I
MATHEMATICAL MODELLING An International Journal EDITORS Ervin Y. Rodin
Xa~erJ.R. Av~a
LIST OF C O N T E N T S and
AUTHOR INDEX VOLUME 3, 1982
Pergamon
Press
New York • Oxford • Toronto • Paris • Frankfurt • Sydney
MATHEMATICAL MODELLING An International Journal Editors
Xavier J.R. Avula
Ervin Y. Rodin
Department of Engineering Mechanics University of Missouri-Rolla Rolla, Missouri 65401, U S A
D e p a r t m e n t o f Systems Science a n d Mathematics Box 1040, W a s h i n g t o n U n i v e r s i t y St. Louis, Missouri 63130, U S A
Editorial Board
Publishing, Subscription and Advertising
R u t h e r f o r d Arts
S i m o n A. Levin
University o f Minnesota
Cornell University
H . T . Banks
William F. L u c a s
Brown University R i c h a r d Bellman
University o f Southern California E d w a r d J. Bcltrami
Cornell University N. M e t r o p o l i s
Los Alamos Scientific Laboratory, New Mexico
State University o f New York at Stony Brook
E.W. Montroll
R a y m o n d Bisplinghoff
J . C . J . Nihoul
Tyco Laboratories, New Jersey Martin Braun
Queens College, New York
University o f Rochester, New York University de Liege, Belgium Hans Oestreicher
R o g e r W. Brockett
Aerospace Medical Research Laboratory, Ohio
Harvard University
E d w a r d C. P o s n e r
Colin W. C l a r k
California Institute o f Technology
Fred S. R o b e r t s
Copyright © 1983 Pergamon Press Ltd.
R o b e r t Rosen
h is a condition of publication that manuscriptssubmitted to this journal have not been published and will not he simultaneously submitted or published elsewhere. By submitting a manuscript, the authors agree that the copyright for their article is transferred to the publisher if and when the article is accepted for publication. The copyrightcovers the exclusiverights to reproduceand distribute the article, including reprints, photographic reproductions, microform or any other reproductions of similar nature and translations. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means,electronic, electrostatic, magnetic tape, mechanical, photocopying, recordingor otherwise,without permission in writing from the copyright holder.
llya P r i g o g i n e
Brussels, Belgium
Stanford University
C.R. Rao
University o f Pittsburgh
R. Glowinski
Laboratorie de Recherche en Informatique et Automatique, Le Chesnay, France
Dalhousie University, Canada
H.S. Green
Massachusetts Institute o f Technology
University o f Adelaide, South Australia
T h o m a s L. Saaty
Gian-Carlo Rota
Frank Harary
University o f Pittsburgh
University o f Michigan
Stephen S m a l e
J.N.R. Jeffers
University o f California
Institute o f Terrestrial Ecology, England
J e r o m e Spanier
M a r k Kac
Rockefeller University, New York R u d o l f E. K a l m a n
Swiss Federal Institute o f Technology, Zurich and University o f Florida H e r b e r t Keller
California Institute o f Technology M u r r a y S. K l a m k i n
University o f Alberta, Canada M.D. Kruskal
Princeton University R o g e r E. Levien
International Institute o f Applied System Analysis, Laxenburg, Austria
tion subscribes at the regular rate (1983) $45.00; Special rate for m e m b e r s o f A M S / M A A , S I A M , I A M M , a n d SES available u p o n request. Prices include surface postage a n d insurance; air mail subscriptions extra.
Rutgers University
University o f British Columbia
Columbia University
Published Bimonthly. (ISSN 0270-0255) Annual subscription rate (1983) $115.00; Two-year rate (1983/84) $218.50; Special individual rate for those w h o s e institu-
Microform Subscriptions: S i m u l t a n e o u s subscriptions on m i c r o f i c h e a n d m i c r o film are available f r o m P e r g a m o n Press a n d / o r its division, M i c r o f o r m s I n t e r n a tional M a r k e t i n g C o m p a n y , Fairview P a r k , E l m s f o r d , New Y o r k 10523, U S A ; a n d H e a d i n g t o n Hill H a l l , O x f o r d O X 3 0BW, England.
G.B. Dantzig
J o h n U. Farley
Offices: P e r g a m o n Press, Inc., Fairview Park, Elmsford, NY 10523, USA; and P e r g a m o n Press Ltd., Headington Hill Hall, Oxford OX3 0BW, England.
Claremont Graduate School, California L y n n A r t h u r Steen
St. Olaf College, Minnesota S a m u e l C . C . Ting
Massachusetts Institute o f Technology Stanislaw M. U l a m
University o f Colorado H. v o n G i e r k e
Yellow Springs, Ohio Lotfi Z a d e h
University o f California, Berkeley O . C . Zienkiewicz
University o f Wales Hans-Jurgen Zimmerman
Rheinisch- Westfalische Technische Hochschule Aachen, FR Germany
U.S. CopyrightLawapplicableto usersin the USA: The Article Fee Code on the first pageof an articlein this journal indicates the copyrightowner's consent that in the U.S.A. copies may be made for personal or internal use provided the stated fee for copying beyond that permitted by Section 107"or 108 of the United States Copyright Law is paid. The appropriate remittanceshould be forwarded with a copy of the first page of the article to the Copyright Clearance Center Inc., 21 Congress Street, Salem, MA 01970. If a code does not appear copies of the article may be made without charge, providedpermissionis obtained from the publisher. The copyrightowner's consent does not extendto copyingfor generaldistribution, for promotion, for creating new works or for resale. Specific written permission must be obtained from the publisher for such copying. In case of doubt please contact your nearest Pergamon office.
MATHEMATICAL MODELLING VOLUME 3, NUMBER 1
Models for Endemic Infections with Asymptomatic Cases. I. One Group
Kenneth L. Cooke
1
A. Grauel
17
Thermodynamic Field Theory of Chemically Reacting Fluids in an Interface. I. A Two-Dimensional Theory of Mixtures of Chemically Reacting Fluids
A. Grauel
35
Thermodynamic Field Theory of Chemically Reacting Fluids in an Interface. II. The Second Law as Constraint to the Constitutive Equations
Parthasaradhi Mallela
59
State Controllability (and Identifiability) of Discrete Stationary Linear Systems with Arbitrary Lag
Luis G. Vargas
69
Reciprocal Matrices with Random Coefficients
A. I. Liapis G. G. Lipscomb O. K. Crosser E. Tsiroyianni-Liapis
83
A model of Oxygen Diffusion in Absorbing Tissue
Leonard R. Anderson
93
Pole Placement and Order Reduction in Two-Time-Scale Control Systems Through Riccati Iteration
VOLUME 3, NUMBER 2
David T. Lynch Thomas D. Rogers Sieghard E. Wanke
103
Chaos in a Continuous Stirred Tank Reactor
Govindasami Naadimuthu E. Stanley Lee
117
Stochastic Modelling and Optimization of Water Resources Systems
Karmeshu
137
Time Lag in a Diffusion Model of Information
Hiroyuki Abe Toshio Nakamura
143
Finite Deformation Model for the Mechanical Behavior of Left Ventricular Wall Muscles
M. Shahinpoor
153
Mathematical Modelling of the Future for Complex Systems
H. S. Green T. Triffet
161
Ionic Currents in the Debye Layers of the Neutral Membrane and Their Relation to Elementary Learning Processes 593
Benjamin Koo
179
Brief Note: A Reliability Model for Fire Safety in Structural Steel Members
David D. Ardayj'io
183
Brief Note: Viscoelastic Modelling of Cantilever Vibration Absorbers
VOLUME 3, NUMBER 3 Arthur David Snider
191
Mathematical Techniques in Extended Surface Analysis
J. R. Pounder Thomas D. Rogers
207
Global Stability in Population Models
Richard D. Noble
215
Mathematical Modelling in the Context of Problem Solving
Bruce Peterson Michael Olinick
221
Leontief Models, Markov Chains, Substochastic Matrices, and Positive Solutions of Matrix Equations
Alain Meritet
241
A Small Radiogoniometric Antenna
Yalcin B. Acar H. T. Durgunoglu Mehmet T. Tumay
259
A Bipolar Analytical and Parametric Finite Element Method Analysis of Surface Loading in Semi-Infinite Mass with a Circular Opening
VOLUME 3, NUMBER 4 V. R. Voller M. Cross
279
A Model of Thermally Induced Strain Development in Coke Oven Walls During Carbonization
K. Gaid A. Y. Le Roux G. Martin
293
A Nonlinear Problem Occurring in Water Purification in Aerated Actix~ated Carbon Biofilters
Vasilis Z. Marmarelis
305
Nonparametric Validation of Parametric Models
G. T. Papaspyropoulos T. S. Papatheodorou Hung Tao Shen
311
Collocation Finite-Element Simulation of Thermal-Ice Regimes in Rivers
James G. Taylor
323
Annihilation Prediction for Lanchester-Type Models of Modern Warfare with Logistics Constraints
E. A. Marshall D. W. Windle
341
A Moving Boundary Diffusion Model in Drug Therapeutics
H. M. Cekirge N. Gunay R. J. Fraga
371
Movements of Sand Dunes: I. TwoDimensional Model
594
VOLUME 3, NUMBER 5 Special Issue Mathematical Modelling at the International Institute for Applied Systems Analysis Roger E. Levien Andrzej P. Wierzbicki Brian Arthur
385
Introduction
Andrzej P. Wierzbicki
391
Mathematical Basis for Satisficing Decision Making
Y. M. Ermoliev G. Leonardi
407
Some Proposals for Stochastic Facility Location Models
Lars Bergman
421
A System of Computable General Equilibrium Models for a Small Open Economy
Ern6 Zalai
437
Computable General Equilibrium Models: An Optimal Planning Perspective
Giinther Fischer Klaus Frohberg
453
The Basic Linked System of the Food and Agriculture Program at IIASA: An Overview of the Structure of the National Models
M. B. Beck
467
Modelling a Complex Environmental System: The Lake Balaton Study
L. Somly6dy
481
Identifying Models of Environmental Systems' Behaviour
VOLUME 3, NUMBER 6 Dan W. Urry
503
Henry Eyring (1901-1981): A 20th Century Physical Chemist and His Models
M. SomviUe G. Billen J. Smitz
523
An Ecophysiological Model of Nitrification in the Scheldt Estuary
Adnan Akay
535
Mathematical Modelling of Transient Vibration and Acoustic Radiation from Impacted Systems
Myron H. Young
543
Implicit Solution for Estuarine Hydrodynamic Modelling
Paul D. Babcock L. F. Stutzman
559
New Developments in Chemical Process Simulation--FLOWSIM
Kenneth O. Kortanek Ralph W. Pfouts
573
A Biextremal Principle for a Behavioral Theory of the Firm
595
MATHEMATICAL
MODELLING
AUTHOR INDEX, VOLUME 3, 1982 Abe, Hiroyuki, 143 Acar, Yalcin B., 259 Akay, Adnan, 535 Anderson, Leonard R., 93 Ardayfio, 183 Arthur, Brian, 385
Marshall, E. A., 341 Martin, G., 293 Meritet, Alain, 241 Naadimuthu, Govindasami, 117 Nakamura, Toshio, 143 Noble, Richard D., 215
Babcock, Paul D., 559 Beck, M. B., 467 Bergman, Lars, 421 Billen, G., 523
Olinick, Michael, 221 Papaspyropoulos, G. T., 311 Papatheodorou, T. S., 311 Peterson, Bruce, 221 Pfouts, Ralph W., 573 Pounder, J. R., 207
Cekirge, H. M., 371 Cooke, Kenneth L., 1 Cross, M., 279 Crosser, O. K., 83
Rogers, Thomas D., 103, 207 Durgunoglu, H. T., 259 Shaninpoor, M., 153 Shen, Hung Tao, 311 Smitz, J., 523 Snider, Arthur David, 191 Somly6dy, L., 481 Somville, M., 523 Stutzman, L. F., 559
Ermoliev, Y. M., 407 Fischer, GOnther, 453 Fraga, R. J., 371 Frohberg, Klaus, 453 Gaid, K., 293 Grauel, A., 17, 35 Green, H. S., 161 Gunay, N., 371
Taylor, James G., 323 Triffet, T., 161 Tsiroyianni-Liapis, E., 83 Tumay, Mehmet T., 259
Karmeshu, 137 Koo, Benjamin, 179 Kortanek, Kenneth O., 573
Urry, Dan W., 503
Le Roux, A. Y., 293 Lee, E. Stanley, 117 Leonardi, G., 407 Levien, Roger E., 385 Liapis, A. I., 83 Lipscomb, G. G., 83 Lynch, David T., 103
Vargas, Luis G., 69 Voller, V. R., 279 Wanke, Sieghard E., 103 Wierzbicki, Andrzej P., 385, 391 Windle, D. W., 341 Young, Myron H., 543
Mallela, Parthasaradhi, 59 Marmarelis, Vasilis Z., 305
Zalai, Ern6, 437 596