The purpose of this paper is to discuss some of the theory of Boolean matrices and apply this theory to construct contact networks by using algebraic methods.
The first section of this paper (Chapter I to III) describes Boolean algebra and its properties, the theory of Boolean matrices, and the...
The thesis discusses stability of procedures based on linear
computing formulas for numerical integration of an ordinary first-order
differential equation. The theorems are proved: (1) If the
procedure is asymptotically stable it is stable for small positive step
size if the Lipschitz number is negative; (2) Relative stability always
exists...
In his book on abstract algebra, Nathan Jacobson
poses and solves the problem of finding the number of
ways of inserting parentheses in a string of given length
with binary operators. We continue the work of Jacobson
and go beyond it in that we no longer consider one binary
operator...
Computational scheme, equivalence, and Turing machine are
defined. Some computational schemes are examined and shown to
be equivalent to the computational scheme of a Turing machine.
A new procedure is developed for computing a root of algebraic equations with real coefficients and a degree n, where n is 2, 4, 6, 10, 14 or any positive odd integer. A heuristic procedure is added to partially lift the restrictions on the degree n. The procedures are written...
It is
well
known
that
two-terminal
switching
circuits
may
be
represented
by
boolean
formulas.
Thus
the
study
of
certain
switching
circuit
problems
leads
to
the
study of
free
boolean
algebras,
in
particular
to
the
free
boolean
algebra
on
a
countably
infinite
set
of
generators.
An
abstract
characterization
of
this
algebra...
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....
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...
This paper is a classification of 181 problems, each of which involves the evaluation or application of determinants. The problems are those which have appeared in the "Problems and Solutions" sections of the American Mathematical Monthly, Deutsche Mathematiker-Vereinigung Jahresbricht, Mathematics Magazine, and School Science and Mathematics. The problems are classified,...
In this paper we present a model of Non-Euclidean geometry
in three dimensions. This will show that the axioms of Non-Euclidean
geometry are consistent if Euclidean geometry and, hence, arithmetic
is consistent. However, the model is incomplete for we have not
included the topic of congruence, the axiom of Archimedes,...
Let A be an n x n real, symmetric matrix with distinct characteristic values λ₁, λ₂,...,λɴ. Then there exists an orthogonal matrix P such that PAPᵀ = Λ = (λi). Given a small symmetric change, ∆A, in the matrix A, we can calculate the resulting changes, ∆P, and ∆Λ, in...
This thesis documents a new language which facilitates
the construction of Turing machines. The language translator
is written in Compass and has been debugged and is
available for use on the CDC 3300.
This thesis describes the design of a syntax directed, production
language compiler called ALG. Special attention is given to the syntax
directed analyzer and the use of sub-syntax types. Relocation
codes are used for storage allocation and address assignment before
generating the relocatable binary object decks. Attention is also
given...
It is established folklore in numerical analysis, for solution
of a square system of linear equations by Gauss elimination, that the
standard method of choice of pivot elements is to search the entire
suppressed matrix for the element largest in absolute value. However,
it was felt by the author, that...
The storage tube computer graphics terminal provides
high resolution, high speed, and comparatively low cost
graphics. Oregon State University currently supports
four such terminals under the OS-3 time sharing system.
The terminals are used for a wide variety of applications
in the physical sciences and engineering.
This thesis describes TEKPLOT...
A solution to the problems of computer scheduling of students
based on course requests rather than section requests is discussed.
The solution involves keeping all course data in core during the
scheduling process to enable the scheduling program to run as fast as
possible and using a scheduling algorithm which...
This thesis documents a method of proving that Turing machines
work for every case, if the construction of the Turing machine is
known. Mathematical Induction is used to construct the proof that the
Turing machine for binary addition will work in every well-formed case
of the input that it receives....
A systematic and rigorous derivation of the Boolean functions that represent the three operations of the ring of integers in the 1-2-4-5 code is developed from their corresponding tables. The same is done for numerical complementation of a number. The equations of the latter are combined with those for addition...
A theory of straight line triangulations of points in the plane is developed. A basic transformation is presented, and it is shown that any triangulation may be transformed into any other triangulation which has the same boundary by a finite sequence of the basic transformations. The proof of the transformation...
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...
A technique of differentiation with respect to the distance to
the boundary of an outer parallel-body is applied to known measures of
sets of p-dimensional linear spaces which intersect a general convex
body in n-dimensional euclidean space in order to obtain an appropriate
definition of the measures of sets of...
This paper gives a proof that the Completeness Axiom of
Lobachevskian geometry -- as formulated in the second English translation
of David Hilbert's Foundations of Geometry (tenth German
edition)--is a theorem in the three dimensional Poincare model. An
explicit canonical isomorphism between all models of Lobachevskian
space is given.
This,...
This paper presents an extension of Hubert's incidence axioms to n dimensions and uses these and his order axioms to prove several theorems. We prove extensions of Pasch's Axiom, the Crossbar Theorem, and Desargues' Theorem for n dimensions. A non-Euclidean model is presented and proved to satisfy the axioms. In...
The author develops an algorithm for the recursive reduction
of Sylvester's determinant and the determination of the eliminant of
three algebraic equations in three unknowns. The ALGOL 60
language is used for the description of this algorithm.
The objective of this paper is to describe the design of a real-time system to control two hydroelectric power plants by a digital
computer. The two controlling relations are stated as the continuity
of water flow and the inequality of power generation requirements.
It contains the logical sequence in finding...
The computation of symmetric functions can be tedious.
For this reason, the object of this paper is to devise a computer
program so that these symmetric functions can be handled automatically.
The contribution of this investigation is a heuristic for
finding the polynomials proved to exist by the Fundamental Theorem...
FORTRAN is readily feasible to translation into ALGOL since
they share many common features. Most of the features that are
unique to FORTRAN can be translated by restricting them somewhat.
The translator will handle explicit declarations of each item
in a block, compensate for the differences in various operators,
compensate...
The enclosed thesis presents an algorithm, programmed
in FORTRAN IV, which generates the radii for
the objective of an astronomical refracting telescope.
The results are analyzed by the Trigonometric Ray
Trace, and found to have tolerable amounts of spherical
aberration, chromatic aberration and coma.
This paper makes available practical algorithms and their associated
FORTRAN IV computer programs for finding the roots of
polynomial equations.
The purpose of this paper is to examine effective algorithms
for solving polynomial algebraic equations in one unknown on a digital
computer. The advent of high - speed digital computing...