PhD
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/50
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Study of Cosmic Acceleration and Thermodynamic Consequences in Alternative Theories of Gravity(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Ayesha Iqbal; FA14-PMATH-002; LHR TP 7450; Dr. Abdul JawadIn this thesis, we discuss two interesting issues: the accelerated expansion of the universe and thermodynamics. We consider flat Friedmann-Robertson-Walker universe model in alternative theories of gravity like loop quantum cosmology, Dvali- Gabadaze-Porrati brane world and fractal universe. We use different models of dark energy like Ricci Gauss-Bonnet dark energy and some latest holographic dark energy models namely Tsallis, Renyi and Sharma-Mittal holographic dark energy models for the analysis of both issues. For accelerated expansion of the universe, we examine the cosmological parameters like effective equation of state parameter, deceleration parameter, statefinder parameters, Om-diagnostic, plane of effective equation of state parameter with its evolutionary parameter and squared speed of sound parameter. We investigate the validity of the generalized second law of thermodynamics and thermodynamical equilibrium for the case of thermodynamic analysis. Firstly, we consider loop quantum cosmology and fractal universe in flat FRW universe with an interacting scenario between a non-canonical scalar field model of dark energy and dark matter. We make the analysis by using constant and variable (CPL parametrization) forms of equation of state parameters. We discuss the deceleration parameter for expansion rate along with squared speed of sound for stability analysis. Taking Bekenstein, logarithmic and power law entropies as the horizon entropy, we examine generalized second law of thermodynamics and thermal equilibrium. Secondly, we study the cosmological implications using Tsallis, Renyi and Sharma- Mittal holographic dark energy models in the interacting framework. We take into account two theories, fractal and Dvali-Gabadaze-Porrati brane world. We discuss the cosmological parameters and planes in both theories for the evolving universe. Finally, we examine the validity of generalized second law of thermodynamics of a physical system enveloped by apparent as well as event horizons. The system is comprised of Ricci Gauss-Bonnet dark energy and dark matter. We use various forms of entropy namely Bekenstein, Renyi, logarithmic and power law entropy corrections. We also examine the thermodynamic equilibrium in case of each entropy.Item Algebraic Characteristics of Graphs(Library Information Services COMSATS University Islamabad Lahore Campus, 2020) Muhammad Asim Razzaq; FA13-PMATH-004; LHR TP 7454; Dr. Kashif AliGraph theory is a vital and special branch of discrete mathematics. It deals with geometric computational study of various objects. The main component and object of the theory is graph and its generalization approach. Therefore, it has vast application to other mathematical and provides computational assistance to non-mathematical sciences. The most prominent use of graph theory as a significant tool in chemistry, this branch is named as chemical graph theory. It provides helpful assistance for obtaining molecular descriptor to develop essential relationship between molecular graphs and chemical compounds. Graph theory also serves its specialization in algebraic graph theory specifically labellings. In this dissertation, we formulate and discuss all these types of indices. We develop a new approach to calculate the eccentricities of vertices of any graph by using computer aid softwares. This approach help us to find the exact expression of the ECI and ABC5 for the butterfly, bene and torodial grid graphs. We also express a new type of counting polynomial associated with the previous counting polynomials. Moreover, we work some topological indices relative to degree dependent on generalized subdivision of line graphs. We also determine the general results about subdivision of line graphs for neighborhood valency-based indices. We also discuss the stability of line graph of chemical molecules.”Line0graphs furnish0a tool for0studying the0topological properties of0alpha-systems.”In addition to this, we study four important counting polynomials called omega, theta, PI and Sadhana for V-Phenylenic. We also introduced a new polynomial Upsilon on the basis of ”co” relation and find new results relative to new counting polynomial.”We also determine that inertia indices for V-phenylenic nanotube and these indices are not0equal for the line0graph of V-phenylenic0nanotube. We also find that the0nullity for this0nanotube and of line0graph of these0nanotube.”Lastly, we also discuss H-group magic labellings of some graphs. We mainly study about the H-groupmagic0total graph0labelings G(v; e) over finite0abelian0group Zt Zv, where H =K2; Ct and e = (t 1)v:Item Generalizations of Cyclic Refinements of Jensen’s Inequalities(Library Information Services COMSATS University Islamabad Lahore Campus, 2020) Nasir Mehmood; FA14-PMATH-005; LHR TP 7451; Dr. Saad Ihsan ButtIn recent years, the concept of convex functions has been generalized extensively. Applications of convex functions are widely seen in many areas of modern analysis. Convex functions also have significant relation with the theory of inequalities and many useful inequalities are the result of the applications of convex functions. The Jensen's inequality has tremendous implications in many fields of modern analysis. It helps computing useful upper bounds for several entropic measures used in information theory. We consider discrete and continuous cyclic refinements of Jensen's inequality and extend them from convex to higher order convex function by using new Green functions introduced by us and employing different interpolating polynomials and identities. We formulate monotonicity of the linear functionals for nconvex functions at a point. We calculate some new Grüss and Ostrowski type bounds. As an application of our obtained results we give new bounds for Shannon, Relative and Zipf-Mandelbrot entropies.Item Predictive Modeling of Diabetes Classification using Artificial Neural Networks(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Muhammad Amin; FA23-RMT-017; Dr. Muhammad Rafiullah; LHR TP 9764Diabetes mellitus is a chronic disease that has become a major global public health challenge. Timely and accurate prediction not only aids in immediate treatment but also plays a crucial role in formulating effective strategies. In this research, we compare the prediction of diabetes using two popular neural network models Multi-Layer Perceptron (MLP) and General Regression Neural Network (GRNN). This analysis is based on the PIMA Indian Diabetes Dataset, which contains medical information of female patients, including glucose levels, BMI, insulin amount, age, etc. In this research, the dataset underwent stages of cleaning, normalization, and division into training and testing sets. Then, the mathematical details of the MLP and GRNN models were described, which included forward propagation, activation functions, and loss formulas. The MLP model used two hidden layers with ReLU and Sigmoid activation functions, while the GRNN model used Gaussian radial basis functions and Euclidean distance. After training, the performance of both models was evaluated using metrics such as accuracy, confusion matrix, and ROC-AUC, revealing that both models proved effective in predicting diabetes. However, GRNN demonstrated better overall performance due to its non-repetitive structure and smooth results, while MLP exhibited more effective adaptation thanks to fast computation and deep network architecture, making it suitable for large and complex data. This research indicates that if ANN models are designed and configured correctly, they can help in the timely and effective diagnosis of diabetes. This analysis provides guidance to healthcare professionals and data scientists in selecting appropriate models.Item A Computational Investigation of Fluid and Air Bubble Dynamics in Two-Phase Flow(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Shamsul Jahan Shamsa (FA23-RMT-038); Dr. Mohsan Hassan; LHR TP 9783This work investigates heat transfer in two–phase flow of Newtonian fluid (water bubbles) and power-law non-Newtonian fluid (carboxymethylcellulose) in a L-shaped pipe geometry. The problem is simulated using Computational Fluid Dynamics (CFD) techniques, specifically the Level Set interface tracking method. Focusing on pressure, velocity and temperature distributions under different flow conditions, the research addresses challenges related to computing efficiency, numerical stability, and interface dynamics. These findings lay a foundation for optimizing fluid system by illustrating how flow parameters affect phase interactions and pressure gradients.Item Mathematical Modeling and Stability Analysis of Monkey Pox Transmission in Rodents and Humans(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Aqsa Shehzaadi; FA23-RMT-006; Dr. Yousaf Bhatti; LHR TP 9754In this thesis, deterministic and stochastic mathematical models for the dynamics of monkey pox transmission across rodent and human populations are developed and analyzed. The study builds systems of nonlinear differential equations to describe disease progression and control strategies, such as vaccination and treatment, using compartmental modeling techniques like SIR and SEIR. Important epidemiological characteristics like interspecies transmission, disease-induced mortality, and incubation times are included in the models. To evaluate the stability of endemic and disease-free equilibria, analytical techniques such as basic reproduction number (R₀) analysis and Jacobian matrices are used. Moreover, random environmental and demographic perturbations are taken into account via stochastic differential equations, and stochastic Euler, Runge-Kutta, and NSFD methods are employed for numerical simulations. The results demonstrate the importance of intervention tactics in lowering the incidence of monkey pox and the usefulness of stochastic modeling in comprehending intricate epidemic dynamics in the face of uncertainty.