M.Phil / MS

Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/52

This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.

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Using Cryptography and Steganography Techniques for Data Security
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Umm e Amara; CIIT/FA23-RMT-041/LHR; Dr. Tariq Javed Zia; LHR TP 10064
This thesis explores a hybrid security framework that integrates cryptographic and stegano- graphic techniques to enhance data security in digital communication. The proposed model combines the RSA encryption algorithm with XOR ciphering and Least Significant Bit (LSB) image steganography. To secure the data, it is first encrypted with both RSA and XOR operations. The resulting ciphertext is then hidden in a digital image by modifying the LSB’s of the image’s pixel data. The analysis focuses on three critical metrics: the amount of data that can be hidden (embedding capacity), the resulting fidelity of the carrier image (image quality), and the processing resources required (computational complexity). Experimental results demonstrate that 1-bit and 2-bit LSB methods provide an optimal balance between security, imperceptibility, and processing efficiency, while deeper em- bedding increases data capacity at the cost of visible distortion and higher computational overhead. Evaluation metrics such as PSNR, MSE, BER, and correlation analysis con- firm the effectiveness of the hybrid approach in securing data transmission with minimal perceptual degradation. The findings highlight the potential of combining cryptography and steganography for robust, multi-layered protection of sensitive information in modern communication systems.
Study of Stochastic Nonlinear Schr¨odinger Equation for Optical Soliton Solutions
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Iqra Anjum; CIIT/FA23-RMT-014/LHR; Dr. Syed Tahir Raza Rizvi; LHR TP 10063
It ﬁnds extensive application in the analysis of nonlinear systems for the detection of ap- proximate solutions and stability analysis. In order to understand nonlinear partial differ- ential equations (NLPDEs), physicists and mathematicians need to study exact solutions. Many NLPDEs such as Korteweg de Vries equation (KdV), Sin-Gordon equation, non- linear Schr¨odinger equation (NLSE), and other equations possess solitons solutions. A soliton, which arises as a result of dispersion and nonlinearity, is a wave that retain their original features while propagating from one medium to another. This thesis discusses the stochastic variants of the well-known non linear Kairat-II and Kairat-X (NLKIIKX) equa- tions in (3+1) space dimensions, those being soliton theory’s major models. Adding the Wiener process to simulate random ﬂuctuations, we study the dynamics of these equations within a probabilistic system. With enhanced direct algebraic technique (EDAT) and novel projective Ricatti equation approach (NPREA), we derive exact soliton solutions for these stochastic equations. The behavior of a stochastic differential equation (SDE) is fundamen- tally different from a deterministic equation due to the presence of randomness and gain an understanding about random ﬂuctuation-inﬂuenced complex system behavior. At last, by using these two methods, we shall develop three-dimensional and two-dimensional plots in order to show soliton solutions. It is used to simulate randomness-inﬂuenced systems, e.g., stock markets or noisy physical systems. We will also study the energy balance approch (EBA) which examines a system by comparing the rate of input and output energy to ﬁnd the steady-state or dynamic state.
Exploring Topological Indices for Magnesium Nitrogen via Curve Fitting Model
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Nida Ahsan (FA23-RMT-046); Dr. Muhammad Kamran Siddiqui; LHR TP 9789
The use of graph theory in many fields of study has increased significantly, especially in the field of chemical graph theory. Many scholars have been able to explore a range of new directions in the last few years. A chemical graph is a named graph in which the atoms of a compound are represented at the vertices, and the edges represent chemical bonds between atoms. Determining various physical and chemical properties of the molecular structures under study requires an examination of topological indices. Firstly, we focused on degree-based topological indices, namely the Randic´ index, atom bond connectivity in- dex, geometric arithmetic index, the first and the second Zagreb indices and co-indices, the first and the second multiple Zagreb indices and co-indices, hyper Zagreb index, for- gotten index, augmented Zagreb index, Balaban index, redefined Zagreb type indices, of Magnesium Nitrogen MgN4. Afterward, we found the physical measures like the heat of formation of Magnesium Nitrogen MgN4. Then, we fitted curves between different indices and the corresponding heat of formation. Curve fitting was done in MATLAB through different methods based on linearity and non-linearity. The performance of the method was tested using mean squared error (MSE), the sum of squared errors (SSE) or R2. Fur- ther, we gave graphical representations of these indices. These mathematical frameworks might provide a way to study the thermo dynamical properties of the chemical structure Magnesium Nitrogen MgN4
Optical Appearance of Kerr Black Hole Surrounded by Cold Dark Matter
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Sadia Aslam (/FA23-RMT-047); Dr. Rabia Saleem; LHR TP 9790
In this work, we provide graphical representation of shadow images of Kerr-like black hole (BH) in the presence of cold dark matter (CDM) halo illuminated with two different accre- tion ﬂow models. The impact of spin parameter a, critical density ρc and the scale radius Rs on the observed images of BHs is carefully addressed. The results indicate that as a in- creases, the circular orbits shifted towards the right, while the larger values of both ρc and Rs caused to enhance the radius of circular orbits of BH shadow. In the case of background light source, the impact of parameter ρc on shadow distortion is extremely negligible, but this inﬂuence is relatively small and becomes appreciable when the parameter Rs has larger values. Next, we expand the interior region of accretion disk to the BH event horizon, and consider the motion of particles inside and outside the regions of inner stable circular or- bit (ISCO). The results exhibit that the intensity as well as the radius of BH shadow are gradually increasing with the increase of both ρc and Rs. On the other hand, in the case of retrograde ﬂow, the intensity of the shadow images signiﬁcantly decreases and a crescent moon emerges in the top of the observer’s frame. Subsequently, we discuss the distinctive features of red-shift conﬁgurations for both prograde and retrograde ﬂows. The obtained results interpret that the conﬁguration of red-shifts and the visual signatures is associated to the behaviour of accreting ﬂow as well as with relevant parameters. Finally, using the recent observational data of EHT results, we found the shadow radius of Sgr A∗ provides the best-ﬁt parameter constraints as compared to M87∗.
Application of Finite Element Method in Structural Analysis of a Cantilever Beam with Varying Material Properties
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Noman Ijaz (FA23-RMT-03); Dr. M. Nauman Bashir; LHR TP 9776
The structural analysis of beam is a fundamental problem in engineering, particularly in the design and evaluation of load-bearing members. This thesis investigates the application of the Finite Element Method(FEM) to analyze the behavior of beams under various boundary and loading conditions, with a specific focus on cantilever beams subjected to uniformly distributed loads and varying material properties. A series of beam configuration including simply supported, clamped-clamped, cantilever, and beams with point of moment loads were modeled using Hermite shape functions to approximate displacement within each finite element. The numerical simulations were implemented to compute deflection, shear force, and bending moment diagrams, providing insight into the structural response of beams. The result obtained from FEM were consistent with classical beam theory, validating the effectiveness of the method for accurate structural prediction. The study also highlighted the material parameters into formulations, the work demonstrates how FEM can be adapted to more realistic structural conditions. This thesis not only confirms the readability of FEM for static beam problems but also establishes a strong foundation for future investigation into more complex and non-linear structural system.
Analysis of Certain Maximal Subgroups in the Monster
(Library Information Services COMSATS University Islamabad Lahore Campus, 2025) Samra Akram (FA23-RMT-036); Dr. Adeel Farooq; LHR TP 9782
The Conjugacy Class Fusions of maximal subgroups 112 : (5×2·A5), (PSL2(11)×PSL2(11)) : 4,72 : SL2(7),PSL2(19) : 2, and PSL2(13) : 2 of the Monster group are thoroughly examined in this thesis, which builds upon the seminal work of Heiko Dietrich, Melissa Lee, and Tomasz Popiel. We’ve provided fresh perspectives on the subgroup structure and fusion patterns of M by examining and analyzing their findings. ix
Study of Nonlocal Differential Equations
(Library Information Services COMSATS University Islamabad Lahore Campus, 2025) Syeda Zurriat Fatima Zaidi (fa23-rmt-039); Prof. Dr. Kashif Ali; LHR TP 9784
This thesis examines the theory, classification, and solution behavior of second-, third, and fourth-order nonlocal differential equations. Nonlocal differential equations, which are distinguished by the occurrence of terms involving integration or dependence on values of the unknown function over an interval or the whole domain, have attracted considerable attention because of their applications in mathematical physics, control theory, and continuum mechanics. We starts with a thorough examination of second-order nonlocal linear differential equations, their overall form, solution techniques, and stability behavior. This is then generalized to third-order nonlocal equations, where complexity increases through derivatives of order greater than one and increased functional dependence. Lastly, a complete framework is established for fourth-order nonlocal differential equations, giving homogeneous and nonhomogeneous cases with different nonlocal kernels. Every order is analyzed with example cases motivated by current literature, and closed-form solutions when possible are obtained. Existence, uniqueness, and qualitative solution behavior are also considered. The thesis adds to the general comprehension of higher-order nonlocal operators and gives one a single way of solving and analyzing these equations systematically
Applications of Extended Physics Informed Neural Network Method for Nonlinear Differential Equations
(Library Information Services COMSATS University Islamabad Lahore Campus, 2025) Muhammad Ismail (FA23-RMT-045); Dr. Syed Tahir Raza Rizvi; LHR TP 9788
Nonlinear partial differential equations featuring nonlinear terms occur in a number of engineering and physical problems, including reaction-diffusion processes, heat conduction, and population dynamics. Classical numerical techniques struggle to efficiently tackle high-dimensional problems and observe intricate nonlinear phenomena. Physics-Informed Neural Networks (PINNs) present a new opportunity in solving PDEs by incorporating physical boundary conditions inside the learning problem. Discontinuities, domain decomposition, and multi-scale phenomena, however, pose a problem to traditional PINNs. Extended PINNs (XPINNs) and conservative PINNs (cPINNs) have been proposed to overcome these drawbacks. In this thesis, we examine the use of PINN, XPINN, and cPINN in solving a reactiondiffusion equation with an exponential nonlinearity. We compare and examine their efficiency, accuracy, and stability in different parameter regimes. We will also examine the dynamics of mean square and absolute error in the given models. We will consider certain specific initial and boundary conditions to train the NN for governing model and will calculate the error of the equations by comparing the result extracted using PINN, cPINN and XPINN with the exact solution. With this, the results depict a sufficiently good agreement in the approximate solution of the governing model, the mean square error of which is of the order of 10−1 to 10−4 in the simulated equations. To the best of our knowledge, we apply this method to this model for the first time and the results are new and novel.
On Statistical Analysis of Topological Indices for Iron Disulfide Network
(Library Information Services COMSATS University Islamabad Lahore Campus, 2025) Saba Hanif (FA23-RMT-035); Dr. Muhammad Faisal Nadeem; LHR TP 9781
The use of graph theory in many fields of study has increased significantly, especially in the field of chemical graph theory. Many scholars have been able to explore a range of new directions in the last few years. A chemical graph is a named graph in which the atoms of a compound are represented at the vertices, and the edges represent chemical bonds between atoms. Determining various physical and chemical properties of the molecular structures under study requires an examination of topological indices. Firstly, we focused on degree-based topological indices, namely the Randic index, atom bond connectivity index, geometric arithmetic index, the first and the second Zagreb indices and co-indices, the first and the second multiple Zagreb indices and co-indices, the hyper Zagreb index, the forgotten index, the augmented Zagreb index, the Balaban index, and redefined Zagrebtype indices, of Iron Disulfide Network FeS2. Afterwards, we found the physical measures like heat of formation of the iron disulfide Network FeS2. Then, we fitted curves between different indices and corresponding heats of formation. Curve fitting was done in MATLAB through different methods based on linearity and non-linearity. The performance of the method was tested using mean squared error(MSE), the sum of squared errors, (SSE) or R2. Further, we gave graphical representations of these indices. These mathematical frameworks might provide a way to study the thermodynamical properties of the chemical structure Iron Disulfide NetworkFeS2
New Generalized Ostrowski, Simpson and Boole’s Type Inequalities
(Library Information Services COMSATS University Islamabad Lahore Campus, 2025) Muhammad Mehtab (FA23-RMT-028); Dr. Saad Ihsan Butt; LHR TP 9774
In this proposal firstly, we introduce a parametric identity for generalized differentiable functions using a generalized fractal-fractional integral operators. Based on this identity, we establish several variants of parameterized inequalities for functions whose local fractional derivatives in absolute value satisfy generalized convexity conditions. Furthermore, we demonstrate that our main results reduce to well-known Ostrowski and Simpson type inequalities by selecting suitable parameters. These inequalities contribute to finding tight bounds for various integrals over fractal spaces. By comparing the classical H¨older and Power mean inequalities with their new generalized versions, we show that the improved forms yield sharper and more refined upper bounds. In particular, we illustrate that the generalizations of H¨older and Power mean inequalities provide better results when applied to fractal integrals, with their tighter bounds supported by graphical representations. Finally, a series of applications are discussed, including generalized special means, generalized probability density functions and generalized quadrature formulas, which highlight the practical significance of the proposed results in fractal analysis.

M.Phil / MS

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