Proceedings of
Dynamic Systems and Application


Volume 4

CONTENTS

Preface
Dynamic Systems and Control
 
 
Optimal Control of Systems Governed by Impulsive Differential Inclusions
N.U.Ahmed
 
1

Optimal Control of Gantry Cranes for Minimum Payload Oscillations
Saroj K. Biswas
 
12

Weighted Polynomial Approximation and Hilbert Transforms: Their
Connections to the Numerical Solution of Singular Integral Equations
S.B. Damelin and K. Diethelm
 
20


White Noise Perturbation in a Model Equation for the Viscoelastic
Response of Rubber in Tensile Deformation
N. Begashaw, N. G. Medhin, and M. Sambandham
 
27


Dynamical Systems and Applications
 
 
An Application of Functional Analysis in a Predator - Prey System
Primitivo B. Acosta-Humanez
 
35

 
Controlled Differential Equations for Solving Two-person Nonzero-sum
Games With Coupled Constraints
Anatoly S. Antipin
 
39


 
Quasiperiodic Flows and Algebraic Number Fields
Lennard F. Bakker
 
46

 
New Sufficient Conditions for Global Stability of a Basic Model Describing
Population Growth in a Polluted Environment
Bruno Buonomo and Deborah Lacitignola
 
53


 
Fixed Points and Coincidence Points of Discontinuous Monotone Operators
Yong-zhuo Chen
 
58

 
Nonlinear Integral Transforms and Dynamical Systems on Hilbert Spaces
Agnieszka Kozak and Yuri Kozitsky
 
63

 
Polynomial Models of Discrete Time Series over Finite Fields
Aihua Li
 
68

 
Optimal Control Problems Arising in Marketing Models
Luigi De Cesare and Andrea Di Liddo
 
74

 
Multiple-period-doubling Bifurcation Route to Chaos in Periodically Pulsed Chaotic Oscillators
S. Parthasarathy and K.Srinivasan
 
80

 
Homoclinic orbits and bifurcation of entropy_carrying hit_sets
Steven M. Pederson
 
87

 
The least vulnerable, the most successful and other such extremes
Bruce J. West
 
95

 
A Geometric Approach to the Legendre Transformation
Enrico Pagani
 
102

 
Partial Differential Equations and Applications
 

 
On a Nonlocal Hyperbolic Model Arising from a Reliability System
Azmy S. Ackleh, and Keng Deng
 
113

 
Blow-Up and Quenching of Solutions due to a concentrated Nonlinear Source
C. Y. Chan
 
121

 
Blow-Up of Solutions for Degenerate Semilinear Parabolic First
Initial-Boundary Value Problems
C. Y. Chan and W. Y. Chan
 
127


 
The Localization of Shear Bands via the Maximum Principle
C. O. Horgan and W. E. Olmstead
 
133

 
Response of Dark-adapted Retinal Rod Photoreceptors
H. Khanal, V. Alexiades, and E. Dibenedetto
 
138

 
Conditions on the Motion of a Heat Source that guarantee a Blow-up Solution of the
Two-dimensional Heat Equation
C. M. Kirk and W. E. Olmstead
 
146


 
Analysis of Conservative Difference Schemes for Materials with Memory
Peter Matus and Roderick V.n. Melnik
 
153

 
A Nonstandard Problem for the Heat Equation
Philip W. Schaefer
 
161

 
Diffusional Release of a Dispersed Solute from a Polymeric Matrix:
Approximation of the Exact Solutions Using Finite Region Continuity
S. Wasuwanich, N. Jinuntuya, P. Petpirom, and R. Collins
 
167


 
Numerical Approximations for Thomas-Fermi Model Using Radial Basis Functions
S. M. Wong and Y. C. Hon
 
175

 
Contraction Mapping and Stability in a Delay-differential Equation
Bo Zhang
 
183

 
On Maximum Principle and Existence of Positive Solutions for Elliptic Systems
A.Yechoui
 
191

 
The Dynamics Around the Ground State of the Timoshenko Equation with a Source Term
Jorge Alfredo Esquivel-Avila
 
198

 
Universal Contingent Claims in a General Market Environment and
Multiplicative Measures
Valery A. Kholodnyi
 
206


 
On the Nonlinear Bi-harmonic Parabolic Equation with Data in Lp Spaces
Tor A. Kwembe
 
213

 
Estimates for Solutions to Optimization Problems on Elliptic Equations
Fabrizio Cuccu, Monica Marras, and Giovanni Porru
 
220

 
Quantum Super Yang-mills Equations: Global Existence and Mass-gap
Agostino Prastaro
 
227

 
Resonance Problems for Hardy-Sobolev Operator with Indefinite Weights
V. Raghavendra and K. Sreenadh
 
233

 
Thin Layers for the Landau-Lifschitz Equation
David Sanchez
 
239

 
Applications of "Best Possible" Maximum Principles to Parabolic Problems in Non-convex Domains
Stella Vernier Piro
 
245

 
On Solutions of Hyperbolic Equations with Damping and Source Terms
Jianmin Zhu
 
250

 
Differential Equations and Applications
 

 
Retarded and mixed Neutral Differential Equations with Continuous Delay
Tuncay Candan and R.S. Dahiya
 
261

 
Approximating Limit Cycles of a Van der Pol Equation with Delay
David E. Gilsinn
 
270

 
Stability of Linear Periodic Differential Delay Equations
Ying Sue Huang
 
277

 
New Matrix Method for Analytical Solution of Linear Ordinary Differential Equations
Sina Khorasani and Ali Adibi
 
283

 
Implicit Compact Scheme for Harmonic Oscillator Equation with Coulomb Friction
James L. Thompson and Chaoqun Liu
 
291

 
Limit Cycles of Lienard Systems
Makhlouf Amar and Badi Sabrina
 
297

 
A Perturbation Method for Truly Nonlinear Oscillator Differential Equations
Ronald E. Mickens and Sandra A. Rucker
 
302

 
Asymptotic Behavior of Nonoscillatory Solutions Of Second-order Nonlinear Differential Equations
Octavian G. Mustafa and Yuri V. Rogovchenko
 
312

 
Fucikís Spectrum in Models of Suspension Bridges
Petr Ne°cesal
 
320

 
Controlling the Bone Marrow Dynamics in Cancer Chemotherapy
Urszula Ledzewicz and Heinz Schattler
 
328

 
Stability Criteria for Certain Third Order Delay Differential Equations
Baruch Cahlon and Darrell Schmidt
 
336

 
Asymptotic Stability of a Mechanical Robotics Model with Damping and Delay
Baruch Cahlon and Darrell Schmidt
 
343

 
A Number Theoretic Application of X n+1 = X n 2 - 2Qn ó Creating a New Primality Test
John H. Jaroma
 
351

 
On the Discrete Model of West Nile-like Epidemics
Tehara Darensburg and Vlajko L. Kocic
 
358

 
Stability Zones and Parametric Resonance for Discrete-time Hamiltonian Systems
Vladimir R Asvan
 
367

 
Stability Theory Methods in Singularly Perturbed Systems Dynamics
Lyudmila K.Kuzmina
 
374

 
Difference Equations and Applications
 

 
Basic theory of a class of linear integro-differential equations
P.C.DAS
 
387

 
Solutions of discrete equations with prescribed asymptotic behavior
Josef Diblik, Denys Khusainov, and Irena Ruzickova
 
395

 
A discrete, hierarchically-structured population model
S. R.-J. Jang
 
403

 
Strong Approximation of Reflecting Brownian Motion Using Penalty Method and its Approximation K. Inoue and S. Kanagawa
 
409

 
Aizermanís Conjecture for Difference Equations
Rigoberto Medina and Michael I.Gil
 
415

 
On Periodic Dynamic Equations on Measure Chains
Christian Potzsche
 
422

 
Boundary Value Problem and Applications
 

 
Positive Solutions of a Three Point Boundary Value Problem for Nonlinear Differential Equations
John R. Graef, Chuanxi Qian, and Bo Yang
 
431

 
A Non-Resonant Multi-Point Boundary Value Problem of Neumann-Dirichelet
type for a p-Laplacian type operator
Chaitan P. Gupta
 
439


 
On a Final Value Problem Connected with the B_S Model
H.C. Jimbo
 
443

 
Coercive Boundary Value Problems for Regular Degenerate Equations
Veli B. Shakhmurov
 
452

 
Geodesic Connectedness in Plane Fronted Waves. A Variational Approach
A.M. Candela, J. L. Flores, and M. Sanchez
 
458

 
A Class of Nonlinear Boundary Value Problems of Second-order Ordinary Differential Equations Lingju Kong and Qingkai Kong
 
465

 
Multiple Radial Solutions for a Superlinear Elliptic Problem in R N
A. Salvatore
 
472

 
Integral Equations and Applications
 

 
Qualitative Analysis of Integral Dynamic Model of Age-structured Population
with Intra-species Competition
Natali Hritonenko
 
483


 
Subexponential Solutions of Linear Integro - Differential Equations
J. A. D. Appleby and D. W. Reynolds
 
488

 
Integral Equations of Dynamic Systems with Controllable Memory
Yuri Yatsenko
 
495

 
Solving Strongly Singular Integral Equations
Johan H. De Klerk
 
501

 
Existence and Uniqueness of Semimonotone Nonlinear Stochastic Integral Equations
Hamideh D. Hamedani
 
509

 
Computational Methods and Applications
 

 
Computer Simulation and Modeling of Multistage Carcinogenesis Mutations
Reza Ahangar
 
519

 
On the Two-step a High Order of Accuracy Difference Schemes for the
Second Order Differential Equations
Allaberen Ashyralyev and Pavel E. Sobolevskii
 
528


 
Davenport Numbers & Generating Functions over Finite Abelian Groups
Chuang Peng
 
535

 
One Approach to Construction of Bilateral Approximations Methods for
Solution of Nonlinear Equations
B. M. Podlevskyi
 
542


 
Error, Confidence, and Cost in Engineering Computations
S. K. Sen
 
548

 
A Note on the Second Order of Accuracy Difference Schemes for
Hyperbolic-parabolic Equations in a Hilbert Space
Allaberen Ashyralyev and Hasan A. Yurtsever
 
556


 
Hexahedral Mesh Generation Using Isoparametric Smoothing
T. S. Li
 
563

 
Applied Mathematics
 

 
Equations of Interface Dynamics For Quasi-stationary Stefan Problem
R. Andrushkiw, V. Gafiychuk, A. Shnyr, and R. Zabrodsky
 
571

 
Impulsive Modelling in Neurophysiology
S. A. Belbas and Sunghee Kim
 
581

 
Gauss Map and its Applications
Hei-chi Chan

 
586

 
On a Class of Stationary Nonlinear Processes: a Review
Kamal C. Chanda
 
592

 
Spatial Analysis of Cumulative Voting with Modeling for Dynamical System Simulation
Duane A. Cooper
 
596

 
The Variable Mass Schroedinger Equation
Daniel Bessis and Andrei Mezincescu
 
602

 
Kelvin-Helmholtz Instability Waves in Supersonic Multiple Rectangular Jets with Large Ratio
Joshua Z.Du
 
607

 
On the Asymptotic Behavior of the Solutions of Parameter-dependent
Matrix Riccati Differential Equations with Respect to the Parameter
Gerhard Freiling and Andreas Hochhaus
 
613


 
Computation and Stability of the Implied Volatility
H.C. Jimbo , A.F. Djouguela , I. Ngongo
 
620

 
On the Convection Flow past an Accelerated Vertical Permeable Plate
M. R. Karim
 
629

 
What does Quantum Chaos mean?
D. Huard, H. Kroger, G. Melkonyan, K.J.M. Moriarty, and L.P. Nadeau
 
640

 
Diffusion in the Mckendrick-von Foerster Equation
R. Dilao and A. Lakmeche
 
647

 
Two Applications of Quantum Memory
Wafik A. Wassef
 
654

 
Transmitted wave in a poroelastic medium and its application in evaluation of osteoporosis
Yongzhi Xu
 
662

 
Gravito-Radiative Force and the Spiral Galaxy
Masataka Mizushima
 
670

 
Hamiltonian Torus Bifurcations Related to Simple Singularities
Heinz Hansmann
 
 679

 
Modeling and stability analysis for a class of dynamical systems with switching inputs
Zvi Retchkiman Konigsberg
 
686

 
Author Index