Numerical simulation of the behaviour of blood flow through a stenosed bifurcated
artery with the presence of single mild stenosis at parent artery is investigated. The
flow analysis applies the incompressible, steady, three-dimensional Navier-Stokes equations
for non-Newtonian generalized power law fluids. Behaviour of blood flow is simulated
numerically using COMSOL Multiphysicsthat based on finite element method.The
results showthe effect of severity of stenosis on flow characteristics such as axial velocity
and its exhibit flow recirculation zone for analysis on streamlines pattern.
Optimization is central to any problem involving decision making. The area
of optimization has received enormous attention for over 30 years and it is still popular
in research field to this day. In this paper, a global optimization method called Improved
Homotopy with 2-Step Predictor-corrector Method will be introduced. The method in-
troduced is able to identify all local solutions by converting non-convex optimization
problems into piece-wise convex optimization problems. A mechanism which only consid-
ers the convex part where minimizers existed on a function is applied. This mechanism
allows the method to filter out concave parts and some unrelated parts automatically.
The identified convex parts are called trusted intervals. The descent property and the
global convergence of the method was shown in this paper. 15 test problems have been
used to show the ability of the algorithm proposed in locating global minimizer.
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, Maxwell fluid over a flat plate for convective boundary layer
flow with pressure gradient parameter is considered. The aim of this study is to compare
and analyze the effects of the presence and absence of λ (relaxation time), and also the
effects of m (pressure gradient parameter) and Pr (Prandtl number)on the momentum
and thermal boundary layer thicknesses. An approximation technique namely Homotopy
Perturbation Method (HPM) has been used with an implementation of Adam and Gear
Method’s algorithms. The obtained results have been compared for zero relaxation time
and also pressure gradient parameter with the published work of Fathizadeh and Rashidi.
The current outcomes are found to be in good agreement with the published results.
Physical interpretations have been given for the effects of the m, Pr and β (Deborah
number) with λ. This study will play an important role in industrial and engineering
Monthly data about oil production at several drilling wells is an example of
spatio-temporal data. The aim of this research is to propose nonlinear spatio-temporal
model, i.e. Feedforward Neural Network - VectorAutoregressive (FFNN-VAR) and FFNN
- Generalized Space-Time Autoregressive (FFNN-GSTAR), and compare their forecast
accuracy to linearspatio-temporal model, i.e. VAR and GSTAR. These spatio-temporal
models are proposed and applied for forecasting monthly oil production data at three
drilling wells in East Java, Indonesia. There are 60 observations that be divided to two
parts, i.e. the first 50 observations for training data and the last 10 observations for
testing data. The results show that FFNN-GSTAR(11) and FFNN-VAR(1) as nonlinear
spatio-temporal models tend to give more accurate forecast than VAR(1) and GSTAR(11)
as linear spatio-temporal models. Moreover, further research about nonlinear spatiotemporal
models based on neural networks and GSTAR is needed for developing new
hybrid models that could improve the forecast accuracy.
The incorporation of non-linear pattern of early ages has led to new research
directions on improving the existing stochastic mortalitymodel structure. Several authors
have outlined the importance of encompassing the full age range in dealing with longevity
risk exposure, by not ignoring the dependence between young and old ages. In this study,
we consider the two extensions of the Cairns, Blake and Dowd model that incorporate the
irregularity profile seen at the mortality of lower ages, which are the Plat, and the O’Hare
and Li models respectively. The models’ performances in terms of in-sample fitting and
out-sample forecasts were examined and compared. The results indicated that the O’Hare
and Li model performs better as compared to the Plat model.
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.
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.
In this paper we consider a harvesting model of predator-prey fishery in which
the prey is directly infected by some external toxic substances. The toxic infection is
indirectly transmitted to the predator during the feeding process. The model is a modified
version from the classic Lotka-Volterra predator-prey model. The stability and bifurcation
analyses are addressed. Numerical simulations of the model are performed and bifurcation
diagrams are studied to investigate the dynamical behaviours between the predator and
the prey. The effects of toxicity and harvesting on the stability of steady states found in
the model are discussed.
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.
Analyzed the effects of thermal radiation, chemical reaction, heat gener-
ation/absorption, magnetic and electric fields on unsteady flow and heat transfer of
nanofluid. The transport equations used passively controlled. A similarity solution is
employed to transformed the governing equations from partial differential equations to
a set of ordinary differential equations, and then solve using Keller box method. It was
found that the temperature is a decreasing function with the thermal stratification due to
the fact the density of the fluid in the lower vicinity is much higher compared to the upper
region, whereas the thermal radiation, viscous dissipation and heat generation enhanced
the nanofluid temperature and thermal layer thickness.
Rainfall is an interesting phenomenon to investigate since it is directly related
to all aspects of life on earth. One of the important studies is to investigate and under-
stand the rainfall patterns that occur throughout the year. To identify the pattern, it
requires a rainfall curve to represent daily observation of rainfall received during the year.
Functional data analysis methods are capable to convert discrete data intoa function that
can represent the rainfall curve and as a result, try to describe the hidden patterns of the
rainfall. This study focused on the distribution of daily rainfall amount using functional
data analysis. Fourier basis functions are used for periodic rainfall data. Generalized
cross-validation showed 123 basis functions were sufficient to describe the pattern of daily
rainfall amount. North and west areas of the peninsula show a significant bimodal pattern
with the curve decline between two peaks at the mid-year. Meanwhile,the east shows uni-
modal patterns that reached a peak in the last three months. Southern areas show more
uniform trends throughout the year. Finally, the functional spatial method is introduced
to overcome the problem of estimating the rainfall curve in the locations with no data
recorded. We use a leave one out cross-validation as a verification method to compare
between the real curve and the predicted curve. We used coefficient of basis functions
to get the predicted curve. It was foundthatthe methods ofspatial prediction can match
up with theexistingspatialpredictionmethodsin terms of accuracy,but it isbetterasthe new
approach provides a simpler calculation.
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.
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.
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
In DNA splicing system, the potential effect of sets of restriction enzymes and
a ligase that allow DNA molecules to be cleaved and re-associated to produce further
molecules is modelled mathematically. This modelling is done in the framework of formal
language theory, in which the nitrogen bases, nucleotides and restriction sites are modelled
as alphabets, strings and rules respectively. The molecules resulting from a splicing system
is depicted as the splicing language. In this research, the splicing language resulting from
DNA splicing systems with one palindromic restriction enzyme for one and two (nonoverlapping)
cutting sites are generalised as regular expressions.
Heat and mass transfer of MHD boundary-layer flow of a viscous incompress-
ible fluid over an exponentially stretching sheet in the presence of radiation is investi-
gated. The two-dimensional boundary-layer governing partial differential equations are
transformed into a system of nonlinear ordinary differential equations by using similarity
variables. The transformed equations of momentum, energy and concentration are solved
by Homotopy Analysis Method (HAM). The validity of HAM solution is ensured by com-
paring the HAM solution with existing solutions. The influence of physical parameters
such as magnetic parameter, Prandtl number, radiation parameter, and Schmidt num-
ber on velocity, temperature and concentration profiles are discussed. It is found that
the increasing values of magnetic parameter reduces the dimensionless velocity field but
enhances the dimensionless temperature and concentration field. The temperature dis-
tribution decreases with increasing values of Prandtl number. However, the temperature
distribution increases when radiation parameter increases. The concentration boundary
layer thickness decreases as a result of increase in Schmidt number.
Cardiovascular disease (CVD) includes coronary heart disease, cerebrovascular disease (stroke), peripheral artery disease, and atherosclerosis of the aorta. All females face the threat of CVD. But becoming aware of symptoms and signs is a great challenge since most adults at increased risk of cardiovascular disease (CVD) have no symptoms or obvious signs especially in females. The symptoms may be identified by the assessment of their risk factors. The Bayesian approach is a specific way in dealing with this kind of problem by formalizing a priori beliefs and of combining them with the available observations. This study aimed to identify associated risk factors in CVD among female patients presenting with ST Elevation Myocardial Infarction (STEMI) using Bayesian logistic regression and obtain a feasible model to describe the data. A total of 874 STEMI female patients in the National Cardiovascular Disease Database-Acute Coronary Syndrome (NCVD-ACS) registry year 2006-2013 were analysed. Bayesian Markov Chain Monte Carlo (MCMC) simulation approach was applied in the univariate and multivariate analysis. Model performance was assessed through the model calibration and discrimination. The final multivariate model of STEMI female patients consisted of six significant variables namely smoking, dyslipidaemia, myocardial infarction (MI), renal disease, Killip class and age group. Females aged 65 years and above have higher incidence of CVD and mortality is high among female patients with Killip class IV. Also, renal disease was a strong predictor of CVD mortality. Besides, performance measures for the model was considered good. Bayesian logistic regression model provided a better understanding on the associated risk factors of CVD for female patients which may help tailor prevention or treatment plans more effectively.
Recent studies have shown that independent identical distributed Gaussian
random variables is not suitable for modelling extreme values observed during extremal
events. However, many real life data on extreme values are dependent and stationary
rather than the conventional independent identically distributed data. We propose a stationary
autoregressive (AR) process with Gumbel distributed innovation and characterise
the short-term dependence among maxima of an (AR) process over a range of sample
sizes with varying degrees of dependence. We estimate the maximum likelihood of the
parameters of the Gumbel AR process and its residuals, and evaluate the performance
of the parameter estimates. The AR process is fitted to the Gumbel-generalised Pareto
(GPD) distribution and we evaluate the performance of the parameter estimates fitted
to the cluster maxima and the original series. Ignoring the effect of dependence leads to
overestimation of the location parameter of the Gumbel-AR (1) process. The estimate
of the location parameter of the AR process using the residuals gives a better estimate.
Estimate of the scale parameter perform marginally better for the original series than the
residual estimate. The degree of clustering increases as dependence is enhance for the AR
process. The Gumbel-AR(1) fitted to the threshold exceedances shows that the estimates
of the scale and shape parameters fitted to the cluster maxima perform better as sample
size increases, however, ignoring the effect of dependence lead to an underestimation of
the parameter estimates of the scale parameter. The shape parameter of the original
series gives a superior estimate compare to the threshold excesses fitted to the Gumbel
distributed Generalised Pareto ditribution.
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.