication in either direction between any two out of
nine different modes of convergence, with the use of any subset of a
set of ten auxiliary hypotheses. The functions are real finite-valued
measurable functions defined on an arbitrary abstract...
Adaptive filtering may be applied in areas where an optimal filtering algorithm
may not be known a-priori and where the filtering operation may be non-stationary. This
field, or more generally, the field of adaptive systems, is one which may be regarded as
mature, having been the subject of considerable research...
Technology is a key determinant of comparative advantage among nations. As information technology improves and the nations of the world become economically integrated, concern arises over the dissipation of high-income economies’ technological advantage. The three essays in this dissertation explore the trade and technology relationship, which is essential to economic...