Showing papers in "The Journal of The Australian Mathematical Society. Series B. Applied Mathematics in 1979"
TL;DR: In this article, the convergence properties of a general class of adaptive recursive algorithms for the identification of discrete-time linear signal models are studied for the stochastic case using martingale convergence theorems.
Abstract: The convergence properties of a very general class of adaptive recursive algorithms for the identification of discrete-time linear signal models are studied for the stochastic case using martingale convergence theorems. The class of algorithms specializes to a number of known output error algorithms (also called model reference adaptive schemes) and equation error schemes including extended (and standard) least squares schemes, They also specialize to novel adaptive Ka]man filters, adaptive predictors and adaptive regulator algorithms. An algorithm is derived for identification of uniquely parametrized multivariabie linear systems. A passivity condition (positive real condition in the time invariant model case) emerges as the crucial condition ensuring convergence in the noise-free cases. The passivity condition and persistently exciting conditions on the noise and state estimates are then shown to guarantee almost sure convergence results for the more general adaptive schemes. Of significance is that, apart from [he stability assumptions inherent in the passivity condition, there are no stability assumptions required as in an alternative theory using convergence of ordinary differential equations.
36 citations
TL;DR: In this paper, the authors studied the analytic solutions for large | S | through the method of matched asymptotic expansions and found that boundary layers exist near the walls for large| S | and that flow reversals and oscillations of the velocity profile occur for large negative S (fast expansion of the tube).
Abstract: Viscous fluid is squeezed out from a shrinking (or expanding) tube whose radius varies with time as (1 – β t ) ½ . The full Navier–Stokes equations reduce to a non-linear ordinary differential equation governed by a non-dimensional parameter S representing the relative importance of unsteadiness to viscosity. This paper studies the analytic solutions for large | S | through the method of matched asymptotic expansions. A simple numerical scheme for integration is presented. It is found that boundary layers exist near the walls for large | S |. In addition, flow reversals and oscillations of the velocity profile occur for large negative S (fast expansion of the tube).
26 citations
TL;DR: A linear programming model for optimally assigning diameters to a gas pipeline network and certain properties that have to be satisfied by an optimal assignment are derived.
Abstract: Abstract A linear programming model for optimally assigning diameters to a gas pipeline network is discussed. Computational results for a real life situation are presented, and certain properties that have to be satisfied by an optimal assignment are derived.
12 citations
TL;DR: In this paper, the problem of determining the temperature, displacement and stress fields around a single crack in an anisotropic slab is considered, and the problem is reduced to Fredholm integral equations which may be solved numerically.
Abstract: Abstract The problem of determining the temperature, displacement and stress fields around a single crack in an anisotropic slab is considered. The problem is reduced to Fredholm integral equations which may be solved numerically.
10 citations
TL;DR: In this paper, the authors considered a topology called the A-topology on Minkowski space, the four-dimensional space-time continuum of special relativity and derived its group of homeomorphisms.
Abstract: We consider in this paper a topology (which we call the A-topology) on Minkowski space, the four-dimensional space–time continuum of special relativity and derive its group of homeomorphisms. We define the A-topology to be the finest topology on Minkowski space with respect to which the induced topology on time-like and light-like lines is one-dimensional Euclidean and the induced topology on space-like hyperplanes is three- dimensional Euclidean. It is then shown that the group of homeomorphisms of this topology is precisely the one generated by the inhomogeneous Lorentz group and the dilatations.
6 citations
TL;DR: In this article, the Hartree hybrid method was applied to one-dimensional nonlinear aortic blood flow models, and the results obtained appear to indicate that shock-waves could only form in distances which exceed physiologically meaningful values.
Abstract: The “Hartree hybrid method” has recently been employed in one-dimensional non-linear aortic blood-flow models, and the results obtained appear to indicate that shock-waves could only form in distances which exceed physiologically meaningful values. However, when the same method is applied with greater numerical accuracy to these models, the existence of a shock-wave in the vicinity of the heart is predicted. This appears to be contrary to present belief.
4 citations
TL;DR: In this article, the existence of optimal control for a system governed by quasilinear parabolic partial differential equations which is linear in the control variables is considered and it is shown that whenever the controls converge in the weak * topology of L ∞, the corresponding solutions converge uniformly.
Abstract: Abstract The question on existence of optimal controls for a system governed by quasilinear parabolic partial differential equations which is linear in the control variables is considered. It is shown that whenever the controls converge in the weak * topology of L∞, the corresponding solutions converge uniformly. Using this result and results on lower semi-continuity of integral functionals, existence theorems for optimal controls are proved.
4 citations
TL;DR: In this paper, a geometrical method for the solution of non-linear boundary value problems is presented, which generalizes those of the standard hypercircle method for linear problems.
Abstract: Abstract We present a geometrical method for the solution of a certain class of non-linear boundary value problems. The results generalize those of the standard hypercircle method for linear problems. Two illustrative examples are described.
4 citations
TL;DR: In this paper, the problem of an infinitely long rigid punch of uniform cross-section moving across a viscoelastic half-space at constant velocity, large enough so that inertial effects cannot be neglected, is examined and solved in various approximations.
Abstract: The problem of an infinitely long rigid punch of uniform cross-section moving across a viscoelastic half-space at constant velocity, large enough so that inertial effects cannot be neglected, is examined and solved in various approximations. Frictional shear is assumed to exist between the punch and the half-space. The method, which is an extension of that developed in previous papers [6, 7], is applicable for any form of viscoelastic behaviour in the half-space. For the special case of discrete spectrum behaviour the method is described in detail. For the case where the punch is cylindrical and viscoelastic effects are small compared with elastic effects, explicit expressions are given for all quantities of interest, in particular the coefficient of hysteretic friction. A general Hilbert transform formula is derived in the appendix.
3 citations
TL;DR: In this paper, the authors considered a class of systems governed by second order linear parabolic delay-partial differential equations with first boundary conditions, and the main results are reported in Theorems 3.1 and 3.2.
Abstract: In this paper, we consider a class of systems governed by second order linear parabolic delay-partial differential equations with first boundary conditions. Our main results are reported in Theorems 3.1 and 3.2. As in [9, Theorems 4.1 and 4.2], the coefficients and forcing terms of the system considered in Theorem 3.1 are linear in the control variables. On the other hand, the forcing terms of the system considered in Theorem 3.2 are allowed to be nonlinear in the control variables at the expense of dropping the control variables in the cost integrand.
2 citations
TL;DR: In this paper, the problem of least square approximation subject to constraints on the range of the approximating polynomial is treated from an optimization theory viewpoint, and Rice's parameter space procedure is discussed.
Abstract: Abstract In this note we consider various theoretical aspects of the problem of least-squares approximation subject to constraints on the range of the approximating polynomial. The problem is treated from an optimization theory viewpoint. Rice's parameter space procedure is discussed.
TL;DR: In this paper, the authors developed a completely symmetric duality theory for mathematical programming problems involving convex functionals. And they set their theory within the framework of a Lagrangian formalism which is significantly different to the conventional Lagrangians.
Abstract: Recently we have developed a completely symmetric duality theory for mathematical programming problems involving convex functionals. Here we set our theory within the framework of a Lagrangian formalism which is significantly different to the conventional Lagrangian. This allows various new characterizations of optimality.
TL;DR: In this article, two basic types of initial conditions are considered: one particle is specified to be at the origin with a given velocity and the positions in phase space of the remaining background of particles are represented by continuous distribution functions.
Abstract: Some initial value problems are considered which arise in the treatment of a one-dimensional gas of point particles interacting with a “hard-core” potential. Two basic types of initial conditions are considered. For the first, one particle is specified to be at the origin with a given velocity. The positions in phase space of the remaining background of particles are represented by continuous distribution functions. The second problem is a periodic analogue of the first. Exact equations for the delta-function part of the single particle distribution functions are derived for the non-periodic case and approximate equations for the periodic case. These take the form of differential operator equations. The spectral and asymptotic properties of the operators associated with the two cases are examined and compared. The behaviour of the solutions is also considered.
TL;DR: A representation result and a characterization of all stabilizing controllers are given in terms of certain fixed polynomial matrices and a stability constraint for decentralized control and stabilization of two-input, two-output finite dimensional linear systems.
Abstract: This paper studies the decentralized control and stabilization of two-input, two-output finite dimensional linear systems. A representation result for the system and a characterization of all stabilizing controllers are given in terms of certain fixed polynomial matrices and a stability constraint.
TL;DR: In this paper, complementary variational principles are presented for a class of nonlinear boundary value problems S* Sφ = g(φ) in which g is not necessarily monotone.
Abstract: Abstract Complementary variational principles are presented for a class of nonlinear boundary value problems S* Sφ = g(φ) in which g is not necessarily monotone. The results are illustrated by two examples, accurate variational solutions being obtained in both cases.
TL;DR: In this paper, a study is made of the branching of time periodic solutions of a system of differential equations in R 2 in the case of a double zero eigenvalue and the stability of these solutions is analyzed.
Abstract: A study is made of the branching of time periodic solutions of a system of differential equations in R 2 in the case of a double zero eigenvalue. It is shown that the solution need not be unique and the period of the solution is large. The stability of these solutions is analysed. Examples are given and generalizations to larger systems are discussed.