Browsing by Author "Dr. Adeel Farooq"

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Analysing Security of Pseudorandom Sequences under Computational Constraints
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Amna Nazir; CIIT/SP20-RMT-037/LHR; Dr. Adeel Farooq; LHR TP 7657
In this thesis, we evaluated Pseudo Random Number Generators (PRNGs) on the basis of a test called Next Bit Test (NBT). To see if a PRNG is suitable for specific purpose, we tested it to see the results. On testing various PRNGs, we got different results that are being discussed in detail. On the basis of our analysis on different PRNGs, we recommend the Logged Fibonacci generator extended to the subtract and borrow generator that holds the properties of NBT and is acceptable to be used in cryptography.
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
Certain Results on m-polar Fuzzy Groups
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Musawwar Hussain; FA18-RMT-015; LHR TP 6455; Dr. Adeel Farooq
In this thesis we have developed some fundamental results from group theory to fuzzy and m-polar fuzzy groups. We have defined some basic characteristics of fuzzy groups and have provided the m-polar fuzzy analogues of fuzzy subsets, groups, level sets, and cosets. We have investigated an equivalence relation to distinguish whether a m-polar fuzzy subgroup of a group G is equivalent to any other m-polar fuzzy subgroup of that same group G, or not. We determined the maximal chains and a general formula for quaternion and dihedral groups to give the cardinality of their fuzzy and m-polar fuzzy subgroups. We intro duced aninequality which gives quantitative relationship between maximal chains, level subgroups and fuzzy subgroups. Moreover, we mainly constructed the m-polar fuzzy analogues of isomorphism theorems and butterfly lemma.
Comparison of Machine Learning Based Prediction Techniques for Diagnosis of chronic Kidney Diseases
(Library Information Services COMSATS University Lahore Campus, 2024-03-14) Amina Yasin; FA22-RMT-026; Dr. Adeel Farooq; LHR TP 9352
Comparison of Machine Learning Based Prediction Techniques for Diagnosis of chronic Kidney Diseases
Consensus Based Group Decision Making With Incomplete Reciprocal Fuzzy Preference Relations Using Product T-norm.
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Mustanser Hussain; FA17-RMT-035; Dr. Adeel Farooq; LHR TP 5661
In this dissertation, a consensus-based method for group decision making (GDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the complete fuzzy preference relation (FPR). Then it is confirmed to be product consistent by using the transitive closure formula. Following this, weights of decision makers (DMs) are evaluated by merging consistency weights and predefined priority weights (if any). The consistency weights for the DMs are estimated through product consistency investigation of the information provided by each DM. The consensus process determines whether the selection procedure should be initiated or not. The hybrid comprises of a quitting process and feedback mechanism, and is used to enhance the consensus level amongst DMs in case of an inadequate state. The quitting process arises when some DMs decided to leave the course, and is common in GDM while dealing with a large number of alternatives. The feedback mechanism is the main novelty of the proposed technique which helps the DMs to improve their given preferences based on this consistency. At the end, a numerical example is deliberated to measure the efficiency and applicability of the proposed method after the comparison with some existing models under the same assumptions. The results show that proposed method can offer useful comprehension into the GDM process. ix
Differentiation and the Maximal Operators
(Library Information Services, CUI Lahore, 2023) Hamza Sani; FA21-PMT-107; Dr. Adeel Farooq
We present an overview of certain maximal operators: the Hardy-Littlewood maximal op- erator and the dyadic maximal operator. We show that the two maximal operators are essentially the same. We study their weak type and strong type boundedness. We then use the weak type bounds of the Hardy-Littlewood maximal operator as a tool to differentiate integrals on dimensions higher than 1. Finally, we then study some construction of the dyadic systems in R
Fractal geometry
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Madiha Iftikhar; SP21-BSM-015; Dr. Adeel Farooq; LHR TP 9884
Fractal geometry explores the complex, self-replicating structures found in mathematical, natural, and computational systems. Originating from the foundational work of Benoˆıt B. Mandelbrot, fractals represent shapes exhibiting self-similarity across scales and fractional dimensions. This study delves into key mathematical constructs like the Cantor set, Koch curve, Mandelbrot set, and Julia sets, showcasing their recursive nature and infinite com plexity. The research emphasizes the significance of fractals in modeling natural phenom ena, including coastlines, mountain ranges, and biological patterns, and highlights their transformative applications in computer graphics, medical imaging, and economic analy sis. The iterative methodologies and Hausdorff dimension analysis offer a framework to describe and simulate intricate, real-world patterns. By bridging theoretical and practical realms, fractal geometry not only enriches mathematical theory but also provides innova tive tools for scientific and artistic endeavors
Geometry of Manifolds and the Gauss-Bonnet Theorem
(Library Information Services, CUI Lahore, 2024) Ayodeji Simeon Farominiyi; CIIT/FA21-RMT-108/LHR; Dr. Adeel Farooq
This thesis delves into the fascinating realm of smooth manifolds, investigating their intri- cate geometry through a comprehensive exploration of tangent spaces, connections, curva- ture and the Gauss-Bonnet theorem, a crucial result in the theory of surfaces. This theorem establishes a connection between a surface’s geometric and topological properties and acts as a model for similar statements that hold true in higher-dimensional contexts. The study is organized into three chapters, each addressing key aspects of this subject and culminating with an illustrative example featuring the sphere.Chapter 1 serves as an introduction to the theory of differential manifolds. It begins with a comprehensive overview of the underlying concepts, including topological spaces, charts, atlases, and smooth maps. The chapter provides a detailed examination of tangent spaces and tangent bundles, shedding light on the notion of derivatives and directional derivatives on manifolds. Vector fields and vector bundles are then introduced, enabling a deeper understanding of the interplay between smooth functions and smooth vector fields. The chapter, after the introduction of tensor products, also explores the concept of a Rie- mannian metric, highlighting its significance in defining lengths, angles, and inner products on manifolds. Additionally, differentiable forms are discussed, unveiling their role in cap- turing the geometric properties of manifolds.
Integration of Machine Learing Algorithms for Early Detection and Diagnosis of Brain Turnor
(2023-03-13) Muhammad Salman Azeem; FA22-RMT-002; Dr. Adeel Farooq; LHR TP 9365
Integration of Machine Learing Algorithms for Early Detection and Diagnosis of Brain Turnor
Locating some Subgroups of the Baby Monster Group
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2022) Abdul Sattar; FA19-RMT-029; LHR TP 7907; Dr. Adeel Farooq
In this thesis, we have computed the generators for some subgroup of Y-Groups. These are the subgroups of the bimonster group whose generators satisfy the coxeter relations. It can be presented by Y-diagrams whose nodes represent the generators and satisfy the coxeter relations. We have computed the coxeter generators satisfying coxeter relations for Y111, Y211, Y411, Y421 and Y441. The generators of Y-group have been determined by computing successive centralizers. We have also surveyed some maximal subgroups of the Baby Monster Group.
Machine Learning: Modern Techniques and Mathematical Approach to Neural Networks
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Sardar Abdul Wahab CH (FA20-BSM-012) : Abdul Raheem (SP20-BSM-003); Dr. Adeel Farooq; LHR TP 9911
This thesis explores the mathematical foundations of machine learning algorithms, providing a comprehensive exploration of various key techniques and models. It covers fundamental concepts and methodologies in regression, classification, support vector machines (SVM), decision trees, neural networks, and perceptrons. Each of these algorithms is analyzed in terms of their mathematical underpinnings, operational mechanisms, and practical applications. The study aims to elucidate the core principles that drive these algorithms, offering insights into their theoretical and practical aspects. By understanding the mathematics behind these models, this research contributes to a deeper appreciation and effective utilization of machine learning techniques in solving complex real-world problems.
Neural Network Based Classifier for Some Permutation Groups
(Library Information Services COMSATS University Lahore Campus, 2023-03-13) Fiaz Ahmad; SP22-RMT-029; Dr. Adeel Farooq; LHR TP 8732
This thesis explores the membership problem within the Symmetric group, specifi cally focusing on determining whether a randomly generated permutation in Symmetric group Sn is a member of Sn . For computational convenience, the study centers on the case where n=5, employing a Neural Network implemented in the Python programming language. Initially, a single perceptron with one neuron was developed. After multiple itera tions of the neural network, accuracy levels ranging from 60% to 85% were achieved. Subsequently, the investigation advanced to a multi-layered neural network. Utilizing this sophisticated architecture, the model was trained to identify the nature of specific permutations, distinguishing between even or odd permutations and determining their membership in S5 . The desired accuracy levels were successfully reached by varying the amounts of data used in the training process.
Norton’s Presentation of the Monster
(Library Information Services COMSATS University Islamabad Lahore Campus, 2025) Syeda Hira Fatima FA23-RMT-052; Dr. Adeel Farooq; LHR TP 9795
In this thesis we have constructed generators for Qx0 = 21+24 + is normal subgroup of the centralizer of the 2B class in the Monster group. We have labeled Y555 identifying each node as a point or a line. Moreover, we have also labeled the projective plane of order 3. We have used the package mmgroup for computations and verifications. Module bimm within this package is used for studying the Norton’s presentation of the Monster.
On the Structure of Unitary Units of F3mC9 and F3m(C3 ×C3)
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) NAJAM UL ABBAS; CIIT/FA17-RMT-038/LHR; Dr. Adeel Farooq; LHR TP 5663
In this thesis, we have constructed the group ring matrix of group algebras F3mC9 and F3m(C3 ×C3). We have found center of group algebras F3mC9 and F3m(C3 ×C3). On the basis of group ring matrix, the center of unitary unit group have been established and then order of unitary unit group has been computed. We have also studied the above group algebras for m = 1 computationally using the GAP package LAGUNA. The orders of normalized unit groups, unitary unitary group and unit group has been computed. Moreover, Augmented Ideals of the above group algebras has been studied and we have provided their basis.
The Fuzzy N-Leibniz Algebras
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Anjum Ali Sher; SP19-RMT-026; Dr. Adeel Farooq; LHR TP 7347
In this thesis we have shown that, 1. The (m + 1)-Leibniz algebras are expressible in the form of m-magma. 2. The homomorphic pre-image of a fuzzy ideal of a m-Leibniz algebra is a fuzzy ideal. 3. If S a fuzzy subset of a m-Leibniz algebra A then, (i) S is either a fuzzy subalgebra or a fuzzy ideal of A, (ii) Every nonempty t-level subset U(s, t) is also a fuzzy subalgebra or ideal of A. 4. Homomorphic image of the fuzzy ideal of a m-Leibniz algebra having the supre- mum property is also a fuzzy Leibniz ideal. 5. If A is a m-Leibniz algebra then the maximal normal fuzzy subalgebra of A is a Boolean algebra.
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 7620
In 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.