Reductions from manipulation to 0–1 integer program-

Paper ID : A001

Isolated Truncated Chain Sampling Plan (ITCSP) for Weibull Product Life Distribution

Braimah Joseph Odunayo

¹

& Osanaiye Peter Adewumi

²

1Department of Mathematics, P.M.B 14, Ambrose Alli University, Ekpoma, Edo State, Nigeria

2Department of Statistics, PMB 1515, University of Ilorin, Ilorin, Kwara State, Nigeria

In this study, an Isolated Truncated Chain Sampling Plan (ITCSP) for Weibull Product Life Distribution is proposed when the testing is truncated at a specified time (t). This type of sampling plan is used to save the testing time in real life situations. The optimal sample sizes (n) required for testing product quality to ascertain a true mean life is obtained under a given Maximum Allowable Percent Defective (β ), test termination ratios (

_µ^t₀

) and acceptance numbers (C). The operating characteristics formula of the proposed plan was developed using addition theorem of probability. The operating characteristics and mean-ratio were used to assess the performance of the sampling plans. Simulated and real life data were used for the study using R software. The following were the findings from the study: Weibull distribution have low failure rate; as mean life ratio increase, the failure rate reduces; the minimum sample size increase as the acceptance number, maximum allowable percent defective and experiment time ratio increases; when the maximum allowable percent defective and acceptance number are fixed, the minimum sample sizes reduce as the experiment time ratio increases; when the acceptance number is fixed and the experiment time ratio varied, the minimum sample size increase as the maximum allowable percent defective increases; the mean life ratios required for smaller acceptance number are higher compared to those of higher acceptance number for any combination of the maximum allowable percent defective and experiment time ratio. The study concluded that the modified required minimum sample sizes were smaller compared to those in the literature making it a more economical plan to be adopted when time and cost of production is expensive and the testing is destructive. The proposed plan was also able to discriminate between good and poor quality lots from the operating characteristics.

Keywords : Minimum Sample size, Mean life; Operating Characteristics; Producers Consumers and Risk

49

Paper ID : A002 Potential Applications of Hourglass Matrix and Its Quadrant Interlocking Factorization

Babarinsa Olayiwola¹, Mandangan Arif²& Kamarulhaili Hailiza³

1Department of Mathematical Sciences, Federal University Lokoja, 1154 Kogi State, Nigeria

2Faculty of Science and Natural Resources, Universiti Malaysia Sabah, 88400 Kota Kinabalu, Malaysia

3School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia Hourglass matrix is recently shown to be a subset of Z-matrix which can be obtained from quadrant interlocking factorization (QIF) of nonsingular matrix. First, we extend the properties of hourglass matrix and its QIF. Then, we highlight possible applications of the matrix together with its factorization. The factorization of hourglass matrix may not exist for every nonsingular matrix. However, the potential applications of hourglass matrix surpasses its counterpart Z-matrix such as in statistics (Markov chains), cryptography (GGH encryption scheme) and in graph theory (mixed graph). Lastly, hourglass matrix can be partitioned into triangular block matrices, like Z-matrix, having property of a matrix group.

Keywords:Hourglass Matrix, Z-matrix, Quadrant Interlocking Factorization, Markov Chains, GGH Encryption, Mixed Graph

Paper ID : A007 Substitution Box Design Based from Symmetric Group Composition

Muhammad Fahim Roslan¹, Kamaruzzaman Seman¹, Azni Haslizan Ab Halim²& M Nor Azizi Syam Mohd Sayuti¹

1Fakulti Kejuruteraan dan Alam Bina, Universiti Sains Islam Malaysia, Nilai, 71800 Negeri Sembilan, Malaysia

2Fakulti Sains dan Teknologi, Universiti Sains Islam Malaysia, Nilai, 71800 Negeri Sembilan, Malaysia In this paper, one heuristic method of constructing substitution box (S-Box) using the concept of permutation composition is presented. Then the constructed S-Box is tested against several cryptography properties such as nonlinearity, differential uniformity, the algebraic degree and the existence of fixed point. The construction is based on composition of permutation within the symmetric group. This paper focus on the AES S-Box class which received 8-bit input and produced 8-bit output. This bijective S-Box consist of 256 elements which later involve in the process of composition. Initially, a set of 30 S-Box with high nonlinearity is generated using 30 irreducible polynomials under the finite fieldGF(2⁸). These S-Box is then undergoing two rounds of composition which finally yield about 1.62 million SBox. More than half of the generated S-Box achieve the nonlinearity of at least 100 with the maximum recorded nonlinearity of 110. This method also guarantee that the generated S-Box is bijective. To show the security level of our construction method, a comparison to other constriction methods is conducted. The methods introduced in this paper have slightly higher nonlinearity compared to several construction with the value of differential uniformity might be lower.

Keywords:Block Cipher; Substitution Box; Irreducible Polynomial; Composition

Paper ID : A009 Stagnation-Point Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Sheet in Hybrid

Nanofluid with Slip Velocity Effect: Stability Analysis

Nur Syazana Anuar¹, Norfifah Bachok^1,2, Norihan Md Arifin^1,2, Haliza Rosali¹& Ioan Pop³

1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

2Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

3Department of Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania

The effect of slip on stagnation point flow and heat transfer over an exponentially stretching/shrinking sheet filled with Cu-Al2O3/water nanofluids is investigated numerically in this paper. The governing boundary layer equations are transformed into a set of ordinary differential equations using a similarity transformation and then solved numerically using the bvp4c function in Matlab. The effects of nanoparticle volume fraction, slip parameter and stretching/shrinking parameter on the flow pattern and heat transfer have been studied. It is found that dual solutions exist for hybrid nanofluid in the case of shrinking sheet. Furthermore, slip parameter and Cu nanoparticle acts in widening the range of solution. Hybrid nanofluids have the higher heat transfer rate compared to nanofluid and viscous fluid. A stability analysis showed that the first solution is linearly stable and physically realizable.

Keywords:Exponentially Stretching/Shrinking; Heat Transfer; Hybrid Nanofluid; Stability Analysis

Paper ID : A012 Numerical Study of Mixed Convection Heat Transfer in a Horizontal Circular Cylinder of Cu, CuO and

GO/Methanol Micropolar Nanofluid

Mohammed Z. Swalmeh^1,2, Hamzeh T. Alkasasbeh², Abid Hussanan^3,4& Mustafa Mamat¹

1Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin (Kampus Gong Badak), 21300 Kuala Terengganu, Terengganu, Malaysia

2Faculty of Arts and Sciences, Aqaba University of Technology, Aqaba-Jordan

3Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

4Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City,Vietnam In this article, the mixed convection boundary layer flow about a horizontal circular cylinder with a micropolar nanofluid, which is maintained at a constant surface heat flux, has been investigated. Three types of nanoparticles with distinct conductivities, namely, graphene oxide, copper and copper oxide are considered and suspended in methanol based micropolar nanofluid. The governing equations are transformed into nonlinear PDEs by applying the similarity transformations and then solved numerically by an implicit finite difference scheme known as Keller-box method. The results for the local wall temperature, local skin friction coefficient, temperature, velocity and angular velocity are plotted and discussed for different parameters such as nanoparticles volume fraction and mixed convection parameter in view of thermo-physical properties of nanoparticles and base fluid. Moreover, numerical results for the local wall temperature and local skin friction coefficient are obtained. It is found that Cu/methanol micropolar nanofluid have higher velocity than the CuO or GO methanol based micropolar nanofluid.

Comparison have been made with published results on Newtonian fluid under special cases and obtained in close agreemen

Keywords:Heat Transfer; Mixed Convection; Micropolar Nanofluid; Keller-box method; Circular Cylinder

Paper ID : A013 Malaysia’s 14th General Election via Twitter: An Analysis Using the Epidemiological Model

Noor Syamsiah Mohd Noor¹, Ku Azlina Ku Akil¹& Latisha Asmaak Shafie²

1Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 02600 Arau, Perlis, Malaysia

2Academy of Language Studies, Universiti Teknologi MARA, 02600 Arau, Perlis, Malaysia Twitter has been prominently used during the electoral campaigns. Twitter helps the politicians to spread and share their political agenda. Through Twitter, every information is accessible to anyone and anybody around the world in keeping up with the latest information like a manifesto and others that relate to political issues. However, the popularity of political parties and leaders that could raise the winning opportunities in the election is not fully understood. This study aims to analyse the spreading of information during Malaysia’s 14th General Election via Twitter. This study employed an epidemiological model which is a system of differential equations known as Susceptible-Infected-Recovered (SIR). The model involves three state variables, which are active Twitter users (S), the transmission node (I) and immune Twitter users (R). The Twitter accounts owned by two political parties and two political leaders have been followed before and after the election. The influence of contact rate between active Twitter users and the transmission node of Twitter users on Malaysia’s 14th General Election was analysed.

The results showed that the contact rate between active Twitter users and the transmission node of the Twitter users has a significant influence on Malaysia’s 14th General Election.

Keywords:Electoral Campaign; Malaysia General Election; Twitter; Epidemiological Model

Paper ID : A014 Natural Convection Flow of Sodium Alginate Base Casson Nanofluid about a Solid Sphere in The Presence

of a Magnetic Field with Constant Surface Heat Flux

Firas A Alwawi^1,2, Hamzeh T Alkasasbeh³, Ahmad M Rashad^2,4& Ruwaidiah Idris¹

1School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia

2Department of Mathematics, Prince Sattam bin Abdulaziz University, College of Sciences and Humanities, Al-Kharj, Saudi Arabia, 11942, Saudi Arabia

3Department of Mathematics, Faculty of Science, Ajloun National University, P.O.Box 43, Ajloun 26810, Jordan

4Department of Mathematics, Aswan University, Faculty of Science, Aswan, 81528, Egypt In this paper, we examined a free convection flow of Sodium Alginate (SA) as a host Casson fluid with three different types of nanoparticles specifically, Silicon Dioxide (SiO2), Copper oxide (CuO), and Copper (Cu) on a solid sphere in the presence of magnetic field along with prescribed surface heat flux. The Keller-box method was carried out for solving the transformed governing partial differential equations. Numerical results for the local skin friction coefficient are obtained and compared with literature. Also, the influences of Casson fluid parameter, magnetic parameter, nanoparticles volume fraction, on local skin friction coefficient, local Nusselt number, temperature, and velocity are analyzed graphically. Our study revealed that the local Nusselt number and velocity profiles of Silicon Dioxide (SiO2) are lower than the other nanoparticles Sodium Alginate base Casson nanofluid, as well as it has the lowest temperature profiles.

Keywords:Casson Nanofluid; MHD; Natural Convection; Sodium Alginate; Solid Sphere; Constant Surface Heat Flux.

Paper ID : A016 Boundary Layer Flow of Williamson Nanofluid over a Stretching Sheet with Varied Wall Thickness and

Slip Effects

Shazwani Md Razi, Siti Khuzaimah Soida, Ahmad Sukri Abd Aziz, Noorashikin Adli & Zaileha Md Ali Faculty of Mathematical & Computer Sciences, Universiti Teknologi MARA, 40500 Shah Alam, Selangor,

Malaysia

This study investigates the effects of slip parameters and velocity power index parameter along with wall thickness on the magnetohydrodynamic (MHD) boundary layer flow of a Williamson nanofluid through a stretching sheet in porous medium. The governing partial differential equations are transformed into nonlinear ordinary differential equations (ODEs) using the relevant similarity variables. These nonlinear ODEs are solved numerically using the Runge-Kutta Fehlberg in MAPLE software. The effects of the pertinent parameters on the velocity, temperature and nanoparticle volume fraction profiles are presented graphically. The impact of the physical parameters on the skin friction coefficient, the local Nusselt number and the local Sherwood number are computed and analyzed.

The velocity profile increases when the velocity slip parameter increases. The temperature slip and nanoparticle fraction slip parameters reduce the temperature and the nanoparticle volume fraction profiles respectively. The temperature and the nanoparticle volume fraction profiles significantly increase due to the increase in the velocity power index. An opposite behaviour is observed on different values of the wall thickness parameter when the power index is less than one compared to greater than one.

Keywords:Boundary Layer Flow; Williamson Nanofluid; Slip; Velocity Power Index; Variable Wall Thickness

Paper ID : A017 MHD Flow and Heat Transfer of Ferrofluid on Stagnation Point along Flat Plate with Convective

Boundary Condition and Thermal Radiation Effect

Siti Hanani Mat Yasin¹, Muhammad Khairul Anuar Mohamed², Zulkhibri Ismail¹, Basuki Widodo³& Mohd Zuki Salleh¹

1Faculty of Industrial Sciences & Technology, Universiti Malaysia Pahang, 26300 Gambang, Pahang, Malaysia

2School of Foundation and Inter Disciplinary Studies, DRB-HICOM University of Automotive Malaysia, Peramu Jaya Industrial Area, 26607 Pekan, Pahang, Malaysia

3Department of Mathematics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia This theoretical study deals with numerical solution of MHD convection laminar boundary layer flow and heat transfer on stagnation point along a stationary horizontal flat plate. For this purpose, ferrofluid which contains magnetite, Fe3O4as a ferroparticles and water as a base fluid is considered. Ferrofluid has shown a particular achievement when the effect of external magnetic field applied, such as helping to control the properties of physi-cal and flow of ferrofluid. The study starts with the formulation of the mathematiphysi-cal equations that governed the ferrofluid flow and heat transfer. The governing equation which is in the form of dimensional nonlinear partial differential equations are reduced to nonlinear ordinary partial differential equations by using appropriate similar-ity transformation and then solved numerically by using the Keller-box method. Numerical result is discussed in terms of pertinent effects that influence the ferrofluid flow and heat transfer like magnetic parameter, ferroparticles volume fraction parameter, Biot number and radiation parameter on velocity and temperature profiles. It is found that the temperature profile will increase with an increase volume fraction of ferroparticles parameter, radiation parameter and Biot number and decrease with increasing magnetic parameter.

Keywords:Ferrofluid; MHD; Flat Plate; Convective Boundary Condition Thermal Radiation

Paper ID : A018 Stagnation Point Flow over an Exponentially Stretching/Shrinking Sheet in a Carbon Nanotubes with Slip

Effect

Nur Hazirah Adilla Norzawary, Norfifah Bachok & Fadzilah Md Ali

Department of Mathematics, Faculty of Sciences and Institute for Mathematical Research, Universiti Putra Malaysia, 43400, UPM Serdang, Selangor, Malaysia

This study is to investigate the problem of stagnation point flow over an exponentially stretching/shrinking sheet in carbon nanotubes with slip effects. Using a similarity transformation, the governing partial differential equa-tions are transformed into a system of nonlinear ordinary differential equaequa-tions which is then solved numerically using a bvp4c solver in Matlab. Two types of carbon nanotubes (CNTs), single- and multi-wall CNTs are used with water as the base fluids with Prandtl number Pr=6.2. The influence of the flow parameters on the dimen-sionless velocity, temperature, skin friction and Nusselts numbers is explored and presented in the form of graphs and interpreted physically. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique. The range of the stretching/shrinking parameterεwhere the similarity solution exists for the steady stagnation-point flow over an exponentially stretching/shrinking sheet is larger compared with the linear stretching/shrinking case.

Keywords:Carbon Nanotubes; Exponentially Stretching/Shrinking Sheet; Heat Transfer; Stagnation Point Flow;

Slip Effects

Paper ID : A019 Evaluation on the Financial Performance of Technology Companies in Malaysia with Zmijewski Model

Weng Hoe Lam^1,3,4, Hong Beng Yeoh^2,4, Weng Siew Lam^1,3,4& Jing Xin Agnes Lai⁴

1Centre for Mathematical Sciences, Department of Physical and Mathematical Science, Faculty of Science, Universiti Tunku Abdul Rahman, Kampar Campus, Jalan Universiti, Bandar Barat, 31900 Perak, Malaysia

2Centre for Learning and Teaching, Department of Physical and Mathematical Science, Faculty of Science, Universiti Tunku Abdul Rahman, Kampar Campus, Jalan Universiti, Bandar Barat, 31900 Perak, Malaysia

3Centre for Business and Management, Department of Physical and Mathematical Science, Faculty of Science, Universiti Tunku Abdul Rahman, Kampar Campus, Jalan Universiti, Bandar Barat, 31900 Perak, Malaysia

4Faculty of Science, Universiti Tunku Abdul Rahman, Kampar Campus, Jalan Universiti, Bandar Barat, 31900 Kampar, Perak, Malaysia

In the era of Industrial Revolution (IR) 4.0, Information and Communications Technology (ICT) sector provides cost effective solution to improve overall organizational performance as well as support sustainable national eco-nomic growth of emerging economies like Malaysia. On top of it, local ICT related companies, especially those are listed in Bursa Malaysia, are expected to work and contribute toward the accomplishment of vision 2050 in transforming Malaysian into smart communities. At the same time, the performance of these companies has to be evaluated as they will become financially distressed if they are not financially stable. The objective of this paper is to evaluate the financial performance of technology companies in Malaysia using Zmijewski model. The model uses financial ratio analysis that measures the performance, leverage and liquidity of these companies. The data of this study comprises technology-based companies that are listed in Malaysia’s stock market. The period of this study is from year 2013 to 2017. The results indicate the financial condition of these companies based on the Zmijewski value computed. This study is significant because it assesses the financial condition of the technology companies in Malaysia. As a result of it, stakeholders will initiate proactive and preventive measures to promote the economic growth of technology sector in Malaysia.

Keywords:Financial Ratios; Technology Sector; Zmijewski Model; Financial Performance

Paper ID : A020 Stagnation Point Flow of a Thermally Stratified Hybrid CuAl2O3/water Nanofluid over a Permeable

Stretching/Shrinking Sheet

Najiyah Safwa Khashi’Ie^1,2, Norihan Md Arifin^1,3, Ezad Hafidz Hafidzuddin⁴, Nadihah Wahi³and Ioan Pop⁵

1Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

2Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia

33Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

4Centre of Foundation Studies for Agricultural Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

5Department of Mathematics, Babe¸s-Bolyai University, R-400084 Cluj-Napoca, Romania The study scrutinizes the coupled effects of thermal stratification and mixed convection on boundary layer flow and heat transfer of a hybrid CuAl2O3/water nanofluid. Stretching/shrinking surface is permeable to allow the wall fluid suction while thermal convection is also included to deal with the thermal stratification phenomenon.

In the present work, the combination of copper (Cu) nanoparticles and Al2O3/water nanofluid is modelled using the analytical hybrid nanofluid model. A similarity transformation is adopted to reduce the governing model into a set of ordinary (similarity) differential equations. The efficient bvp4c function in MATLAB software is utilized to solve the transformed model. An astonishing result is obtained where the heat transfer rate of hybrid nanofluid intensifies when small suction parameter is imposed on the stretching/shrinking sheet while a contrary result is obtained when higher value of suction is applied. Suction and opposing buoyancy parameters are among the control parameters that induce the existence of two solutions. Stability analysis affirms that the first solution is mathematically stable. The present results are conclusive to the combination of alumina and copper nanoparticles only and other combination of nanoparticles may produce different flow and heat transfer characteristics.

Keywords:Stagnation Point Flow; Stretching/Shrinking; Hybrid Nanofluid; Thermal Stratification; Dual Solu-tions

Paper ID : A021 Pseudospecteral Method with Linear Damping Effect and De-aliasing Technique in Nonlinear PDEs

Azwani Alias, Nik Nur Amiza Nik Ismail& Fatimah Noor Harun

School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia.

Pseudospectral method is an alternative of finite differences and finite elements method to solve nonlinear partial differential equations, especially in nonlinear waves. The Pseudospectal method is very efficient because it used the fast fourier transform to calculate discrete Fourier transform in the algorithm. Therefore, in this paper, the Pseudospectral scheme is modified by adding the linear damping region and de-alisiang technique, and has been tested in Ostrovsky equation, where Ostrovsky equation is a modified of Korteweg-de Vries equation with an addition of background Earth’s rotation. In order to prevent the possibility of radiated waves re-entering from the boundaries and disturbing the main wave structure, linear damping region is added to the numerical discretization.

Besides, the numerical simulations occur with the aliasing errors due to pollution of numerically calculated Fourier transform by higher frequencies component because of the truncation of the series. To prevent this, the de-aliasing technique is implemented on the nonlinear term and linear damping region by setting of the amplitudes to zero at the end of both boundaries. Therefore, the simulation results of Pseudospectral method will be smooth without any high frequency errors even for the high amplitude of the waves

Keywords: Pseudospectral Method; De-aliasing Technique; Linear Damping; Partial Differential Equation;

Ostrovsky equation.

Paper ID : A022 Solving Variable Coefficient Korteweg-de Vries Equation Using Pseudospectral Method

Nik Nur Amiza Nik Ismail & Azwani Alias

School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia.

Korteweg-de Vries (KdV) equation usually describes internal solitary waves in shallow water and in the coastal ocean. However, KdV equation only assuming a uniform background state and it is not sufficient to describe the waves propagation as the topography can vary horizontally. In this paper, we are mainly focused on the behaviour of solitary waves as they propagate over variable topography. By incorporating a variable medium in the model, the propagation of solitary water waves in the framework of a variable-coefficient Korteweg-de Vries (vKdV) is studied and numerical solutions of the problem is obtained. Besides to study the effects of this factor on the formation of the waves, this general approach enables us to improve known results on periodic wave trains and the adiabatic evolution of solitary waves in the presence of variable topography. Simulations studied included the solution of vKdV equation for arbitrary initial condition as well as the migration of a single solitary wave and the time evaluation of the solitary waves in various depth. In this research, we carried out the methodology based on a vKdV equation using pseudospectral (PS) method with different types of variable depth selections. Simulations undertaken and result discussions proved that the PS method is efficient in solving the KdV equation as well as the vKdV equation. Our results show that the presented method is in a good agreement with the previous method to solve the model.

Keywords:Solitary Waves; Pseudo Spectral Method; Variable Topography; Variable-Coefficient Korteweg-de Vries Equation.

Paper ID : A024 Mathematical Models of Heterogeneity in Cancer Cell Growth

Priscilla Macansantos

University of the Philippines Baguio, Baguio City 2600, Philippines

Cancer is characterized by unregulated growth of certain cells in the body, often leading to a rapid growth of tumors in vital organs. Various treatments have been proposed and given to cancer patients, including combi-nations of radiation, chemotherapy, and immunotherapy, with varying rates of success. Characterization of the disease (and the search for a cure) is made more challenging by the observed heterogeneous behavior and vari-ability of growth rates of cells, particularly cells forming tumors in various stages of development. Heterogeneity refers to apparently dissimilar traits and behavior of individual cells or cell subpopulations, despite originating from a common tumor or parental line. In the last several decades, developments in mathematical biology, together with increasing availability of sophisticated laboratory equipment (aided by powerful computers) has provided a framework for the quantification and study of cell traits, including variability. We review some recent work on heterogeneity and growth variability in the context of mathematical models proposed

Keywords:Cancer Heterogeneity, Growth Variability

In document Manipulation of elections by minimal coalitions (Page 70-84)