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.
The Schwarz-Christoffel transformation is used to map simply connected polygons onto the upper half plane and can be applied to problems in which the validity of Laplace's equation is assumed. However the direct integration of the resulting complex integral is often not possible and some approximate method must be used....
This thesis is concerned with the detailed derivation
of Sheppard's Correction Formula relating the true to the
raw moments by the use of Euler-MacLaurin formula. Special
moment relationships have been derived using different
special functions, whose application is made to derive correction
formula for the semi-invariants. Special investigation
is carried...
In this thesis we consider computer techniques for inverting
n X n matrices and linear Fredholm integral operators of the
second kind. We develop techniques which allow us to prove the
existence of and find approximations to inverses for the above
types of operators. In addition, we are able to...
It is well -known that a topology for a space can be described in
terms of neighborhood systems, closed sets, closure operator or convergence
as well as open sets. In fact, it is also possible to describe
a topology in terms of interior operator or boundary operator. This
paper is...
G. F. Drukarev has given a method for solving the Fredholm
equations which arise in the study of collisions between electrons
and atoms. He transforms the Fredholm equations into Volterra
equations plus finite algebraic systems. H. Brysk observes that
Drukarev's method applies generally to a Fredholm integral equation
(I-λ G)u...
This thesis develops recursion formulas for least-squares
data smoothing with regard to four classes of functions: linear,
quadratic, exponential and trigonometric, which in a linear fashion
involve 2, 3, 2 and 2 parameters respectively. The term recursion
implies here that the estimates for the parameters of the preceding
fit are...
Some of the properties of the numbers of two quadratic number
fields are explored. Among these properties is the existence of
unique prime factorization of the integers of the field and the importance
of the concept of ideal numbers in restoring unique factorization
when it does not exist. Some consideration...
This paper defines and discusses some of the separation
axioms of topological spaces. In the cases considered,
a search is made for sets of conditions which
would be equivalent in a space satisfying a given separation
axiom to the existence of a family of real valued,
continuous functions which separates...
Let A and B be two subsets of the set of all non-negative
integers with 0 ε A and O ε B. The sum of the sets A and B is
the set C = A + B = {a + b: a ε A, b ε B). For n...
The work in this thesis falls into two parts. The first part
presents a rigorous theory of probability densities and correlation
functions within the framework of the exponential spaces of D. S.
Carter. The second part extends this discussion to include infinite
systems.
The first part begins by considering an...