A mixed initial and boundary value problem is considered for
a partial differential equation of the form Muₜ(x, t)+Lu(x, t)=0,
where M and L are elliptic differential operators of orders 2 m
and 2l, respectively, with m ≤ l. The existence and uniqueness
of a strong solution of this equation...
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...
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...
The purpose of this paper is to show that arithmetic
is consistent if Euclidean geometry is. Specifically, a
model of Peano's axioms [2] is defined in the space of
Euclidean geometry, where Hilberts axioms [3] are taken
to be the axioms of Euclidean geometry.
This paper defines four function space topologies,
characterizes two of them in terms of more familiar
concepts, and compares the four topologies. Then in the
cases of the two less familiar topologies we have considered
several common properties of topological spaces
and attempted to answer the following question: If the...
This thesis introduces a technique for approximating to a desired
degree of accuracy a linear parabolic equation of two spatial
dimensions with given initial data and prescribed boundary conditions.
The technique is generalized to non-linear parabolic equations.
It is stable for all mesh ratios, and it is second order accurate...
This thesis examines various net or finite difference methods
for solving parabolic partial differential equations in one space variable
with constant coefficients. Included in this investigation are
explicit, implicit and multi-step methods of varying orders of accuracy.
These methods are compared with respect to accuracy, speed,
efficiency, stability, simplicity of...
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.
A mathematical model simulating mass transport of chemicals
in saturated porous medium is given in four parts. Included in the
development is the physical phenomenon of adsorption of molecules
of chemicals on the surrounding walls of the porous medium. The
four main areas of study are:
(1) Simple one dimensional...
In this paper we use the set of all positive integers as a sample space whose probability density function is unknown. Then a generalization of the probability distribution of the most significant digits of the set of all physical constants is obtained on the strength of (i) a very general...
A geometric condition on differentiable maps is given which is
equivalent to the set of critical values being nowhere dense. In particular,
the geometric condition is satisfied for radially ductile maps.
On the other hand it is proved that the induced map on the de Rham
complex will be a...
The effect of a time harmonic electric source ring placed
axially symmetric between the walls of a double conical structure of
finite slant height is investigated. The bases of the conical structures
are spherical caps of radii equal to the slant height.
The Green's function for ideally conducting walls is...
The electromagnetic field in a cone of arbitrary slant
height with a symmetrically placed time harmonic ring source is
studied. Through the use of the modified Helmholtz equation as
an intermediate, we obtain the solution of the semi-infinite
cone directly from the finite cone. To demonstrate the need
for the...
In this paper a direct, constructive proof of the equivalence of the Normal Algorithm and Turing machine using the Turing machines NAS (Normal Algorithm Simulator) and NAC (Normal Algorithm Converter) is presented. The Turing machine NAS can simulate any particular Normal Algorithm, and NAG can convert the quintuples of a...
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...
