As indicated by the title, this thesis generalizes the Main Inertia
Theorem of Ostrowski and Schneider [8]. The first three results
concern the formation of a polynomial function f(A, A*, H) so that
the existence of an hermitian H for which f(A, A*, H) is positive
definite is a necessary...
Three special cases of the resection problem of surveying
are examined and solved. The coordinates of unknown points are
found with respect to given points in a rectangular coordinate system.
This is accomplished in the case of (a) one unknown point and three
given points (Snell's problem), (b) two unknown...
General techniques for constructing Scheduling Algorithms
are described as well as their applications to two diverse problems,
namely the scheduling at a university and the imitation of the activity
of a taxonomist in microbiology.
This thesis contains a collection of properties of the greatest integer part function which were obtained by an extensive literature search. A few original properties are stated and proved and some of the properties which were found unproved in the literature are proved.
Since the advent of the modern computer there has been great interest in simulation of all types. It is not possible to simulate very large systems on computers. This thesis presents the algorithms necessary to simulate a college with respect to the academic relationship of the student with the college....
The indicated sum of a real scalar and a real or imaginary
vector is called a scator. Either the scalar part or the vector part
may be null. Scators generalize the complex variable to n-space.
The algebra of scators is not generally associative under multiplication
but the commutative and distributive...
Among the geometries with n points on every line (with n
an integer greater than one), those in which there are no parallels
and those in which the axiom of parallels holds have been discussed
(as finite projective and affine geometries) in the literature. This
paper contrasts such geometries with...
The Euler-MacLaurin sum formula has appeared in the titles
of two quite recent papers whose authors were primarily interested
in certain applications. In this paper a somewhat different approach
to the myriad of formulas for summation, integration, differentiation,
etc. , is based on the simple identity which defines the set...
