Department of Mathematics
Permanent URI for this communityhttps://repository.cuilahore.edu.pk/handle/123456789/21
Browse
16 results
Search Results
Item 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 7657In 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.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 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 7347In 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.Item 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 5661In 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. ixItem Geometry of Manifolds and the Gauss-Bonnet Theorem(Library Information Services, CUI Lahore, 2024) Ayodeji Simeon Farominiyi; CIIT/FA21-RMT-108/LHR; Dr. Adeel FarooqThis 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.Item Differentiation and the Maximal Operators(Library Information Services, CUI Lahore, 2023) Hamza Sani; FA21-PMT-107; Dr. Adeel FarooqWe 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 RItem 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 9352Comparison of Machine Learning Based Prediction Techniques for Diagnosis of chronic Kidney DiseasesItem 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 9365Integration of Machine Learing Algorithms for Early Detection and Diagnosis of Brain TurnorItem 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 8732This 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.Item 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 FarooqIn 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.