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%3Stanford University Computer Science Reports
%3List Number 9↔? 1980%1

@Listed here are abstracts of the most recent reports published by the
Department of Computer Science at Stanford University.

@%3Request Reports:%1 Complete the enclosed order
form, and return the entire order form page (including mailing label) 
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@%3Alternatively:%1 Copies of most Stanford CS Reports may be obtained by writing
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Stanford Ph.D. theses are available from %2University Microfilms%1, 300 North
Zeeb Road, Ann Arbor, Michigan 48106.
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%3STAN-CS-80-806:
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@%2On the Approximate Solution of Hyperbolic Initial-Boundary Value Problems%1
by William M. Coughran, Jr. (Thesis, 177 pages, June 1980)

@Hyperbolic initial-boundry value problems arise in a number of scientific
disciplines, such as meteorology, ocanography, geophysics, aerodynamics, acoustics,
and magnetohydrodynamics.  These problems usually cannot be solved analytically,
so approximate methods must be used.  Unfortunately, the construction of stable
finite difference approximations is a subtle matter, which often confuses the
practitioner; the existing theories for establishing the well-posedness of
continuous initial-boundary value problems and the stability of discrete analogs
involve the verification of complicated algebraic conditions.  Moreover, the
stability theory fo discrete initial-boundary value problems in more than one
space dimension is not well developed.

@In this thesis, the existing stability theory for discrete initial-boundary value
problems, which has only been applied to (essentially) salar model problems, is
used to analyze the stability of some %22 %4x %22%1 model problems, not written
in characteristic variables; it is noted that the most accurate interior/boundary
difference scheme combinations are the least stable to perturbations in the
coefficients.  (A practical numerical procedure for verifying the stability of
discrete initial-boundary value problems is also introduced.)  The stability
results for %22 %4x %22%1 systems can be used in the stability analysis of larger
systems where characteristics occur only singly and in pairs; in particular,
discretizations of the wave equation, the shallow  water equations, and the Eulerian
equations for gas dynamics, which involve boundary conditions written in "natural"
variables, are examined.  The stability theory is also extended to multi-dimensional
initial-bondary value problems by means of the concept of "tangential dissipativity";
as an application, a tangentially dissipative leap-frog metho is shown to be stable
with Euler boundary conditions for a two-dimensional wave equation problem.  The
viability and limitations of the theory are demonstrated with some computational
experiments.  Finally, combining stability results with accuracy considerations,
various approximations and boundary conditions are ranked.
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%3STAN-CS-80-807:
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@%2Path-Regular Graphs%1 by David W. Matula and Danny Dolev
(39 pages, June 1980)

@A graph is vertex-[edge-]path-regular if a list of shortest paths, allowing
multiple copies of paths, exists where every pair of vertices are the endvertices
of the same number of paths and each vertex [edge] occurs in the same number of
paths of the list.  The dependencies and independencies between the various
path-regularity, regularity of degree, and symmetry properties are investigated.
We show that every connected vertex-[edge-]symmetric graph is vertex-[edge-]path-regular,
but not conversely.  We show that the product o any two vertex-path-regular
graphs is vertex-path-regular but not conversely, and the iterated product
%2G %4x %2G %4x * * * x %2G%1 is edge-path-regular if and only if %2G%1 is
edge-path-regular.  An interpretation of path-regular graphs is given regarding
the efficient design of concurrent communication networks.
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%3AIM-338 (STAN-CS-80-809):%1
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@%2An Extention of Screw Theory and its Application to the Automation of
Industrial Assemblies%1 by Jorgan S. Ohwovoriole (Thesis, 186 pages, April 1980)

@Interest in mathematical models that adequately predict what happens in the
process of assembling industrial parts has heightened in recent times.  This is
a result of the desire to automate the assembly process.  Up to this point there
has not been much success in deriving adequate mathematical models of the assembly
process.

@This thesis is an attempt to develop mathematical models of parts assembly.
Assembly involves motion of bodies which generally contact each other during
the process.  Hence, we study the kinematics of the relative motion of contacting
bodies.

@Basic to the theory of assembly is the classical theory of screws which,
however, required substantial extensions for this application.  The thesis begins
with a review of basic screw theory, including line geometry and reciprocal screw
systems, and new and more general derivations of some of these screw systems.
We then extend the screw theory by introducing such concepts as "repelling" and
"contrary" screw pairs, and "total freedom."

@Finally, we give a method of characterizing assemblies of industrial parts.
Using the extended screw theory, we then analyze the "general peg-in-hole assembly"
and subsequently give a mathematical description of this particular assembly.
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