Homotopy continuation methods (HCMs) can be used to find the solutions
of polynomial equations. The advantages of HCMs over classical methods such as the
Newton and bisection methods are that HCMs are able to resolve divergence and starting
value problems. In this paper, we develop Super Ostrowski-HCM as a technique to
overcome the starting value problem. We compare the performance of this proposed
method with Ostrowski-HCM. The results provide evidence of the superiority of Super
In the recent economic crises, one of the precise uniqueness that all stock
markets have in common is the uncertainty. An attempt was made to forecast future
index of the Malaysia Stock Exchange Market using artificial neural network (ANN)
model and a traditional forecasting tool – Multiple Linear Regressions (MLR). This
paper starts with a brief introduction of stock exchange of Malaysia, an overview of
artificial neural network and machine learning models used for prediction. System
design and data normalization using MINITAB software were described. Training
algorithm, MLR Model and network parameter models were presented. Best training
graphs showing the training, validation, test and all regression values were analyzed.
An accurate forecasting of tropospheric ozone (O3) concentration is benefi-
cial for strategic planning of air quality. In this study, various forecasting techniques are
used to forecast the daily maximum O3 concentration levels at a monitoring station
in the Klang Valley, Malaysia. The Box-Jenkins autoregressive integrated movingaverage
(ARIMA) approach and three types of neural network models, namely, backpropagation
neural network, Elman recurrent neural network and radial basis function
neural network are considered. The daily maximum data, spanning from 1 January
2011 to 7 August 2011, was obtained from the Department of Environment, Malaysia.
The performance of the four methods in forecasting future values of ozone concentrations
is evaluated based on three criteria, which are root mean square error (RMSE),
mean absolute error (MAE) and mean absolute percentage error (MAPE). The findings
show that the Box-Jenkins approach outperformed the artificial neural network
It has come to attention that Malaysia have been aiming to build its own
nuclear power plant (NPP) for electricity generation in 2030 to diversify the national
energy supply and resources. As part of the regulation to build a NPP, environmental
risk assessment analysis which includes the atmospheric dispersion assessment has to
be performed as required by the Malaysian Atomic Energy Licensing Board (AELB)
prior to the commissioning process. The assessment is to investigate the dispersion of
radioactive effluent from the NPP in the event of nuclear accident. This article will focus
on current development of locally developed atmospheric dispersion modeling code
based on Gaussian Plume model. The code is written in Fortran computer language
and has been benchmarked to a readily available HotSpot software. The radionuclide
release rate entering the Gaussian equation is approximated to the value found in the
Fukushima NPP accident in 2011. Meteorological data of Mersing District, Johor of
year 2013 is utilized for the calculations. The results show that the dispersion of radionuclide
effluent can potentially affect areas around Johor Bahru district, Singapore
and some parts of Riau when the wind direction blows from the North-northeast direction.
The results from our code was found to be in good agreement with the one
obtained from HotSpot, with less than 1% discrepancy between the two.
Replicated linear functional relationship model is often used to describe
relationships between two circular variables where both variables have error terms and
replicate observations are available. We derive the estimate of the rotation parameter
of the model using the maximum likelihood method. The performance of the proposed
method is studied through simulation, and it is found that the biasness of the estimates
is small, thus implying the suitability of the method. Practical application of the
method is illustrated by using a real data set.
Real life phenomena found in various fields such as engineering, physics,
biology and communication theory can be modeled as nonlinear higher order ordinary
differential equations, particularly the Duffing oscillator. Analytical solutions for these
differential equations can be time consuming whereas, conventional numerical solutions
may lack accuracy. This research propose a block multistep method integrated with a
variable order step size (VOS) algorithm for solving these Duffing oscillators directly.
The proposed VOS Block method provides an alternative numerical solution by reducing
computational cost (time) but without loss of accuracy. Numerical simulations
are compared with known exact solutions for proof of accuracy and against current
numerical methods for proof of efficiency (steps taken).
Medical diagnosis is the extrapolation of the future course and outcome
of a disease and a sign of the likelihood of recovery from that disease. Diagnosis
is important because it is used to guide the type and intensity of the medication
to be administered to patients. A hybrid intelligent system that combines the fuzzy
logic qualitative approach and Adaptive Neural Networks (ANNs) with the capabilities
of getting a better performance is required. In this paper, a method for modeling
the survival of diabetes patient by utilizing the application of the Adaptive NeuroFuzzy
Inference System (ANFIS) is introduced with the aim of turning data into
knowledge that can be understood by people. The ANFIS approach implements the
hybrid learning algorithm that combines the gradient descent algorithm and a recursive
least square error algorithm to update the antecedent and consequent parameters. The
combination of fuzzy inference that will represent knowledge in an interpretable manner
and the learning ability of neural network that can adjust the membership functions
of the parameters and linguistic rules from data will be considered. The proposed
framework can be applied to estimate the risk and survival curve between different
diagnostic factors and survival time with the explanation capabilities.
The constraint of two ordered extreme minima random variables when one
variable is consider to be stochastically smaller than the other one has been carried
out in this article. The quantile functions of the probability distribution have been
used to establish partial ordering between the two variables. Some extensions and
generalizations are given for the stochastic ordering using the important of sign of the
In this paper, we consider the system of Volterra-Fredholm integral equations
of the second kind (SVFI-2). We proposed fixed point method (FPM) to solve
SVFI-2 and improved fixed point method (IFPM) for solving the problem. In addition,
a few theorems and two new algorithms are introduced. They are supported by
numerical examples and simulations using Matlab. The results are reasonably good
when compared with the exact solutions.
In this paper, we study the numerical method for solving second order Fuzzy
Differential Equations (FDEs) using Block Backward Differential Formulas (BBDF)
under generalized concept of higher-order fuzzy differentiability. Implementation of
the method using Newton iteration is discussed. Numerical results obtained by BBDF
are presented and compared with Backward Differential Formulas (BDF) and exact
solutions. Several numerical examples are provided to illustrate our methods.
In this paper, we propose a method how to manage the convergence of
Newton’s method if its iteration process encounters a local extremum. This idea establishes
the osculating circle at a local extremum. It then uses the radius of the
osculating circle also known as the radius of curvature as an additional number of
the local extremum. It then takes that additional number and combines it with the
local extremum. This is then used as an initial guess in finding a root near to that
local extremum. This paper will provide several examples which demonstrate that the
proposed idea is successful and they perform to fulfill the aim of this paper.
A new method to construct the distinct Hamiltonian circuits in complete
graphs is called Half Butterfly Method. The Half Butterfly Method used the concept
of isomorphism in developing the distinct Hamiltonian circuits. Thus some theoretical
works are presented throughout developing this method.
In this paper, the application of the method of lines (MOL) to the Forced
Korteweg-de Vries-Burgers equation with variable coefficient (FKdVB) is presented.
The MOL is a powerful technique for solving partial differential equations by typically
using finite-difference approximations for the spatial derivatives and ordinary differential
equations (ODEs) for the time derivative. The MOL approach of the FKdVB
equation leads to a system of ODEs. The solution of the system of ODEs is obtained
by applying the Fourth-Order Runge-Kutta (RK4) method. The numerical solution
obtained is then compared with its progressive wave solution in order to show the
accuracy of the MOL method.
The box plot has been used for a very long time since 70s in checking the existence
of outliers and the asymmetrical shape of data. The existing box plot is constructed
using five values of statistics calculated from either the discrete or continous data. Many
improvement of box plots have deviated from the elegant and simplier approach of exploratory
data analysis by incorporating many other statistic values resulting the turning
back of the noble philosophy behind the creation of box plot. The modification using
range value with the minimum and maximum values are being incorporated to suit the
need of selected discrete distribution when outliers is not an important criteria anymore.
The new modification of box plot is not based on the asymmetrical shape of distribution
but more on the spreading and partitioning data into range measure. The new propose
name for the box plot with only three values of statistics is called range-box plot.
Hantaviruses are etiological agents of zoonotic diseases and certain other dis-
eases, which pose a serious threat to human health. When rodent and predator popula-
tions share in an ecology, the competitive force of the populations can lead to a reduction
or elimination of a hantavirus outbreak. The effect of the predator eliminating rodents
and predator populations that tends to reduce or eliminate hantavirus infection is investi-
gated. The existence of several equilibrium points of the model is identified and local and
global stabilities of the model at these equilibrium points are analysed in detail. Numerical
simulations are carried out to illustrate our model results.
Subsea cable laying process is a difficult task for an engineer due to many
uncertain situations which occur during the operation. It is very often that the cable being
laid out is not perfectly fit on the route being planned, which results in the formation of
slack. In order to control wastages during installation, the slack needs to be minimized
and the movement of a ship/vessel needs to be synchronized with the cable being laid out.
The current problem was addressed using a mathematical model by considering a number
of defining parameters such as the external forces, the cable properties and geometry. Due
to the complexity, the model is developed for a steady-state problem assuming velocity
of the vessel is constant, seabed is flat and the effect of wind and wave is insignificant.
Non-dimensional system is used to scale the engineering parameters and grouped them
into only two main parameters which are the hydrodynamic drag of the fluid and the
bending stiffness of the cable. There are two solutions generated in this article; numerical
and asymptotic solutions. The result of these solutions suggests that the percentage of
slack can be reduced by the increase of the prescribed cable tension, and also the increase
in either the drag coefficient of the sea water or the bending stiffness of the cable, similarly
will result in lower slack percentage
Symmetric methods such as the implicit midpoint rule (IMR), implicit trapezoidal
rule (ITR) and 2-stage Gauss method are beneficial in solving Hamiltonian problems
since they are also symplectic. Symplectic methods have advantages over non-symplectic
methods in the long term integration of Hamiltonian problems. The study is to show
the efficiency of IMR, ITR and the 2-stage Gauss method in solving simple harmonic
oscillators (SHO). This study is done theoretically and numerically on the simple harmonic
oscillator problem. The theoretical analysis and numerical results on SHO problem
showed that the magnitude of the global error for a symmetric or symplectic method
with stepsize h is linearly dependent on time t. This gives the linear error growth when
a symmetric or symplectic method is applied to the simple harmonic oscillator problem.
Passive and active extrapolations have been implemented to improve the accuracy of the
numerical solutions. Passive extrapolation is observed to show quadratic error growth
after a very short period of time. On the other hand, active extrapolation is observed to
show linear error growth for a much longer period of time.
Markov map is one example of interval maps where it is a piecewise expanding
map and obeys the Markov property. One well-known example of Markov map is the
doubling map, a map which has two subintervals with equal partitions. In this paper, we
are interested to investigate another type of Markov map, the so-called skewed doubling
map. This map is a more generalized map than the doubling map. Thus, the aims of this
paper are to find the fixed points as well as the periodic points for the skewed doubling
map and to investigate the sensitive dependence on initial conditions of this map. The
method considered here is the cobweb diagram. Numerical results suggest that there exist
dense of periodic orbits for this map. The sensitivity of this map to initial conditions is
also verified where small differences in initial conditions give different behaviour of the
orbits in the map.
The selection criteria play an important role in the portfolio optimization
using any ratio model. In this paper, the authors have considered the mean return as
profit and variance of return as risk on the asset return as selection criteria, as the first
stage to optimize the selected portfolio. Furthermore, the sharp ratio (SR) has been
considered to be the optimization ratio model. In this regard, the historical data taken
from Shanghai Stock Exchange (SSE) has been considered. A metaheuristic technique
has been developed, with financial tool box available in MATLAB and the particle swarm
optimization (PSO) algorithm. Hence, called as the hybrid particle swarm optimization
(HPSO) or can also be called as financial tool box particle swarm optimization (FTBPSO).
In this model, the budgets as constraint, where as two different models i.e. with
and without short sale, have been considered. The obtained results have been compared
with the existing literature and the proposed technique is found to be optimum and better
in terms of profit.
Logging activity is one of the most important activities for tropical countries
including Malaysia, as it produces quality trees for papers. One of the important tree
species is the Acacia Mangium which it produces a soft tree for papermaking enterprises.
The papers are exported to Europe and countries which have high demand for paper
due to the rapid development of the printing industry. Thus we analyzed the height for
individual trees. We investigate the maximum height of the trees from 1990 to 2006
and we fit the data using extreme value model. Some of the data are missing and three
imputation methods we used to solve this problem.