In this work, a non-abelian metabelian group is represented by G while represents conjugacy class graph. Conjugacy class graph of a group is that graph associated with the conjugacy classes of the group. Its vertices are the non-central conjugacy classes of the group, and two distinct vertices are joined by an edge if their cardinalities are not coprime. A group is referred to as metabelian if there exits an abelian normal subgroup in which the factor group is also abelian. It has been proven earlier that 25 non-abelian metabelian groups which have order less than 24, which are considered in this work, exist. In this article, the conjugacy class graphs of non-abelian metabelian groups of order less than 24 are determined as well as examples of some finite groups associated to other graphs are given.
In this paper, we look at the propagation of internal solitary waves over three
different types of slowly varying region, i.e. a slowly increasing slope, a smooth bump and
a parabolic mound in a two-layer fluid flow. The appropriate mathematical model for this
problem is the variable-coefficient extended Korteweg-de Vries equation. The governing
equation is then solved numerically using the method of lines. Our numerical simulations
show that the internal solitary waves deforms adiabatically on the slowly increasing slope.
At the same time, a trailing shelf is generated as the internal solitary wave propagates
over the slope, which would then decompose into secondary solitary waves or a wavetrain.
On the other hand, when internal solitary waves propagate over a smooth bump or a
parabolic mound, a trailing shelf of negative polarity would be generated as the results of
the interaction of the internal solitary wave with the decreasing slope of the bump or the
parabolic mound. The secondary solitary waves is observed to be climbing the negative
trailing shelf.
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.
Abstract Demographers and actuaries are very much conscious of the trend of mortality in their own country or in the world in general. This is because mortality is the basis for longevity risk evaluation. Mortality is showing a declining trend and it is expected to further decline in the future. This will lead to continuous increase in life expectancy. Several stochastic models have been developed throughout the years to capture mortality and its variability. This includes Lee Carter (LC) model which has been extended by various researchers. This paper will be focusing on comparing LC model and another mortality model proposed by Cairns, Blake and Dowd (CBD). The LC uses the log of central rate of mortality and CBD uses logit of the mortality odds as dependent variable. Analysis of comparison is done using a few techniques including Akaike information criteria (AIC) and Bayesian information criterion (BIC). From the overall results, there is no model better than the other in every aspect tested. We illustrate this via visual inspection and in sample and outof sample analysis using Malaysian mortality data from 1980 to 2017.
A mechanistic model has been used to explain the effect of radiation. The
model consists of parameters which represent the biological process following ionizing
radiation. The parameters in the model are estimated using local and global optimiza-
tion algorithms. The aim of this study is to compare the efficiency between local and
global optimization method, which is Pattern Search and Genetic Algorithm respectively.
Experimental data from the cell survival of irradiated HeLa cell line is used to find the
minimum value of the sum of squared error (SSE) between experimental data and sim-
ulation data from the model. The performance of both methods are compared based on
the computational time and the value of the objective function, SSE. The optimization
process is carried out by using the built-in function in MATLAB software. The parameter
estimation results show that genetic algorithm is more superior than pattern search for
this problem.
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
Ostrowski-HCM.
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.
In irradiation process, instead of traverse on the targeted cells, there is side
effect happens to non-targeted cells. The targeted cells that had been irradiated with
ionizing radiation emits damaging signal molecules to the surrounding and then, dam-
age the bystander cells. The type of damage considered in this work is the number of
double-strand breaks (DSBs) of deoxyribonucleic acid (DNA) in cell’s nucleus. By us-
ing mathematical approach, a mechanistic model that can describe this phenomenon is
developed based on a structured population approach. Then, the accuracy of the model
is validated by its ability to match the experimental data. The Particle Swarm (PS)
optimization is employed for the data fitting procedure. PS optimization searches the
parameter value that minimize the errors between the model simulation data and exper-
imental data. It is obtained that the mathematical modelling proposed in this paper is
strongly in line with the experimental data.
In this paper, the combined influences of biotic interactions, environmental components and harvesting strategy on the spread of Hantavirus are investigated. By employing a multi-species model consisting of (susceptible and infected) rodents and alien species, we show that interspecific competition from alien species has an effect in reducing the spread of infection, and this species could be employed as a potential biocontrol agent. Our analysis using numerical continuation and simulation also reveals the conditions under which Hantavirus infection occurs and disappears as the environmental conditions and the intensity of harvesting change. Without harvesting, infection emerges when environments are conducive. Inclusion of moderate harvesting in favourable environments can lead to disappearance of infection among rodent species. However, as the intensity of harvesting increases, this situation can cause extinction of all rodents species and consequently, jeopardise biodiversity. Overall, our results demonstrate how the interplay of different factors can combine to determine the spread of infectious diseases.
Free convection flow in a boundary layer region is a motion that results from the interaction of gravity with density differences within a fluid. These differences occur due to temperature or concentration gradients or due to their composition. Studies per- taining free convection flows of incompressible viscous fluids have received much attention in recent years both theoretically (exact or approximate solutions) and experimentally. The situation where the heat be transported to the convective fluid via a bounding sur- face having finite heat capacity is known as Newtonian heating (or conjugate convective flows). In this paper, the unsteady free convection flow of an incompressible viscous fluid between two parallel plates with Newtonian heating is studied. Appropriate non- dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions into dimensionless forms. The exact solutions for velocity and temperature are obtained using the Laplace transform technique. The corresponding expressions for skin friction and Nusselt number are also calculated. The graphical results are displayed to illustrate the influence of various embedded parameters such as Newtonian heating parameter and Grashof number. The results show that the effect of Newtonian heating parameter increases the Nusselt number but reduces the skin friction.
A new topic of Zero Energy Building (ZEB) is getting famous in research area
because of its goal of reaching zero carbon emission and low building cost. Renewable
energy system is one of the ideas to achieve the objective of ZEB. Genetic Algorithm (GA)
is widely used in many research areas due to its capability to escape from a local minimal
to obtain a better solution. In our study, GA is chosen in sizing optimization of the
number of photovoltaic, wind turbine and battery of a hybrid photovoltaic-wind-battery
system. The aim is to minimize the total annual cost (TAC) of the hybrid energy system
towards the low cost concept of ZEB. Two GA parameters, which are generation number
and population size, have been analysed and optimized in order to meet the minimum
TAC. The results show that the GA is efficient in minimizing cost function of a hybrid
photovoltaic-wind-battery system with its robustness property.
Price stability is one of the main policy objectives that is targeted by policymakers in many countries. Price uncertainty occurs due to the changes in market structure and consumer preference and expectation, which may affect price stability. In this study, the researchers aimed to examine the effects of price uncertainty of consumer price disaggregation in Malaysian sectors. To be specific, the researchers were seeking to discover on how domestic and global commodity prices can affect sectoral Consumer Price Index (CPI) on price inflation in Malaysia and most importantly, whether the effect is different for economic sectors in Malaysia. In addition, the effects of other factors (i.e., internal and external factors) on Malaysian sectoral CPI inflation were also studied. The threshold generalized autoregressive conditional heteroscedasticity (TGARCH) model was used to generate the price uncertainties. For the purpose of analysis, the threshold regression approach was applied based on time series of each single sector, followed by a combination of panel data of all sectors. The results differed across sectors, revealing that the impact of price uncertainties was determined by the sensitivity of each sector towards the price uncertainties. The effect of price increase is larger than the effect of price decrease. Price fluctuations were obvious in sectors that were dependent on consumer price or commodity price. Exchange rate and oil price inflation had also greatly influenced the CPI inflation.
Coxmodel is popular in survival analysis. In the case of time-varying covariate;
several subject-specific attributes possibly to change more frequently than others. This
paper deals with that issue. This study aims to analyze survival data with time-varying
covariate using a time-dependent covariate Cox model. The two case studies employed in
this work are (1) delisting time of companies from IDX and (2) delisting time of company
from LQ45 (liquidity index). The survival time is the time until a company is delisted
from IDX or LQ45. The determinants are eighteen quarterly financial ratios and two
macroeconomics indicators, i.e., the Jakarta Composite Index (JCI) and BI interest rate
that changes more frequent. The empirical results show that JCI is significant for both
delisting and liquidity whereas BI rate is significant only for liquidity. The significant
firm-specific financial ratios vary for delisting and liquidity.
Dengue is a mosquito-borne disease caused by virus and found mostly in urban and semi-urban areas, in many regions of the world. Female Aedes mosquitoes, which usually bite during daytime, spread the disease. This flu-like disease may progress to severe dengue and cause fatality. A generic reaction-diffusion model for transmission of mosquito-borne diseases was proposed and formulated. The motivation is to explore the ability of the generic model to reproduce observed dengue cases in Borneo, Malaysia. Dengue prevalence in four districts in Borneo namely Kuching, Sibu, Bintulu and Miri are compared with simulations results obtained from the temporal and spatio-temporal generic model respectively. Random diffusion of human and mosquito populations are taken into account in the spatio-temporal model. It is found that temporal simulations closely resemble the general behavior of actual prevalence in the three locations except for Bintulu. The recovery rate in Bintulu district is found to be the lowest among the districts, suggesting a different dengue serotype may be present. From observation, the temporal generic model underestimates the recovery rate in comparison to the spatio-temporal generic model.
A mathematical model is considered to determine the effectiveness of disin-
fectant solution for surface decontamination. The decontamination process involved the
diffusion of bacteria into disinfectant solution and the reaction of the disinfectant killing
effect. The mathematical model is a reaction-diffusion type. Finite difference method and
method of lines with fourth-order Runge-Kutta method are utilized to solve the model
numerically. To obtain stable solutions, von Neumann stability analysis is employed to
evaluate the stability of finite difference method. For stiff problem, Dormand-Prince
method is applied as the estimated error of fourth-order Runge-Kutta method. MATLAB
programming is selected for the computation of numerical solutions. From the results
obtained, fourth-order Runge-Kutta method has a larger stability region and better ac-
curacy of solutions compared to finite difference method when solving the disinfectant
solution model. Moreover, a numerical simulation is carried out to investigate the effect
of different thickness of disinfectant solution on bacteria reduction. Results show that
thick disinfectant solution is able to reduce the dimensionless bacteria concentration 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.
Pressurized water reactor (PWR) type AP1000 is a third generation of a nuclear
power plant. The primary system of PWR using uranium dioxide to generate heat energy
via fission process. The process influences temperature, pressure and pH value of water
chemistry of the PWR. The aim of this paper is to transform the primary system of PWR
using fuzzy autocatalytic set (FACS). In this work, the background of primary system
of PWR and the properties of the model are provided. The simulation result, namely
dynamic concentration of PWR is verified against published data.
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.
DNA computing, or more generally, molecular computing, is a recent development on computations using biological molecules, instead of the traditional silicon-chips. Some computational models which are based on different operations of DNA molecules have been developed by using the concept of formal language theory. The operations of DNA molecules inspire various types of formal language tools which include sticker systems, grammars and automata. Recently, the grammar counterparts of Watson-Crick automata known as Watson-Crick grammars which consist of regular, linear and context-free grammars, are defined as grammar models that generate double-stranded strings using the important feature of Watson-Crick complementarity rule. In this research, a new variant of static Watson-Crick linear grammar is introduced as an extension of static Watson-Crick regular grammar. A static Watson-Crick linear grammar is a grammar counterpart of sticker system that generates the double-stranded strings and uses rule as in linear grammar. The main result of the paper is to determine some computational properties of static Watson-Crick linear grammars. Next, the hierarchy between static Watson-Crick languages, Watson-Crick languages, Chomsky languages and families of languages generated by sticker systems are presented.
Let G be a dihedral group and ??cl G its conjugacy class graph. The Laplacian energy of the graph, LE(??cl G) is defined as the sum of the absolute values of the difference between the Laplacian eigenvalues and the ratio of twice the edges number divided by the vertices number. In this research, the Laplacian matrices of the conjugacy class graph of some dihedral groups, generalized quaternion groups, quasidihedral groups and their eigenvalues are first computed. Then, the Laplacian energy of the graphs are determined.