Mathematics
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- ItemNORMAL COMPOSITION OPERATORS ON SUB-HARDY SPACES(An-Najah National University, 2024-03-31) Sarsour, Doua
- ItemA COMPARISON OF NUMERICAL SOLUTIONS FOR ONE FREDHOLM INTEGRAL EQUATIONS SYSTEM OF THE SECOND KIND(An-Najah National University, 2025-02-06) Badrien, MohammedThe main goal of this work is to propose various numerical techniques for approximating the solution of a system of Fredholm integral equations of the second kind. The methods proposed involve the Chebyshev collocation method, the Haar wavelet method and the reconstruction of the variational iteration method. After reviewing the basic concepts of Fredholm integral equations and addressing the mathematical framework of these numerical methods, we provide some illustrative numerical examples with known exact solution to illustrate the effectiveness and the efficiency of these methods. Numerical results show clearly that Chebyshev collocation method is one of the most efficient method for solving system of Fredholm integral equations in comparison with its counterparts.
- ItemEXPLORING THE CAPACITY AND PERFORMANCE OF SUPERVISED LEARNING METHODS FOR LABEL CLASSIFICATION IN CAUSAL INFERENCE: A COMPARATIVE STUDY(An-Najah National University, 2024-08-08) Abu Saqer, OlaIn fact, discussions about machine learning are increasingly prevalent due to its accuracy in prediction and its ability to handle vast amounts of data. Furthermore, many relationships in life are causal, which motivates the efforts to comprehend the cause-and-effect relationships among variables. For instance, understanding the extent of the effect of a particular medicine on an individual with an illness becomes crucial. While it might seem straightforward at first glance, a deeper examination tell the complexity inherent in such endeavors when using machine learning in causality. Machine learning methods have made a valuable contribution to the field of causal inference because unlike traditional approaches, machine learning methods offer greater flexibility in estimating causal effects, since machine learning techniques do not require modelling hypotheses., yet there is still a research in estimation causal effect when both treatment and outcome are binary variables, because machine learning has proven its ability to predict, and prediction does not mean causality. Perhaps this is the challenge for machine learning in obtaining more accurate and less biased estimates of causal effects. This study conducts a comparative analysis of supervised learning methods for label classification in causal inference. We evaluate the performance and capacity of four techniques: Causal Forest (CF), Support Vector Machine (SVM), Generalized Linear Models (GLM), and Linear Probability Models (LPM) in estimating the causal effects for categorical response variable. In a randomized controlled trial simulation and real experiments were performed to evaluate the methods’ performance under varying conditions, by xi changing the main characteristics of the data including the sample size, and the number of the explanatory variables. We have focused on these four methods because of their specific advantages: Causal Forests are particularly adept at making causal inferences easily; Support Vector Ma chines are recognised for their effectiveness in binary classification tasks; Generalised Linear Models are well established as optimal for modelling the binary response vari able; and Linear Probability Models are used for their ability to provide predictions as probabilities. The results provide valuable insights into the strengths and limitations of each method in each scenario in the causal effects simulation study. Furthermore, the methods are able to detect heterogeneity in the real data results, and it was expected that SVM, GLM and LPM would detect more heterogeneity than Causal Forest. This thesis helps us to improve our knowledge of machine learning techniques in causal inference and emphasizes the importance of carefully evaluating their performance in real-world applications
- ItemNUMERICAL COMPARISON OF METHODS FOR SOLVING SECOND ORDER ODES(An-Najah National University, 2024-07-11) Ali, EkremaIn this study, two numerical methods for solving second order ODEs were tested, namely finite difference method and Runge _ Kutta method . The study aims to find out which of the two methods is more efficient and accurate. To obtain this result we solved one of the most important second order ODE, called damped harmonic oscillator equation. The result was that Runge _ Kutta method was more accurate and effective .
- ItemRADIUS OF CONVERGENCE FOR SOME (MULTIVARIABLE) HYPERGEOMETRIC FUNCTIONS(An-Najah National University, 2024-07-15) Kashou, LaythBackground: Hypergeometric functions are a class of special functions in mathematics that play a crucial role in various branches of science and engineering. Its importance lies in their versatility and their ability to represent a vast array of mathematical and physical phenomena. The key aspects that underscore their significance and applications include solutions to differential equations, solving Schrödinger's equation for various physical systems, studying complex integrals and contour integrals, solving problems involving electromagnetic fields and wave propagation in different media and they have applications in celestial mechanics for predicting the positions and orbits of celestial bodies. Aims: We have two main objectives. The first one is deriving new transformation formulas for the Kampé de Fériet function taking into account the radius of convergence of each transformation. While the other is developing alternative methods for determining the radius of convergence for well-known multivariable (double and triple) hypergeometric series. Methods: In this thesis, we will use Miller-Paris transformation formulas for generalized hypergeometric functions ${}_{r+1}F_{r+1}(z)$, ${}_{r+2}F_{r+1}(z)$ and its radii of convergence to derive new transformation formulas for the Kampé de Fériet function. Also, we will use Mathematica to develop an alternative method to calculate the radii of convergence for some well-known multivariable hypergeometric series. Results: While testing the Kampé de Fériet transformations we derived using various parameter values and variables within the radius of convergence on Mathematica, we found that the left-hand side and the right-hand side are equal for all tested cases. Also, when we try to calculate the radii of convergence for the selected well-known multivariable hypergeometric series by plotting them on Mathematica the results indicate that our findings are identical with the ones presented in Srivastava’s book.