Pusat Pengajian Sains Matematik - Tesis

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Interpolasi Data Berselerak
(1994-03)
Rahmita Wirza
Tesis ini bertujuan untuk meninjau teknik-teknik bagi memodelkan permukaan yang licin bagi data berselerak dan penganggaran data berselerak tiga dimensi yang diberikan. Kaedah yang akan dibincangkan melibatkan tiga langkah iaitu, penyegitigaan data domain; penganggaran terbitan separa pada setiap data yang diberi untuk menghasilkan permukaan yang licin dan penakrifan skema interpolasi.
Assessment Of Hydraulic Response Due To Flood Mitigation Measures In Sg. Pinang Catchment, Penang
(1995-02)
Low Chee Soon
The current study aims to assess the hydraulic response of Sg. Pinang catchment under both existing and proposed conditions, by means of the advanced flow simulation model SWMM developed by the USEPA.
Preprocessing And Clustering Short Time-Series Microarray
(2008-06)
Loh Wei Ping
In this thesis, we addressed a general survey on issues dealing with clustering time-series microarray. Two sets of temporal microarray study data originate from Nonobese Diabetic mice (NOD mice) species; publicly available at RAO (RNA Abundance Database) and Drosophila Melanogaster species expression data; available at GEO (Gene Expression OMR Datasets) are employed.
Robust Wavelet Regression With Automatic Boundary Correction
(2012-12)
Alsaidi Almahdi Mohamed Altaher
This thesis proposes different robust methods in an attempt to keep using the idea of PWR and LP\iVR even beyond the usual assumptions of such outliers, independent or correlated non Gaussian noises and random missing data. Therefore, this thesis is divided into three parts. The first part introduces five different robust methodologies to extend the validity of PWR and LPWR to describe data contaminated with outliers and independent noises. The second part pays special exception when the noise structure is correlated.
A Weighted Least Squares Estimation Of The Polynomial Regression Model On Paddy Production For The Muda Agriculture And Development Authority (Mada) Area
(2016-01)
Musa, Rosliza
The curvilinear relationship between a dependent variable and several independent variables can be represented by a polynomial regression model. This model is used to study the relationship between response variable and predictor variable which contain square and higher-order term. Polynomial regression model is a special case of multiple regression model. The building of polynomial regression model has the same characteristics as multiple linear regressions in term of parameter estimation, regression inference, variable selection and model diagnostic. Weighted least square estimation is used as a remedy for non-constant variance. This study used polynomial regression model with weighted least square estimation to investigate paddy production of different paddy lots based on environmental and cultivation characteristics in Muda Agriculture and Development Authority (MADA) area.
Bayesian Networks With Greedy Backward Elimination In Feature Selection For Data Classification
(2019-03)
Ang, Sau Loong
Naive Bayes (NB) is an efficient Bayesian classifier with wide range of applications in data classification. Having the advantage with its simple structure. Naive Bayes gains attention among the researchers with its good accuracy in classification result. Nevertheless, the major drawback of Naive Bayes is the strong independence assumption among the features which is restrictive. This weakness causes not only confusion in the causal relationships among the features but also doubtful representation of the real structure of Bayesian Network for classification. Further development of Naive Bayes in augmenting extra links or dependent relationships between the features such as the Tree Augmented Naive Bayes (TAN) end up with slight improvement in accuracy of classification result where the main problems stated above remain unsolved.
Efficient Entropy-Based Decoding Algorithms For Higher-Order Hidden Markov Model
(2019-03)
Chan, Chin Tiong
Higher-order Hidden Markov model (HHMM) has a higher prediction accuracy than the first-order Hidden Markov model (HMM). This is due to more exploration of the historical state information for predicting the next state found in HHMM. State sequence for HHMM is invisible but the classical Viterbi algorithm is able to track the optimal state sequence. The extended entropy-based Viterbi algorithm is proposed for decoding HHMM. This algorithm is a memory-efficient algorithm due to its required memory space that is time independent. In other words, the required memory is not subjected to the length of the observational sequence. The entropybased Viterbi algorithm with a reduction approach (EVRA) is also introduced for decoding HHMM. The required memory of this algorithm is also time independent. In addition, the optimal state sequence obtained by the EVRA algorithm is the same as that obtained by the classical Viterbi algorithm for HHMM.
Numerical Solutions For Two Dimensional Time-Fractional Differential Sub-Diffusion Equation
(2019-04)
Ali, Umair
In the past several decades, fractional differential equations (differential equation involving arbitrary order derivatives) have acquired much popularity in the area of science and engineering. This is because such equations can better model certain problems of fluid mechanics, physics, biological science, chemistry, hydrology and finance, amongst others, due to the fact that it can better represent system with memory. However, most fractional differential equations cannot be solved by exact analytical techniques.
Arrangement Of Letters In Words Using Parikh Matrices
(2019-04)
Poovanandran, Ghajendran
The Parikh matrix mapping is an ingenious generalization of the classical Parikh mapping in the aim to arithmetize words by numbers. Two words are M-equivalent if and only if they share the same Parikh matrix. The characterization of M-equivalent words remains open even for the case of the ternary alphabet. Due to the dependency of Parikh matrices on the ordering of the alphabet, the notion of strong M-equivalence was proposed as an order-independent alternative to M-equivalence. In this work, we introduce a new symmetric transformation that justifies strong M-equivalence for the ternary alphabet. We then extend certain work of §erbanuja to the context of strong ^-equivalence and show that the number of strongly M-unambiguous prints for any alphabet is always finite.
B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation
(2021-01)
Saiful Anuar, Hanis Safirah Binti
In this study, the Coupled Nonlinear Schrödinger Equation (CNLSE) which models the propagation of light waves in optical fiber is solved using numerical methods namely Finite Difference Method (FDM) and B-Spline collocation methods. The equation was discretized in space and time. We propose the discretization of the nonlinear terms in the CNLSE following the Taylor approach and a newly developed approach called Besse. The theta-weighted method is used to generalize the scheme whereby the Crank-Nicolson scheme (i.e θ = 0.5) is chosen. The time derivatives are discretized by forward difference approximation. For each approach, the space dimension is then discretized by five different collocation methods independently. The first method for Taylor approach is based on FDM whereby the space derivatives are replaced by central difference approximation.
Rivulet Flows And Flows Around Dry Patches On An Inclined Plane
(2021-11)
Nurul Ainina Binti Redwan
This thesis presents a study on the thin-film flows of Newtonian and non-Newtonian power-law fluids on an inclined plane. Specifically, flow of slender rivulet and flow around slender dry patch are considered. The gravity or shear stress at the free surface drives the flow in the case of strong surfacetension effects.
Hierarchical Gaussian Process Models For Loss Reserving
(2021-12)
Ang,Zi Qing
Loss reserving is one of the main activities of actuaries in the insurance industry and is done to ensure the financial health of companies as well as protecting consumers’ interest. Techniques applied by the practitioners are highly regulated, but researchers are still ongoing in the pursuit of finding methods to improve predictive accuracy and to establish a measure of predictive uncertainties. Diverting from the link ratio methods, researchers have experimented with parametric models such as growth-curve models and models involving dynamical systems, as well as nonparametric models. Researchers in this field have increasingly shown interests in utilizing Bayesian methods to measure predictive uncertainties.
New Traveling Wave Solutions For Some Nonlinear Fractional Differential Equations By Extensions Of Basic
(2022-02)
Ali Al-Shawba, Altaf Abdulkarem
Due to varied and important applications of nonlinear fractional differential equations in real world problems, it is often required to construct their exact analytical solutions. With the help of exact analytical solutions, if they exist, the modelled phenomena can be better understood. Generally, an important class of solutions of nonlinear evolution equations (EEs) is their travelling wave solutions.
On Some Properties Of 0-Expansions Of Real Numbers Related To Regular Continued Fraction Expansion
(2022-02)
Muhammad, Khairun Nisak
This introductory chapter discusses background study of continued fraction expansions of real numbers which highlights the development of various types of continued fraction expansions. Apart from the regular continued fractions, this chapter also reviews some other variants of it such as optimal continued fraction (OCF) (Bosma, 1987), nearest integer continued fraction (NICF) (Tong, 1992), Engel continued fraction (ECF) (Hartono et al., 2002),
Development Of Variable Sampling Interval Run Sum T Chart And Triple Sampling X ̅ Chart With Estimated Process Parameters
(2022-03)
Nahar Mim, Faijun
The Shewhart x ̅ control chart is a useful chart in process monitoring. However, the Shewhart x ̅ chart’s performance is significantly affected if the process standard deviation is erroneously estimated. To circumvent this problem, the t chart is commonly used as an alternative to the Shewhart x ̅ chart. The first and second objectives of this thesis aim at enhancing the performance of the basic t chart by proposing the variable sampling interval run sum (VSI RS) t charts for monitoring the mean of a process from a normal distribution, based on known and estimated process mean, respectively. The Markov chain technique is used to compute the optimal parameters for the new charts.
Model Building And Forecasting Of Climate Data For Tourism Area In Bangladesh
(2022-06)
Hossen, Sayed Mohibul
Climatic variables such as temperature, rainfall, and humidity affect the choice of destination and the distribution pattern of tourists in different seasons. So, the main objective of this research is to modelling and forecasting the climatic variable of different tourist spots. More specifically, to examine the impact of seasonality on tourist’s arrival and income from tourism that contributes to the national economy of Bangladesh. Wherein, the effect of these climatic variables was assessed using the SANCOVA modelling framework modified by the ANCOVA model, to explain the current contribution of climate change on GDP. SARIMA model was applied for modelling at seven attractive sightseeing diverse places in Bangladesh and forecast up to the year 2050. From the analysis, we have found that the maximum and minimum temperature is slightly increasing at approximately 10C but decreasing approximately 20C. In July, rainfall amounts to 800 mm (31.5 in) in Sylhet, to 750 mm (29.5 in) in Chittagong, to 900 mm (35.5 in) in Cox's Bazar. Visitors belonging to low humidity countries can travel to Bangladesh in the rainy season, and from high humidity countries can discover all year-round. In the analysis, we found that seasonality has 91% effect on tourist’s arrival in Bangladesh and recommends that, if tourist’s arrival will increase thousand per season, then income will increase on average by 0.527 million Taka per season. Also, if expenditure for tourism development will increase 0.1 million Taka per year, then income will increase 0.181 million Taka every season.
Hybridization Model For Capturing Long Memory And Volatility Of Brent Crude Oil Price Data
(2022-07)
Al-Gounmeein, Remal Shaher Hussien
The Brent crude oil price indices are typically nonlinear, nonstationary, and non-normal behavior with a long memory and high heteroscedasticity; hence, capturing the controlling properties of their changes is difficult. Subsequently, these phenomena weaken the validity and the accuracy of the result of the forecasting methods. Therefore, this study focuses on the hybridization method to capture long memory behavior and heteroscedasticity in the dataset and improve Brent crude oil price forecasting accuracy. Recently, the hybridization method for the autoregressive fractionally integrated moving average (ARFIMA) model has been introduced as an effective technique for overcoming the nonlinear, nonstationary, and non-normal behavior with high heteroscedasticity in a time series dataset. ARFIMA hybridization method presents several characteristics that other traditional methods do not have. Thus, this thesis proposed three new models and employed 12 different techniques based on combining and hybridizing the ARFIMA model with traditional forecasting techniques to forecast the Brent crude oil price. The three new models, namely, ARFIMA with the asymmetric power autoregressive conditional heteroscedasticity (ARFIMA-APARCH), ARFIMA with the Glosten, Jagannathan, and Runkle generalized autoregressive conditional heteroscedasticity (ARFIMA-GJRGARCH), and ARFIMA with the component standard GARCH (ARFIMA-csGARCH) are proposed. This proposal aims to obtain improved forecasting results and solve the forecasting inaccuracy problem in oil price series.
On The Solvability Of Some Diophantine Equations Of The Form ax+by = z2
(2022-07)
Amr Moustafa Mohamed Aly, Elsayed Elshahed
The Diophantine equation ax+py = z2 where p is prime is widely studied by many mathematicians. Solving equations of this type often include Catalan’s conjecture in the process of proving these equations. Here, we study the non-negative integer solutions for some Diophantine equations of such family. We will use Mihailescu’s theorem (which is the proof of Catalan’s conjecture) and elementary methods to solve the Diophantine equations 16x −7y = z2, 16x − py = z2 and 64x − py = z2, then we will study a generalization where (4n)x − py = z2 and x, y, z,n are non-negative integers. By using Mihailescu’s theorem and a fundamental approach in the theory of numbers, namely the theory of congruence, we will determine the solution of the Diophantine equations 7x+11y = z2, 13x+17y = z2, 15x+17y = z2 and 2x+257y = z2 where x, y and z are non-negative integers. Also, we will prove that for any non-negative integer n, all non-negative integer solutions of the Diophantine equation 11n8x+11y = z2 are of the form (x, y, z) = (1,n,3(11) n2 ) where n is even, and has no solution when n is odd. Finally, we will concentrate on finding the solutions of the Diophantine equation 3x+ pmny = z2 where y = 1,2 and p > 3 a prime number.
Topological Data Analysis Via Unsupervised Machine Learning For Recognizing Atmospheric Rivers Conditions On Flood Detection
(2022-08)
Obi, Ohanuba Felix
Flooding is a natural disaster that annually destroys buildings, farmland, properties, and life in many regions of the world. Less than two decades ago, Topological data analysis (TDA) and machine learning (ML) were used in predictions, which have advantages over the common method. Thus, the present work introduces a hybrid method of TDA and unsupervised ML (TDA-uML) for flood management. The TDA-uML blends topological algebra with computer science to become a new study area in statistics, handling shapes in big data. Three properties make TDA distinct from common methods; they are coordinate invariance, deformation invariance, and compressed representation. The method involves training, testing, computation, obtaining of optimal values and validation of optimal value. Some common flood management models such as Hydrologic, hydraulic, and statistical models that researchers had used are inaccurate in the prediction, costly, lack the implementation of hybrid models, and are not validated compared to the TDA-uML method. The technique is aimed at developing a hybrid method of TDA-uML for flood prediction; evaluating the accuracy of the hybrid method (TDA-uML) in predicting flood, choosing the best validity tests for the study, and determining whether there is a relationship in the feature patterns.
Evaluating The Effectiveness Of Monetary Versus Fiscal Policies In Malaysia Using Macroeconometric Approaches
(2022-09)
Ismail, Siti Fatimah
The purpose of this thesis is to examine the roles of monetary and fiscal policies in achieving Malaysia's basic macroeconomic goals of price stability and long-term growth. This thesis is divided into two main parts. The first part employs nonlinear modelling techniques to investigate the nonlinear effect of policy stances on GDP growth and inflation using Malaysian data from 1980Q1 to 2018Q1. The results of the STAR and TAR approaches reveal the existence of a nonlinear relationship. The results show that no single policy tool can lead to the policy objectives of high GDP growth and low inflation at once. Both STAR and TAR results evident that the fiscal tools of government expenditure, current account balance and debt are harmful to the economic growth and the impact on inflation is either negative or not significant. In terms of monetary policy, the policy rate is a less effective tool to stimulate GDP growth but is a better option to control or reduce inflation. Meanwhile, real effective exchange rate encourages GDP growth but it does not influence price level significantly. The STAR model is a preferred model in capturing the gradual threshold adjustment in economic variables. In the second part of the analysis, a macroeconometric model is developed to evaluate the performance of Malaysia's monetary and fiscal policies as well as to project different economic outcomes and scenarios through numerical simulations.

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