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...