This paper is a continuation of William Zell's thesis, A Model of Non-Euclidean Geometry in Three Dimensions. The purpose of that thesis was to show that the axioms of non-Euclidèan geometry are consistent if Euclidean geometry an& hence arithrnetic is consistent. Mr. Zell. discussed the axioms of connection and order...
The classical theory of elasticity and plasticity does
not recognize explicitly the existence of a "transition
zone" between elastic and plastic states, which instead,
makes extensive use of ad-hoc, semi-empirical laws, such as
yield conditions, at the "yield surface" to match both the
extreme states. In the present investigation, it...
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...
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...
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...
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...
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...
Integral representations for the generalized measures of deformation
and deformation-rates have been obtained and suitable constitutive
equations using these measures have been developed for
viscoelastic materials, These new constitutive equations are then
applied to study some flow problems, In order to assess the comparative
advantage of this approach over the...
In this paper, the general mathematical theory of linear
passive one-ports and the class of positive real functions are briefly
reviewed as background material. Then a time domain method for
synthesis of a finite lumped RC system is given, which involves
breaking down the given system into n subsystems. Finally,...
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...
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...