Topological indices are numerical values that can be analysed to predict the chemical properties of the molecular structure and the topological indices are computed for a graph related to groups. Meanwhile, the conjugacy class graph of is defined as a graph with a vertex set represented by the non-central conjugacy classes of . Two distinct vertices are connected if they have a common prime divisor. The main objective of this article is to find various topological indices including the Wiener index, the first Zagreb index and the second Zagreb index for the conjugacy class graph of dihedral groups of order where the dihedral group is the group of symmetries of regular polygon, which includes rotations and reflections. Many topological indices have been determined for simple and connected graphs in general but not graphs related to groups. In this article, the Wiener index and Zagreb index of conjugacy class graph of dihedral groups are generalized.
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.
Let g be a finite group. The probability of a random pair of elements in g are
said to be co-prime when the greatest common divisor of order x and y where x and y in
g, is equal to one. Meanwhile the co-prime graph of a group is defined as a graph whose
vertices are elements of g and two distinct vertices are adjacent if and only if the greatest
common divisor of order x and y is equal to one. In this paper, the co-prime probability
and its graphs such as the types and the properties of the graph are determined.
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.
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.
The modelling of splicing systems is simulated by the process of cleaving and recombining DNA molecules with the presence of a ligase and restriction enzymes which are biologically called as endodeoxyribonucleases. The molecules resulting from DNA splicing systems are known as splicing languages. Palindrome is a sequence of strings that reads the same forward and backward. In this research, the splicing languages resulting from DNA splicing systems with one non-palindromic restriction enzyme are determined using the notation from Head splicing system. The generalisations of splicing languages for DNA splicing systems involving a cutting site and two non-overlapping cutting sites of one non-palindromic restriction enzyme are presented in the first and second theorems, respectively, which are proved using direct and induction methods. The result from the first theorem shows a trivial string which is the initial DNA molecule; while the second theorem determines a splicing language consisting of a set of resulting DNA molecules from the respective DNA splicing system.
Preventive maintenance (PM) planning becomes a crucial issue in the real world of the manufacturing process. It is important in the manufacturing industry to maintain the optimum level of production and minimize its investments. Thus, this paper focuses on multiple jobs with a single production line by considering stochastic machine breakdown time. The aim of this paper is to propose a good integration of production and PM schedule that will minimize total completion time. In this study, a hybrid method, which is a genetic algorithm (GA), is used with the Monte Carlo simulation (MCS) technique to deal with the uncertain behavior of machine breakdown time. A deterministic model is adopted and tested under different levels of complexity. Its performance is evaluated based on the value of average completion time. The result clearly shows that the proposed integrated production with PM schedule can reduce the average completion time by 11.68% compared to the production scheduling with machine breakdown time.
The proposed modified methods of Cramer's rule consider the column vector as well as the coefficient matrix concurrently in the linear system. The modified methods can be applied since Cramer's rule is typically known for solving the linear systems in $WZ$ factorization to yield Z-matrix. Then, we presented our results to show that there is no tangible difference in performance time between Cramer's rule and the modified methods in the factorization from improved versions of MATLAB. Additionally, the Frobenius norm of the modified methods in the factorization is better than using Cramer's rule irrespective of the version of MATLAB used.
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.
Aging is a good indicator in demographic and health areas as the lifespan
of the elderly population increases. Based on the government’s Economic Outlook 2019,
it was found that an aging population would increase the government pension payments
as the pensioners and their beneficiaries have longer life expectancy. Due to mortality
rates decreasing over time, the life expectancy tends to increase in the future. The
aims of this study are to forecast the mortality rates in the years 2020 and 2025 using
the Heligman-Pollard model and then analyse the effect of mortality improvement on
the pension cost (annuity factor) for the Malaysian population. However, this study
only focuses on estimating the annuity factor using life annuities through the forecasted
mortality rates. The findings indicated that the pension cost is expected to increase if
the life expectancy of the Malaysian population increases due to the aging population
the near future. Thus, to reduce pension costs and help the pensioners from insufficient
financial income, the government needs to consider an extension of the retirement age in
future.
The commutativity degree is the probability that a pair of elements chosen randomly from a group commute. The concept of commutativity degree has been widely discussed by several authors in many directions. One of the important generalizations of commutativity degree is the probability that a random element from a finite group G fixes a random element from a non-empty set S that we call the action degree of groups. In this research, the concept of action degree is further studied where some inequalities and bounds on the action degree of finite groups are determined. Moreover, a general relation between the action degree of a finite group G and a subgroup H is provided. Next, the action degree for the direct product of two finite groups is determined. Previously, the action degree was only de?ned for ?nite groups, the action degree for ?nitely generated groups will be de?ned in this research and some bounds on them are going to be determined.
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.
Riverbank filtration (RBF) system is a surface water technology that is based
on the natural treatment of filtration instead of the use of chemicals, to pre-treat sur-
face water and provides public water supplies. Hydraulic conductivity value is one of the
significant factors affecting the water quality in RBF systems. In this article, an analyti-
cal modelling is developed to investigate the effect of this parameter on one dimensional
contaminant transport in RBF system. The model is solved by using Green’s function
approach. The model is applied for the first RBF system conducted in Malaysia. Gener-
ally, the results show that increasing the hydraulic conductivity value lead to an increase
in contaminant concentration in pumping well area.
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.
Simulation is used to measure the robustness and the efficiency of the forecasting
techniques performance over complex systems. A method for simulating multivariate
time series was presented in this study using vector autoregressive base-process. By
applying the methodology to the multivariable meteorological time series, a simulation
study was carried out to check for the model performance. MAPE and MAE performance
measurements were used and the results show that the proposed method that consider
persistency in volatility gives better performance and the accuracy error is six time smaller
than the normal hybrid model.
Since rice is a staple food in Malaysia, its price fluctuations pose risks to the producers, suppliers and consumers. Hence, an accurate prediction of paddy price is essential to aid the planning and decision-making in related organizations. The artificial neural network (ANN) has been widely used as a promising method for time series forecasting. In this paper, the effectiveness of integrating empirical mode decomposition (EMD) into an ANN model to forecast paddy price is investigated. The hybrid method is applied on a series of monthly paddy prices from February 1999 up to May 2018 as recorded in the Malaysian Ringgit (MYR) per metric tons. The performance of the simple ANN model and the EMD-ANN model was measured and compared based on their root mean squared Error (RMSE), mean absolute error (MAE) and mean percentage error (MPE). This study finds that the integration of EMD into the neural network model improves the forecasting capabilities. The use of EMD in the ANN model made the forecast errors reduced significantly, and the RMSE was reduced by 0.012, MAE by 0.0002 and MPE by 0.0448.
This paper revisits the comrade matrix approach in finding the greatest com-
mon divisor (GCD) of two orthogonal polynomials. The present work investigates on the
applications of the QR decomposition with iterative refinement (QRIR) to solve certain
systems of linear equations which is generated from the comrade matrix. Besides iterative
refinement, an alternative approach of improving the conditioning behavior of the coeffi-
cient matrix by normalizing its columns is also considered. As expected the results reveal
that QRIR is able to improve the solutions given by QR decomposition while the nor-
malization of the matrix entries do improves the conditioning behavior of the coefficient
matrix leading to a good approximate solutions of the GCD.
The heat and mass transfer of steady magnetohydrodynamics of dusty Jeffrey fluid past an exponentially stretching sheet in the presence of thermal radiation have been investigated. The main purpose of this study is to conduct a detailed analysis of flow behaviour of suspended dust particles in non-Newtonian fluid. The governing equations hav been converted into dimensionless form, and then solved numerically via the Keller-box method. The expression of Sherwood number, Nusselt number and skin friction have been evaluated, and then displayed in tabular forms. Velocity, temperature and concentration profiles are presented graphically. It is observed that large value of dust particles mass concentration parameter has reduced the flow velocity significantly. Increase in radiation parameter enhances the temperature, whereas the increment in Schmidt number parameter reduces the concentration.
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.
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.