William Arloff; Karl R.B. Schmitt; Luke J. Venstrom

We propose a two-step method for fitting stiff ordinary differential equation (ODE) models to experimental data. The first step avoids integrating stiff ODEs during the unbounded search for initial estimates of model parameters. To avoid integration, a polynomial approximation of experimental data is generated, differentiated and compared directly to the ODE model, obtaining crude but physically plausible estimates for model parameters. Particle swarm optimisation (PSO) is used for the parameter search to overlook combinations of model parameters leading to undefined solutions of the stiff ODE. After initial estimates are determined, the second step numerically solves the ODE. This refines model parameter values through a bounded search. We demonstrate this method by fitting the model parameters (activation energies and pre-exponential factors) of the Arrhenius-based temperature-dependent kinetic coefficients in the shrinking core solid-state chemical kinetics model for the reduction of Cobalt (II, III) Oxide (Co\(_3\)O\(_4\)) particles to Cobalt (II) Oxide (CoO).]]>

Guo Zhou; Ruixin Zhao; Yongquan Zhou

This paper uses the social-spider optimisation (SSO) algorithm to solve large-scale 0-1 knapsack problems. The SSO algorithm is based on the simulation of cooperative behaviour of social-spiders. In SSO algorithm, individuals emulate a group of spiders which interact to each other based on the biological laws of the cooperative colony. The algorithm considers two different search agents (spiders): males and females. Depending on gender, each individual is conducted by a set of different evolutionary operators which mimic different cooperative behaviour which are typically found in the colony. The experiment results show that the social-spider optimisation algorithm can be an efficient alternative for large-scale 0-1 knapsack problems.]]>

Jingzong Yang; Zao Feng; Xiaodong Wang; Guoyong Huang

Aiming at the problem of recognition on pipeline blockage, a method based on mixed domain feature and KPCA-ELM is proposed. Firstly, the original acoustic impulse response signals are analysed by statistical analysis and local mean decomposition (LMD), in order to construct the mixed domain features, which are made up of time, frequency and time-frequency domain features. Then the kernel principal component analysis (KPCA) is adopted to reduce the high-dimensional features of mixed domain and extract the main features which reflect the operation state of main components. Finally, the main features are input to extreme learning machine (ELM) for state recognition. After the feature extraction by KPCA, the redundancy of input features is eliminated. The simulation results show that KPCA is more sensitive to the nonlinear characteristics of the pipeline blockage signal when compared with PCA. Meanwhile, ELM is superior to BP in terms of classification accuracy and time consuming.]]>

Sandile S. Motsa; Isaac Lare Animasaun

The problem of unsteady micropolar fluid flow over a surface in which the heat energy falls at a lower limit of thermodynamic temperature scale due to impulsive is investigated. In this article, a new spectral method (BSQLM) for solving the partial differential equation is shown to unravel the heat transfer within the boundary layer. Some fluid layers at the free stream were given an impulsive motion in the horizontal direction. The thermal conductivity of the non-Newtonian fluid is assumed to be temperature dependent due to the influence of internal heat source; hence modified to suit the case of melting heat transfer following all the fundamental theories. The mathematical model was non-dimensionalised and parameterised using similarity transformation suitable to unravel the flow at short-time and long-time periods. Smooth transitions within the time frame 0 ≤ <i>ξ</i> ≤ 1 in the domain 0 ≤ <i>η</i> ≤ 1 are observed. The minimum temperature distribution is ascertained when the magnitude of Prandtl number is significantly large.]]>

Hongmei Bao

This paper deals with the existence and global exponential stability of anti-periodic solutions for fuzzy cellular neural networks (FCNNs) with time-varying delays and impulsive effects on time scales. Using the theory of coincidence degree, inequality technique and constructing some suitable Lyapunov functional, some sufficient conditions are obtained for the existence and global exponential stability of anti-periodic solutions for FCNNs with time-varying delays and impulsive effects on time scales. These results are less restrictive than those given in the earlier references. Moreover an example is provided to illustrate results obtained.]]>

Ajaz Ahmad Dar; K. Elangovan

The problem of blood flow through a horizontal non-symmetric artery with a mild stenosis in a porous medium has been investigated. The natures of blood in small arteries are analysed mathematically by considering it as a homogeneous and incompressible micropolar fluid. The effect of both rotation and inclined magnetic field are studied analytically and computed numerically. To evaluate the influence of the stenosis shape, an appropriate geometry has been considered such that the shape of the stenosis can be changed simply just by varying a parameter (referred to as the shape parameter). The expressions for the flow characteristics such as velocity, the impedance (resistance to flow), the wall shear stress distribution and its magnitude at the stenosis throat have been derived and analysed for different values of shape parameter n, rotation parameter Ω, the magnetic field parameter <i>M</i>, inclination angle of the magnetic field parameter (<i>θ</i>), permeability parameter (<i>K</i><SUB align="right">1), the coupling number N and the micropolar fluid parameter <i>m</i>.]]>

Anuradha Singh

In this paper, we present a three-step Steffensen-type iterative method of order five for solving systems of nonlinear equations. Various particular cases of the proposed method are considered. The general form of computational efficiency of the proposed scheme is compared to existing techniques. Numerical examples are given to show the performance of the proposed method with some existing schemes. We observed from the comparison of the new scheme with some known methods that the proposed scheme shows high efficiency index than others.]]>

Shaik Sharief Basha

A reverse magic labelling of a graph G(V, E) is a bijection <i>f</i>: <i>V</i> ∪ <i>E</i> → {1, 2, 3, ......, <i>v</i> + <i>ε</i>} such that for all edges <i>xy</i>, <i>f</i>(<i>xy</i>) - {<i>f</i>(<i>x</i>) + <i>f</i>(<i>y</i>)} is a constant which is denoted by <i>c</i>(<i>f</i>). A reverse magic labelling of a graph G(V, E) is called reverse super edge-magic labelling of G if <i>f</i>(<i>V</i>) = {1, 2, ...... <i>v</i>} and f(E) = {<i>v</i> + 1, <i>v</i> + 2, ......, <i>v</i> + <i>ε</i>}. <i>The reverse super edge-magic strength of a graph G,rsm</i>(<i>G</i>), is defined as the minimum of all c(f) where the minimum is taken over all reverse edge-magic labelling f of G. In this paper we invented the reverse super edge-magic strength of banana trees.]]>