The author shows that a necessary and sufficient condition
for a convex polyhedron to be representable as a finite vector sum
of line segments is that each of its faces possesses central symmetry.
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...
In this paper, we are concerned with the very general notion of
a universal algebra. A universal algebra essentially consists of a set
A together with a possibly infinite set of finitary operations on. A.
Generally, these operations are related by means of equations, yielding
different algebraic structures such as...
In the study of uniform convergence, one is led naturally to
the question of how uniform convergence on subsets relates to uniform convergence on the whole space. This paper develops theorems on how pointwise convergence relates to uniform convergence
on finite sets, how uniform convergence on finite subsets relates to...
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...
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...
This paper is the record of an exploration of two quadratic
number fields. The first section is devoted to the field with elements
of the form a +b√3 where a and b are rational numbers.
This field contains an integral domain in which unique factorization
holds. The second section is...
This paper records a study of two quadratic number fields. In the first field, denoted by Ra[[square root] 11], the unique factorization theorem holds. In the second field, denoted by Ra[[square root] 10], it is demonstrated that the unique factorization theorem does not hold and therefore ideals are introduced to...
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 author studies the class of rectangular arrangements in
terms of two binary relations on the objects of the arrangement.
He shows how a univalent matrix determines a unique rectangular
arrangement, and how each rectangular arrangement is associated
with one, two, or four distinct matrices, according to the number
of...
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...