Table of contents

Preface

Mastery and perfection in mathematics is a mandatory pre-requisite in advancing the frontiers of science. Mathematics provides the methodology and framework of rigorous thoughts in understanding and unveiling the beauty of the physical universe. It is often astonished how simple mathematical expressions are sufficed in describing complex physical phenomena.

Today, the rapid development in science and technology poses new challenges to mathematicians and scientists that requires innovative approach and methodology or eventually new mathematical theories. As such, the Kulliyyah of Engineering, International Islamic University Malaysia (IIUM) in collaboration with MIMOS Bhd. are therefore proud to present the 4^th International Conference on Mathematical Modelling in Engineering 2017 (ICMAE4). We aspire ICMAE to serve as an effective platform for academicians and researchers internationally to share ideas, state-of-the-art innovations and future developments of mathematical methods in diverse field of studies. The specific conference topics include:

Mathematical physics and differential equations

Algebra & analysis

Mathematical modelling & simulation

Probability & mathematical statistics

Analytical & numerical methods

This publication contains papers presented during ICMAE4 which was held on the 8-9 August 2017 in the Faculty of Engineering, International Islamic University Malaysia. All 25 papers selected have been subjected to peer reviewing process. As such, we would like to thank all reviewers, type-setting editors and last but not least all committee members for the successful publication of this special issue of ICMAE4.

Guest Editors,

Abdumalik Rakhimov

Bekbaev Ural

Jamal I. Daoud

Khikmat Saburov

Md. Sazzad H. Chowdhury

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

In this paper we prove a precise equiconvergence relation between index of the Bochner-Riesz means of the expansions and power of the singularity of the distributions with compact support in summation associated with the elliptic operator.

The term 'survival analysis' has been used in a broad sense to describe collection of statistical procedures for data analysis. In this case, outcome variable of interest is time until an event occurs where the time to failure of a specific experimental unit might be censored which can be right, left, interval, and Partly Interval Censored data (PIC). In this paper, analysis of this model was conducted based on parametric Cox model via PIC data. Moreover, several imputation techniques were used, which are: midpoint, left & right point, random, mean, and median. Maximum likelihood estimate was considered to obtain the estimated survival function. These estimations were then compared with the existing model, such as: Turnbull and Cox model based on clinical trial data (breast cancer data), for which it showed the validity of the proposed model. Result of data set indicated that the parametric of Cox model proved to be more superior in terms of estimation of survival functions, likelihood ratio tests, and their P-values. Moreover, based on imputation techniques; the midpoint, random, mean, and median showed better results with respect to the estimation of survival function.

In this paper, we observe some effects of schedule perturbations to the performance of aircraft routings. We show that moving departure time of flights to adding their block-time do not guarantee that the departure delay of the flights will be reduced. Contrarily, moving arrival time of flights always improve the performance of aircraft routings, especially for reducing arrival delay. The computational results also show that by adding more slacks, we obtain better performance of aircraft routings.

The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by attaching them some quadratic forms.

Finding accurate and efficient methods for solving nonlinear hyper chaotic problems has long been an active research undertaking. Like the well-known Adomian decomposition method (ADM) and based on observations, it is hopeless to find HPM solutions of hyper chaotic systems valid globally in time. To overcome this shortcoming, we employ the multistage homotopy-perturbation method (MHPM) to the nonlinear hyperchaotic Chen system. Based on the cases investigated, MHPM is more stable for a longer time span than the standard HPM. Comparisons with the standard HPM and the well-known purely numerical fourth-order Runge-Kutta method (RK4) suggest that the MHPM is a powerful alternative for nonlinear hyper chaotic system. The new algorithm and the new technique for choosing the initial approximations were shown to yield rapidly convergent series solutions.

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.

We investigate the impact of donor-acceptor morphology on the generation of charge carriers in organic photovoltaic cells and photodiodes based on a recently proposed model. It is found that for devices with typical values of permittivity and actual charge carrier mobilities, the donor-acceptor morphology plays an important role in the charge carrier generation, practically at all operating electric fields. Higher permittivity and actual mobilities increase the charge carrier generation, and also decrease the effect of donor-acceptor morphology on the charge carrier generation. Although the donor-acceptor morphology is important for charge carrier generation in general, but having permittivity and/or actual mobilities that are significantly higher than the typical values are more desirable in order to maximize the charge carrier generation.

The network model is a database model conceived as a flexible way of representing objects and their relationships. Its distinguishing feature is that the schema, viewed as a graph in which object types are nodes and relationship types are arcs, forms partial order. When a database is large and a query comparison is expensive then the efficiency requirement of managing algorithms is minimizing the number of query comparisons. We consider updating operation for network model database management systems. We develop a new sequantial algorithm for updating operation. Also we suggest a distributed version of the algorithm.

In regression analysis it is obvious to have a correlation between the response and predictor(s), but having correlation among predictors is something undesired. The number of predictors included in the regression model depends on many factors among which, historical data, experience, etc. At the end selection of most important predictors is something objective due to the researcher. Multicollinearity is a phenomena when two or more predictors are correlated, if this happens, the standard error of the coefficients will increase [8]. Increased standard errors means that the coefficients for some or all independent variables may be found to be significantly different from In other words, by overinflating the standard errors, multicollinearity makes some variables statistically insignificant when they should be significant. In this paper we focus on the multicollinearity, reasons and consequences on the reliability of the regression model.

Many studies have been conducted to investigate the effect of environmental, mechanical and electrical stresses on insulator. However, studies on physical process of discharge phenomenon, leading to the breakdown of the insulator surface are lacking and difficult to comprehend. Therefore, this paper analysed charge carrier generation mechanism that can cause free charge carrier generation, leading toward surface discharge development. Besides, this paper developed a model of surface discharge based on the charge generation mechanism on the outdoor insulator. Nernst's Planck theory was used in order to model the behaviour of the charge carriers while Poisson's equation was used to determine the distribution of electric field on insulator surface. In the modelling of surface discharge on the outdoor insulator, electric field dependent molecular ionization was used as the charge generation mechanism. A mathematical model of the surface discharge was solved using method of line technique (MOL). The result from the mathematical model showed that the behaviour of net space charge density was correlated with the electric field distribution.

In this study, the soil temperature profile was computed based on the harmonic heat transfer equations at various depths. The meteorological data ranging from January, 1^st 2016 to December, 31^st 2016 measured by local weather stations were employed. The findings indicted that as the soil depth increases, the temperature changes are negligible and the soil temperature is nearly equal to the mean annual air temperature. Likewise, the results have been compared with those reported by other researchers. Overall, the predicted soil temperature can be readily adopted in various engineering applications in Malaysia.

A hot gas rise towards ceiling due to fire buoyancy will cause severe damage to the building structure. The temperature rises need to be controlled as among the elements of compliance in performance-based design. The channel flow between beams has used in this study to mitigate hot gases out of the enclosure by mean of response surface methodology. Fire Dynamic Simulator was employed as a simulation tool while the result was statistically examined using analysis of variance via Minitab application. It was found that the result was linear with predicted R² (93.25%) and within the permissible R² (98.13%). The ceiling height has been identified not affect in controlling hot gases while four control parameters which are beam spacing, transversal beam, extraction rate and longitudinal beam with p-values of 0.00, 0.000, 0.023 and 0.000 respectively, have been found to have the significant effect on the smoke temperature control. This study contributes a good input to the fire safety community in providing the initial design of enclosed car park with better condition.

The existence of dark strongly localized modes of binary discrete media with cubic-quintic nonlinearity is numerically demonstrated by solving the relevant discrete nonlinear Schrödinger equations. In the model, the coupling coefficients between adjacent sites are set to be relatively small representing the anti-continuum limit. In addition, approximated analytical solutions for vectorial solitons with various topologies are derived. Stability analysis of the localized states was performed using the standard linearized eigenfrequency problem. The prediction from the stability analysis are furthermore verified by direct numerical integrations.

The purpose of this study is to determine the instability of Doha stock market and develop forecasting models. Linear time series models are used and compared with a nonlinear Artificial Neural Network (ANN) namely Multilayer Perceptron (MLP) Technique. It aims to establish the best useful model based on daily and monthly data which are collected from Qatar exchange for the period starting from January 2007 to January 2015. Proposed models are for the general index of Qatar stock exchange and also for the usages in other several sectors. With the help of these models, Doha stock market index and other various sectors were predicted. The study was conducted by using various time series techniques to study and analyze data trend in producing appropriate results. After applying several models, such as: Quadratic trend model, double exponential smoothing model, and ARIMA, it was concluded that ARIMA (2,2) was the most suitable linear model for the daily general index. However, ANN model was found to be more accurate than time series models.

In this paper, we are interested in the numerical simulation of the mathematical model of Keller-Segel Elliptic-Parabolic problem using finite volume scheme. The finite volume scheme is applied to the elliptic-parabolic model's problem and we have shown under certain assumptions, the existence of a unique and positive approximate solution. Moreover, under adequate regularity assumption of the exact solution, the finite volume scheme is the first order accurate. A good agreement between our numerical simulation and the theoretical results has been obtained.

A theoretical study that describes the magnetohydrodynamic mixed convection boundary layer flow with heat transfer over an exponentially stretching sheet with an exponential temperature distribution has been presented herein. This study is conducted in the presence of convective heat exchange at the surface and its surroundings. The system is controlled by viscous dissipation and internal heat generation effects. The governing nonlinear partial differential equations are converted into ordinary differential equations by a similarity transformation. The converted equations are then solved numerically using the shooting method. The results related to skin friction coefficient, local Nusselt number, velocity and temperature profiles are presented for several sets of values of the parameters. The effects of the governing parameters on the features of the flow and heat transfer are examined in detail in this study.

This paper describes an application of a statistical technique one-way ANOVA in completely randomized experiments with three replicates. This technique was employed to a single factor with four levels and multiple observations at each level. The aim of this study is to investigate the relationship between chemical oxygen demand index and location on-sites. Two different approaches are employed for the analyses; critical value and p-value. It also presents key assumptions of the technique to be satisfied by the data in order to obtain valid results. Pairwise comparisons by Turkey method are also considered and discussed to determine where the significant differences among the means is after the ANOVA has been performed. The results revealed that there are statistically significant relationship exist between the chemical oxygen demand index and the location on-sites.

To implement quantum gates stimulated Raman adiabatic passage (STIRAP) can be used. This STIRAP requires high Rabi frequencies and to overcome this problem we use superadiabatic approach. Our model is a tripod consisting of four-level system driven by three resonant fields. These fields are modulated by Gaussian pulses with different amplitudes, phases and time delays. We investigate the robustness of our model against dephasing which are caused by collisions or phase fluctuations of the fields.

The non-adiabatic effects which is manifested in the electric properties of low-lying states of even-even deformed nuclei are studied. A simple phenomenological model which takes into account the Coriolis mixing of ${K}^{\pi }={0}_{n}^{+},{2}_{n}^{+}$ and ${K}^{\pi }={1}_{\nu }^{+}$ state bands.

The Calculations for isotopes ^170–174Yb, are carried out. The reduced probability of electric quadrupole transitions from the states ${0}_{\nu }^{+}$ and ${2}_{\nu }^{+}$ - bands to the ground (gr) state band is calculated and non adiabatic effect is discussed. The ratio of E2– transitions R_IK from ${0}_{2}^{+}$, ${0}_{3}^{+}$, ${2}_{1}^{+}$, and ${2}_{2}^{+}$ bands are calculated and compared with the experimental data.

Nowadays, microgrid system technology is becoming popular for small area power management systems. It is essential to be less harmonic-distortion and high efficiency of the inverter for microgrid applications. Pulse width modulation (PWM) controller is a conventional switching control technique which is suitable to use in the microgrid connected power inverter system. The control method and algorithm of this technique are challenging, and different approaches are required to avoid the complexity for a customized solution of the microgrid application. This paper proposes a comparative analysis of different controller and their operational methods. A PWM controller is used to reduce the ripple voltage noise while a continuous current mode provides a small output ripple which gives steady-state error as zero on fundamental and cutoff frequency. To reduce the ripple current, higher frequency harmonic distortion, switching loss and phase noise, LC low pass filter is used on either side of input and output terminals. The proposed inverter is designed by MATLAB 2016a simulation software. A balanced load resistance (RL = 20.5 Ω) of star configuration and a dual input DC voltage of ± 35V are considered. In this design, the circuit parameters, the fundamental frequency of 50 Hz, the PWM duty cycle of 95%, the cutoff frequency of the switching controller of 33 kHz are considered. The inverter in this paper exhibits THD of 0.44% and overall efficiency approximately of 98%. The proposed inverter is expected to be suitable for microgrid applications.

In this paper we consider the λ-model on the Cayley tree of order two. We describe the periodic and weakly periodic ground states for the considered model.

In the present paper, we study the existence of Lyapunov functions for Volterra qudratic stochastic operators(QSO) on infinite dimensional simplex. We provide a construction of Lyapunov functions for such kind of operators, which allows us to estimate their limiting points.

For every finite group G the ergodicity of any map p: S → S on S is shown, where R[G] is the real group algebra of G,

$$\begin{eqnarray}&&S=\{x=\displaystyle \sum _{g\in G}{x}_{g}g\in \Re [G]:\displaystyle \sum _{g\in G}{x}_{g}=1,{x}_{g}\ge 0\ \mathrm{for}\ \mathrm{any}\ g\in G\}-\mathrm{the}\ \mathrm{simplex},\end{eqnarray}$$

$p(x)={a}_{0}+{a}_{1}x+{a}_{2}{x}^{2}+\ldots$

$x\in S$

${a}_{i}\ge 0$

$\displaystyle {\sum }_{i=0}^{\infty }{a}_{i}=1$

$x\in S$

In the solving the boundary value problems of equations of mathematical physics in bounded domains it is important to adjust the solution on the closed domain. This leads to the investigation of convergence and sumability problems near the boundary of the domain. In the present paper we study this problem for the eigenfunction expansions associated with the polyharmonic operator.

In recent years, Active Disturbance Rejection Control (ADRC) has become a popular control alternative due to its easy applicability and robustness to varying processes. In this article, ADRC with input decoupling transformation (ADRC-IDT) is proposed to improve ride comfort of a vehicle with an active suspension system using half-car model. The ride performance of the ADRC-IDT is evaluated and compared with decentralized ADRC control as well as the passive system. Simulation results show that both ADRC and ADRC-IDT manage to appreciably reduce body accelerations and able to cope well with varying conditions typically encountered in an active suspension system. Also, it is sufficient to control only the body motions with both active controllers to improve ride comfort while maintaining good road holding and small suspension working space.