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.
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.
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.
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.
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).
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.
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.
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.
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
shape parameter.
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.
1Malaysia
2 (UKM)43600 Bangi, Selangor, Malaysia
∗Corresponding author:
Numerous studies have linked biodiversity with zoonotic disease control. However, researchers have warned against simply believing that the increase in biodiversity can reduce the infection disease in the community. They proposed that amplification effect (increase in biodiversity accompanied by an increase in disease prevalence) might sometimes occur. Thus, we formulated a deterministic model to consider the impact of an amplification or dilution agent on the SNV transmission in the deer mouse population. Bifurcation analysis was carried out to examine the combined influences of the environmental carrying capacity, the interspecific competition strength and the impact of amplification or dilution agent on the deer mouse population. Our results showed that the system with amplification agent required a higher carrying capacity or stronger interspecific strength to compensate for its amplification effect in suppressing the SNV prevalence; this situation explains the lack of reduction in SNV prevalence despite the presence of high biodiversity in some empirical studies. In this study, we highlight the importance of investigating the roles of the additional species in an assemblage to better understand their relationship with the SNV prevalence in deer mouse population.
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.
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.
Let g be a finite group and s be a subset of g, where s does not include
the identity of g and is inverse closed. A cayley graph of a group g with respect to the
subset s is a graph, where its vertices are the elements of g and two vertices a and b
are connected if ab-1 is in the subset s. The energy of a cayley graph is the sum of all
absolute values of the eigenvalues of its adjacency matrix. In this paper, we consider a
specific subset s = {b, ab, . . . , An-1b} for dihedral groups of order 2n, where n 3 and find
the cayley graph with respect to the set. We also calculate the eigenvalues and compute
the energy of the respected cayley graphs. Finally, the generalization of the energy of the
respected cayley graphs is found.
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.
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.
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.
Successful oil palm plantation should have high profit, clean and environmental friendly. Since oil palm trees have a long life and it takes years to be fully grown, controlling the felling rate of the oil palm trees is a fundamental challenge. It needs to be addressed in order to maximize oil production. However, a good arrangement of the felling of the oil palm trees may also affect the amount of carbon absorption. The objec- tive of this study is to develop an optimal felling model of the oil palm plantation system taking into account both oil production and carbon absorption. The model facilitates in providing the optimal control of felling rate that results in maximizing both oil produc- tion and carbon absorption. With this aim, the model is formulated considering oil palm biomass, carbon absorption rate, oil production rate and the average prices of carbon and oil palm. A set of real data is used to estimate the parameters of the model and numerical simulation is conducted to highlight the application of the proposed model. The resulting parameter estimation that leads to an optimal control of felling rate problem is solved.
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.
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.