Table Of Contentu. S. ARMY RESEARCH 0FFICE
Report No. 76-1
February 1976
TRANSACTIONS OF THE TWENTY-FIRST CONFERENCE
OF ARMY MATHEMATICIANS
Sponsored by the Army Mathematics Steering Committee
Host
U. S. Army White Sands Missile Range
White Sands Missile Range, New Mexico
14-16 May 1975
•.• I
Approved for public release; distribution unlimited.
The findings in this report are not to be construed
as an official Department of the Army position, un
less so designated by other authorized documents.
U. S. Army Research Office
P. O. Box 12211
Research Triangle Park, North Carolina
· I
FOREWORD
These Transactions preserve in print most of the invited addresses
and contributed papers of the Twenty-first Conference of Army Mathemati
cians. These meetings are sponsored by the Army Mathematics Steering
Committee (AMSC) on behalf of the Office of the Chief of Research, Develop
ment and Acquisition. Members of this Committee request that the guest
lecterers be effective researchers who are in frontier fields of live
current interest. They feel that the addresses by the invited speakers
as well as contributed papers by Army per~onnel will stimulate the inter
changes of ideas among the scientists attending said meetings.
In June of 1973, Messrs. W. A. McCool and William Sheperd of the
White Sands Missile Range called the Army Research Office (ARO) to inquire
about the possibility of holding either the Twentieth or the Twenty-first
Conference of Army Mathematicians at their installation. Since the next,
the Twentieth Conference, had been scheduled for the US Army Natick Labor
aotires, these gentlemen were thanked and advised that a written offer to
host the 1975 meeting would be appreciated. Dr. Richard H. Duncan, Tech
nical Director and Chief Scientist of the White Sands Missile Range, in a
letter dated 10 May 1974 issued a formal invitation to hold this meeting
at his installation. Part of his letter is quoted below:
I cordially invite the Applied Mathematics Subcommittee, US Army
Mathematics Steering Committee, to hold the Twenty-First Confer
ence of Army Mathematicians at the US Army White Sands Missile
Range, NM, in May 1975. We would be pleased to serve as host to
the conference.
iii
I believe a conference held here would attract a number of
Western Army Mathematicians who do not normally attend the
conferences. Their attendance and participation would be
of substantial benefit to the Army installations in our
area.
If the conference is held here, Mr. P. J. Higgins, Chief of the
Analysis and Computation Division, National Range Operations
Directorate, will be in charge of local arrangements. Please
contact him for additional information.
Over 115 Army and academic scientists attended this 14-16 May 1975
conference, which convened in E1 Paso, Texas. It is pleasing to note
that over hald of these individuals were from the host installation. On
the afternoon of the second day of the meeting, Mr. P. J. Higgins, the
Chairman on Local Arrangments, arranged a trip to the White Sands Missile
Range and a very interesting tour of that base. Those in attendance are
indebted to him and members of his staff for this three day meeting.
The success of this conference was due to many persons, including
the active and enthusiastic members of the audience, the chairmen of the
sessions, and authors of the many papers. The members of the AMSC would
like to thank these gent1ement for taking time to prepare papers for
these Transactions so that many persons unable to attend this symposium
can profit by their contributions to the scientific literature.
;v
TABLE OF CONTENTS*
TITLE PAGE
.
Foreword .. .. .. .. iii
Table of Contents v
Program . . . . . viii
On spectrally Bounded Signed Graphs
A. J. Hoffman . 1
• • f • • '" • • • • • ill •
Effects of Concentrated Mass and Thrust Directional Control on the
Stability of Free-Free Beams
Julian J. Wu ...•... . . . . . . . . . . . . . . . 7
The Standard Linear Model in the Stability and Mass Optimization of
~onconservative Euler Beams
Charles R. Thomas . . • . . . . . . . . . . . . . . . . . . 27
Buckling of Orthotropic Rectangular Cylinders
Earl C. Steeves . 79
Energy Release Rate in Terms of Complex Analytic Functions
M. A. Hussain and S. L. Pu . . . . . . . . . . . . . 81
Development and Application of Dynamic r~athematical Models for
Evaluation of Military Systems, Forces and Doctrine
Roger F. Wi11is. . . . . . . . . . . . . . . . . . 93
Homeostatic Criteria for Assessment of the Morphological State of
Large Scale Hybrid Analytical-Simulation Models
Howard M. Bratt. . . . . . . . . . . . . . . . . 117
The Application of Infinitesimal Transformation Groups to the
Solution of Nonlinear Partial Differential Equations
George W. Ullrich. . . . . . . . . . . . . . • . . . . . 125
On Uniqueness of Piecewise Polynomial Approximation
C. K. Chui, P. W. Smith, and J. D. Ward .... 141
Linear Generalizations of the Gronwall-Reid-Bellman Lemma
Jagdish Chandra and Paul Wi11iam Davis . . . . . 149
*Th;s table of contents contains only the papers that are published in this
technical manual. For a list of all papers presented at the Twenty-first
Conference of Army Mathematicians, see the program of the agenda.
v
AMethod for the Numerical Solution of Two-Point Boundary Value
Problems based on the Use of Volterra Integral Operations
Ho Fujita and Lo Bo Rall 151
0 0 0 0 0 0 0 0 0 0 0 0 0 0
Nonlinear Vibration Theory of Pavements
. . . . . .
Richard Ao Weiss .. ... .. .. .. .. 187
0 0 0 0 0 • 0 0 •
Application of the Theory of Slender Curved Rods to the Analysis of
Elastic Yarns
No Co Huang • 217
0 • 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 •• 0 •
AMaximum Likelihood Decision Algorithm for Markov Sequences with
Multiple Applications to Digital Communications
Andrew J. Viterbi . 251
0 0 0 • 0 0 0 0 0 0
The Calculation of Unsteady Shear Stresses in Gun Barrels
Ro Yalamanchili 277
0000000000000000
Nonlinear Problems in the Interaction of a Steel Cartridge Case and
the Chamber
Jo Jo Toal and So Co Chu 299
0
Nine-Point Difference Solutions for Poisson's Equation
J Barkley Ross . 313
0 0 • 0 0 • 0 0 0 0 0 0 0 0 0 III .. • III • • •
Illuminating Round Effectiveness Modeling
Martin Messinger and Leonard Oleniczak 335
Launching of Electromagnetic Surface Waves at a Planar Metal-Air
Interface
J. M. Zavada and Eo Lo Church • 351
0 0 0 0 • 0 ••• 0 •
Comparison of Perturbation-Theoretic and Exact Calculations of
Nonlinear Optical Properties of Optoelectronic Materials
So So Mitra, L. Mo Narducci, and Ro Ao Shatas •• 363
0 •
ATime-Dependent Quantized Natural Collision Coordinates Method
Norman Mo Witriol 397
0 0 0 0 0 ••• 0 • 0 0 •• 0 •• 0 0 0
Computer Simulation of the Intermediate Ballistic Environment of a
Small Arm
Csaba Ko Zoltani 399
0 0 0 0 0 • 0 0 • 0 0 0 0 0 0 0 • 0 0 0 • 0 • 0
Generalized Shock Wave Physics: Electromagnetic and Second Sound
Shocks
Paul Harris 415
0 0 0 0 0 ••
On Riemann's Invariant and Schock Impedance of Solids
Yo Ko Huang 423
0 0 0 0 0 0 0 0 0 0 0 • 0 0 0 • 0 0 o 0
vi
Frequency Dependent Wave Arrival Time Delays in Dispersive and
Nondispersive Media
J. R. Stabler, E. A. Baylot, and D. H. Cress. . . . . 431
The Method of Parabolic Substitution for High Subsonic Flow
Klaus Oswatitsch and Robert E. Singleton .....•. 445
The Backward Beam Equation and the Numerical Computation of
Dissipative Equations Backwards in Time
Alfred Carasso ..•.......•••••••••• 457
Special Solutions of the One-Dimensional Parabolic Equation
Siegfried H. Lehnigk . . . . . . . . . . . . . . . . . . . . . . 503
r
Integration of ~ F{x)J (ax)Jl{bx)dx
o 0
Shunsuke Takagi 511
Singular Perturbations in Heat Conduction and Diffusion Problems
John F. Polk . . . . • • . . . . • . . . • • . . • . • . • . 543
Sample Sizes for Missile in Flight Reliability Determination
Edward F. Southworth . . . . . . . . . . . . . . . . . . 559
DOVAP Best Estimate of Trajectory
. . .
Robert H. Turner and William S. Agee .. .' .. . ,. .. . ,. " . .. 587
Optimal DOVAP Instrumentation Planning
William S. Agee and Jerry L. Meyer. 605
• ,. til • .. • • .. 11II • .' • • •
Proving Programs Correct
Elwood D. Baas • . . . • . . 615
.. • • • • .. 11II • • 11II • • • • .. • • •
Generalized Plane Strain in an Elastic, Perfectly Plastic Cylinder,
With Reference to the Hydrau1ic Autofrettage ProcesS
Alexander S. Elder, Robert C. Tompkins and Thomas L. Mann 623
Nonlinear Problems in Chemically Reacting Diffusive Systems
Donald S. Cohen ......•.......••..• 661
ANew Numerical Method of Solution of Schrodinger's Equation
George Morales and Robert G. McIntyre . • . . . • 671
List of Attendees . . . . . • . . . • . . . . . . . . . . . . 707
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PROGRN1
21st CONFERENCE OF ARMY MATHEMATICIANS
US Army White Sands ~1i ssile Range, NevI t1exico
All general and technical sessions will be held in the Rodeway Inn (Bassett
Center) 6201 Gateway West. El Paso, Texas.
REGISTRATION - ERICA ROOM
0845--0900 OPENING OF THE CONFERENCE WELCOMING REMARKS - ERICA ROOM
0900-1000 GENERAL SESSION I - ERICA ROOM
SPEAKER: Professor A1drl J. Hofflnan
Mathematical Sciences
IBM Thomas J. Watson Research Center
P.O. Box 218
Yorktown Heights, New York 10598
TITLE: Graph Theory and Eigenvalues of Mcttrices
CHAIRr\1AN: Dr. Ivan R. Hershner, Jr.
Room 3E 453
The Pentagon
HQDA (DAt-1A-ARZ-D)
Washington, D. C. 20310
1000··'020 BREAK
1020-1200 TECHNIC.t\L SESSION I - ERICA ROor·l
CHAIRr~AN : Dr. Edl-/al'd \·1. Ross, .Jr.
Staff Mathematician
US Arn~ Natick Laboratories
Natick, Massachusetts 01760
viii
Hednesday AM
1020-1200 TECHNICAL SESSION I (Continued)
EFFECTS OF CONCENTRATED MASS AND THRUST DIRECTIONAL
CONTROL ON THE STABILITY OF FREE-FREE BEAMS
Julian J. Wu. B~n~t Weapons Laboratory. Watervliet
Arsenal. Watervliet. New York
THE STANDARD LINEAR MODEL IN THE STABILITY AND MASS
OPTI~lI ZATION OF NONCONSERV,UIVE EULER BEAr·1S
Charles R. Thomas. B~n~t \'Jeapons LaboratoY'y, Water'll iet
Arsenal. Watervliet, New York
BUCKLING OF ORTHOTROPIC RECTANGULAR CYLINDERS
Earl C. Steeves, US Army Natick Laboratories. Natick.
Massachusetts
ENERGY RELEASE RATE IN TERMS OF COMPLEX ANALYTIC
FUNCTIONS
M. A. Hussain and S. L. Pu, Watervliet Arsenal~ Watervliet,
New York
1020-1200 TECHNICAL SESSION II - TROPHY ROOM
CHAIRMAN: Dr. Badrig M. Kurkjian
At-1CRD-R
5001 Eisenhower Avenue
Alexandria. Virginia 22304
DEVELOPMENT AND APPLICATION OF DYNA~lI Cr·1ATHH1ATICAL
MODELS FOR EVALUATION OF MILITARY SYSTEMS, FORCES
AND DOCTRINE
Roger F. ~;i 11is, US Army Combined Arms Combat
Development Activity, Ft. Leavem-lOrth, Kansas
APPLIED TECHNIQUES OF ACQUISITION AND PRODUCTION COST
ANALYSIS
Van A. Puryear. US Army Troop Support Command.
St. Louis, Missouri
HOMEOSTATIC CRITERIA FOR ASSESSMENT OF THE MORPHOLOGICAL
STATE OF LARGE SCALE HYBRID ANALOG-SInULATION Cor·1PUTER
MODELS
HOI'/ard ~t Bratt. US Army Air r~obi1ity Research and
Development Laboratory, Ft. Eustis. Virginia
ix
