Properties of Mellin transforms are applied to the summation
of infinite series. A specific example of this application leads to the
establishment of certain properties of a generalization of Lerch's zeta
function.
Nine powerful methods of generating new tables of Mellin
transforms from existing tables of Mellin and other integral...
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.
In this paper we consider the behavior of certain surfaces at
certain boundary points. The surfaces under consideration satisfy
a topological definition and are of 2-dimension in 3-dimensional
Euclidean space with the boundary a finite set of straight line
segments. It is shown that the surface of minimum area with...
This thesis treats the problem of enumerating equivalence
classes of Euler paths of full graphs. A full graph
is a complete, unordered, graph with no loops or repeated
edges. Two Euler paths are equivalent if and only if one
can be transformed into the other by a finite sequence of...
The indicated sum of a real scalar and a real or imaginary
vector is called a scator. Either the scalar part or the vector part
may be null. Scators generalize the complex variable to n-space.
The algebra of scators is not generally associative under multiplication
but the commutative and distributive...
An algorithm is described for determining the vertices
and supporting planes (or lines) of the convex hull
of a given set of N distinct points in 3-space. The
method involves determining a finite sequence of convex
hulls, each successive convex hull being a better approximation
to the convex hull of...
The Euler-MacLaurin sum formula has appeared in the titles
of two quite recent papers whose authors were primarily interested
in certain applications. In this paper a somewhat different approach
to the myriad of formulas for summation, integration, differentiation,
etc. , is based on the simple identity which defines the set...