Department of Mathematics
Permanent URI for this communityhttps://repository.cuilahore.edu.pk/handle/123456789/21
Browse
47 results
Search Results
Item Words for generators of some subgroups of the Baby Monster group(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Hafiz Sami Ullah; CIIT/FA19-RMT-110/LHR; Dr. Adeel Farooq; LHR TP 7620In this thesis we have computed the generators for some subgroups of the Baby monster group B[1], which is the second largest group in sporadic simple groups. Here we have S10 < S8(2) < Fi23 < B. To compute the generators for the subgroups of Baby Monster group we have used two softwares namely GAP and MeatAxe. Also we have computed the coxeter generators[2] satisfying coxeter relations for Y311, Y221, Y321, Y421, Y331, Y431, Y222, Y322, Y422, Y332 and Y432. Finally, we have expressed all the coxeter generators in terms of generators of Fi23 inside the Baby Monster monster group B.Item Extension of Isotropic Solutions into Anisotropic Domain Via Gravitational Decoupling Approach(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) MOBEEN AMIN; CIIT/FA19-RMT-048/LHR; Dr. Muhammad Zubair; LHR TP 7437In this thesis, we study known charged and uncharged isotropic Heintzmann solution and Durgapal IV solution and extend it to its well anisotropic domain by manipulating gravitational decoupling through extended geometric defor- mation (EGD) approach. We employ linear transformation on both metric po- tentials and convert the single set of EFEs into two less-complicated subsys- tems. The first one is related to the standard Einstein-Maxwell field equations (EFEs), while the other one is related to additional source. The matching con- ditions at the stellar surface are discussed in detail, where outer geometry is represented by Reissner-Nordstrom solution in the presence and schwarzschild solution in the absence of charge and also evaluate the expressions for ther- modynamical quantities ρtot, ptot r and ptot t using mimic constraint and equation of state (EoS).We discuss the physical properties of the stellar model. Physical analysis is carried out using different physical indicators i.e, energy conditions, equilibrium equation, casualty condition, Herrera’s cracking concept, adiabatic index, compactness and surface redshift. In order to check the viability of the anisotropic version of the solution, we consider three different realistic stars, namely SAXJ1808.4 − 3652, SMCX − 4 and PSRJ1614 − 2230, and analyze the behavior of the model against different values of intensity parameter, i.e., γ = 0, 0.2 and 0.3 and also evaluate the graphical behavior of compact star PSRJ1614 − 2230 against different values of γ = 0.25, 0.55 and 0.75 for different model.Item Computational Invariants of Some Chemical Structures(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Abdur Rehman Hashmi; CIIT/FA19-RMT-004/LHR; Dr. Kashif Ali; LHR TP 7435In this study we will focus on computational invariants of different structures of chemical graphs. We will focus on the bond additive invariant, new bond additive invariant especially Mostar invariant, edge Mostar invariant and Total Mostar invariants of some graphs like Hydrogen Depleted molecular graph of Vulcanized Rubber and Poly-Methyl Methacrylate(PMMA).Item Comparative Study of Different Fractional Operators on the Stochastic Diffusion Equation(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Rana Talha Ahmad; CIIT/FA19-RMT-021/LHR; Dr. Ayesha Sohail; LHR TP 7436In this work, we studied ecological model of fractional order prey-predator with Holling type II functional response and harvesting effect. Fractional Order Operators along with existence and uniqueness properties are defined. Finally, numerical simulations are performed to see the convergence of solutions with the help of Backward Euler’s method.Item Cosmic Expansion Phenomenon in Specific Scalar Field Theory(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Farwa Khurshid; CIIT/FA19-RMT-105/LHR; Dr. Shamaila Rani; LHR TP 7430The interaction of newly proposed holographic dark energy model, Bar- row holographic dark energy model is being used to analyze the cosmic expansion phenomenon. We consider the interaction between dark energy and dark matter in the realm of scalar field theory. For the power law, quadratic and quartic (positive and negative) potentials, we investigate the different cosmological implications. This includes the equation of state pa- rameter ωD which identifies different eras of the expanding universe, cosmic plane ωD − ω0 D (where ω0 D shows the evolution of equation of state para- meter ωD where prime shows derivative with respect to ln a) and squared speed of sound parameter v2 s for the stability analysis of the models.Item Barrow Holographic Dark Energy in Extended Teleparallel Theories of Gravity(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Ghulam Murtaza; CIIT/FA19-RMT-085/LHR; Dr. Shamaila Rani; LHR TP 7424In this thesis, we reconstruct some solutions in the context of telepar- allel based extended theories coupled with trace of energy-momentum ten- sor, boundary term and Gauss-Bonnet term. For this purpose, we ob- tain the effective energy density and pressure for these theories for flat FRW universe model. The reconstruction is made through the compari- son of these effective energy densities with the energy density of Barrow holographic dark energy model. In this regards, we use scale factor in terms of power-law form and find some gravitational Lagrangian functions as f(T ) = T +g(T ), f(T, τ ) = T +γh(τ ), f (T, τ ) = βτ +g(T ), f(T, TG) = TGg(T ), f(T, TG) = −T + TGg(T ), f(T, TG) = TG + g(T ), f(T, TG) = T + j(TG), f(T, B) = T + σy(B) and f(T, B) = B + ξg(T ). In order to discuss the cosmic analysis related to these models, we plot equation of state parameter for each model. We investigate the squared speed of sound parameter for these models to determine the stability of the models. We obtain some favorable results related to specific values of model parameters.Item Molecular Interpretation Of Indium Phosphate Using(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Waqar Asghar; FA19-RMT-061; Dr. Sana Javed; LHR TP 7403This study presents a molecular interpretation of indium phosphate using chemical graph theory and structural modeling approaches. Indium phosphate is analyzed at the molecular level by representing its atomic structure as a graph, where vertices correspond to atoms and edges correspond to chemical bonds. The research focuses on understanding the structural arrangement, bonding characteristics, and topological properties of the compound. Various molecular descriptors and topological indices are computed to capture the physicochemical behavior of the material. The study highlights how graph-theoretical techniques can be used to interpret the stability, reactivity, and electronic properties of indium phosphate, providing a mathematical framework for analyzing complex inorganic materials.Item On Spanning Simplicial Complexes Associated to Ladder Graph(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) MUHAMMAD AZIZ; CIIT/FA19-RMT-011/LHR; Dr. Hani Shaker; LHR TP 7427In this thesis, we are going to discuss the algebraic and combinatorial aspects of span- ning simplicial complex ∆s(G) associated with the simple connected graph G, namely Ladder graph Ln. We mainly emphasis the characterization of s(Ln), all spanning tree, of Ln. We intend to provide the algebraic and combinatorial characterization of SSC ∆s(Ln) associated with the ladder graph Ln. In particular, we compute the formula for the f -vector of the SSC associated with the ladder graph Ln.Item Hybrid Modeling Approach for the Forecasting of the Fibrilization Process and the Resulting AD(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Mudassar Fiaz; CIIT/FA19-RMT-112/LHR; Dr. Ayesha Sohail; LHR TP 7429Imaging has played a variety of roles in the study of Alzheimer disease (AD) over the past four decades. Initially, computed tomography (CT) and then magnetic resonance imaging (MRI) were used diagnostically to rule out other causes of dementia. More recently, a variety of imaging modalities including structural and functional MRI and positron emission tomography (PET) studies of cerebral metabolism with fluoro- deoxy-D-glucose (FDG) and amyloid tracers such as Pittsburgh Compound-B (PiB) have shown characteristic changes in the brains of patients with AD. These modalities and their particular utilities are discussed in this thesis. Machine learning and deep learning have demonstrated a wonderful performance in the classification task. Important progress has been made in image recognition, mainly due to the availability of large-scale annotated datasets and the revival of convolutional neural networks (CNNs). The aim of this study is to help the neurologists in selection of appropriate classification method based on several parameters like accuracy, computer complexity, and low training data availability. The challenge for the future will be to combine imaging biomarkers to most efficiently facilitate diagnosis, disease staging, and, most importantly, development of effective disease-modifying therapies.Item Reverse Degree Based Topological Indices of Chemical Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Tayyab Younas; CIIT/FA19-RMT-064/LHR; Dr. Muhammad Kamran Siddiqui; LHR TP 7428Graph theory is playing a key role in applied and pure mathematics. The scope of graph theory is expanding day by day. In this thesis, we have evaluated some reverse degree based topological indices, namely, the reverse general Randic index for ∝= 1, −1, 1 2 , − 1 2 , the reverse atom bond connectivity index, the reverse geometric arithmetic index, the reverse first and second Zagreb indices, the reverse first and second Zagreb co-indices, the reverse forgotten index, the reverse hyper Zagreb index, the reverse Balaban index, the reverse first and second multiple Zagreb indices, the reverse redefined first, second and third Zagreb indices for some chemical and lattices graphs like as Remdesivir, transition metal tetra cyano benzene organic network (𝑇𝑀 − 𝑇𝐶𝑁𝐵),metal organic superlattice and trans-Pd-(𝑁𝐻2)S lattice. My thesis comprising of five chapters. In the first chapter we will define some fundamental definitions. In the 2nd chapter, we will find reverse degree based topological indices for Remdesivir and transition metal tetra cyano benzene organic network (𝑇𝑀 − 𝑇𝐶𝑁𝐵). In the 3rd chapter, we will find reverse degree based topological indices for metal organic superlattice and trans-Pd-(𝑁𝐻2)S lattice. In the 4th chapter, we will present the conclusion of our thesis. In the 5th chapter, we will present the references of our thesis.