Self-heating in packed paniculate that is exothermically reactive is a major cause of fire and explosion in the powder industry. This study is focused on part of the Auckland development of a mathematical model dealing with this hazardous process in industry using milk powder as an example. Milk powder is a primary powdered food product around the world.

An update of the detailed mathematical model is given here, and predictions are made using the model to simulate the basket-heating behaviour of a milk powder in the laboratory (so the model can thus be validated). Basket heating in an oven is a standard laboratory technique for measuring the exothermic reactivity of a solid material.

After a favorable comparison with the laboratory results, several aspects of basket-heating were investigated with a view to further improving the technique. Firstly, the model was used to explore the effect of elevated ambient humidity and initial sample water content upon the heating process in the basket. Secondly, the model was used to explore the cross over phenomenon which is related to a novel procedure for measuring activation energy and exothermicity (that is, the Crossing-Point-Temperature (CPT) method, which is a new version of the basket heating technique). The predictions together with the experimental evidence show that the reaction kinetics obtained using the Heat Release (HR) method (another version of the basket heating technique well published in the literature) may not be correct, especially for those measured at elevated oven temperatures and for larger basket sizes. Thirdly, simulations were performed to illustrate that the CPT phenomenon does not just occur at the center of the basket but also occurs everywhere else in the sample. This can become a significant advantage for further development of the CPT method in terms of reducing experimental duration and improving reproducibility.

The main object of present paper is to obtain a finite summation of Srivastava's general triple hypergeometric series in terms of Kampé de Fériet's double hypergeometric series. A number of finite sums of Kampé de Fériet's double hypergeometric polynomials in terms of different kinds of single hypergeometric polynomials of higher order, are obtained. Some known results of Manocha and Sharma [9], [10], Munot [11], Pathan [12], Qureshi [15], Qureshi and Pathan [16] and Srivastava [26] are deduced as special cases. A result of Pathan [13, page 316 (1.2)] is also corrected here.

This paper is concerned with constructing polynomial solutions to ordinary boundary value problems. A semi-analytic technique using two-point Hermite interpolation is compared with conventional methods via a series of examples and is shown to be generally superior, particularly for problems involving nonlinear equations and/or boundary conditions.

A multiple fractional Brownian motion (FBM)-based traffic model is considered. Various lower bounds for the overflow probability of the associated queueing system are obtained. Based on a probabilistic bound for the busy period of an ATM queueing system associated with a multiple FBM-based input traffic, a minimal dynamic buffer allocation function (DBAF) is obtained and a DBAF-allocation algorithm is designed. The purpose is to create an upper bound for the queueing system associated with the traffic. This upper bound, called a DBAF, is a function of time, dynamically bouncing with the traffic. An envelope process associated with the multiple FBM-based traffic model is introduced and used to estimate the queue size of the queueing system associated with that traffic model.

The Rapp formula of teletraffic dimensioning is generalized to admit an arbitrary renewal stream of offered traffic. The derivation proceeds from a heavy traffic approximation and provides also an estimate of the order of error involved in the Rapp formula. In principle, the method could be used to seek convenient higher order approximations.

Our equations give an incidental theoretical substantiation of an empirical result relating to marginal occupancy found recently by Potter.

An improvement is made to two results of Brown and Shepp which are useful in calculations with fractal sets.

We examine the piecewise-constant collocation method, with collocation points the mid-points of subintervals, for first-kind integral equations with logarithmic kernels on polygonal boundaries. Previously this method had been shown to converge subject to certain restrictions on the angles at the corners of the polygon. Here, by considering a slightly modified collocation method, we are able to remove any restrictions on these angles, and to generalise slightly the meshes which may be used. Moreover, the modification leads to new results on the convergence of preconditioned two-(or multi-) grid methods for solving the resultant linear systems.

We study differential game problems in which the players can select different maximal monotone operators for the governing evolution system. Setting up our problem on a real Hilbert space, we show that the Elliott-Kalton upper and lower value of the game are viscosity solution of some Hamilton-Jacobi-Isaacs equations. Uniqueness is obtained by assuming condition analogous to the classical Isaacs condition, and thus the existence of value of the game follows.

In this paper we prove some inequalities for finite sums and infinite series with positive terms. As an application of these results we obtain some inequalities for entropies of discrete probability distributions.

We propose and analyze the spectral collocation approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomial and the Sobolev regularity of the solution.

Short-crested waves are defined as propagating surface gravity waves which are doubly-periodic in the horizontal plane. Linearly, the short-crested wave system we consider occurs when two progressive wavetrains of equal amplitude and frequency are propagating at an angle to each other.

Solutions are calculated via a computer-generated perturbation expansion in wave steepness. Harmonic resonance affects the solutions but Padé approximants can be used to estimate wave properties such as maximum wave steepness, frequency, kinetic energy and potential energy.

The force exerted by waves being reflected by a seawall is also calculated. Our results for the maximum depth-integrated onshore wave force in the standing wave limit are compared with experiment. The maximum force exerted on a seawail occurs for a steep wave in shallow water incident at an oblique angle. Results are given for this maximum force.

A class of discrepancy principles for the choice of parameters for the simplified regularization of ill-posed problems is proposed. This procedure does not require knowledge of the unknown solution, and if the smoothness of the unknown solution is known then the convergence rate obtained is optimal. The results of this paper include the Arcangeli's method considered by Groetsch and Guacaneme (1987) for which the convergence rate was not known and also of a result of Guacaneme (1988) for which there is a gap in the proof.

This paper deals with the convergence aspect of diffusive delay Lotka-Volterra systems with infinite delays. It is well known that such a system has a globally asymptotically stable steady state if the negative feedbacks of the intraspecific competitions are dominant and instantaneous. It is shown here that such a globally asymptotically stable steady state continues to exist even if the instantaneous assumption is removed, provided that solutions of the system are eventually uniformly bounded and the delays involved in the intraspecific competitions are small. This work generalises several recent related ones.

Gauss' Theorema Egregium produces a partial differential equation which relates the Gaussian curvature K to components of the metric tensor and its derivatives. Well-known partial differential equations (PDEs) such as the Schrödinger equation and the sine-Gordon equation can be derived from Gauss' equation for specific choices of K and coördinate systems. In this paper we consider a class of Bäcklund Transformations which corresponds to coördinate transformations on surfaces with a given Gaussian curvature. These Bäcklund Transformations lead to the construction of solutions to certain classes of non-linear second order PDEs of hyperbolic type by identifying these PDEs as the Gauss equation in some coördinate system. The possibility of solving the Cauchy Problem has also been explored for these classes of equations.

Second order necessary and sufficient conditions are given for a class of optimization problems involving optimal selection of a measurable subset from a given measure subspace subject to set function inequalities. Relations between twice-differentiability at Ω and local convexity at Ω are also discussed.

“Steady state” periodic solutions are sought to the forced Duffing equation. The solutions are expressed as formal Fourier series, giving rise to an infinite system of non-linear algebraic equations for the Fourier coefficients. This system is then solved using perturbation series in the amplitude of the forcing term. Solution profiles of high accuracy and phase-plane orbits are presented. The existence of limiting values of the forcing amplitude is discussed, and points of non-linear resonance are identified.