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Item Graph theory behind Sudoku(UMT Lahore, 2022-07-07) Hasnat AhmadThe objective of this project is to explore the mathematics of the issue of popular placement numbers, Sudoku, by means to help to comprehend clearly and fully. The Sudoku issue is in particular 9 to 9 grids in the first row and the first column of every single row and column with some cells containing 1 to 9 numbers. A Sudoku issue has 81 cells (or slots). The remaining grid spaces must be completed using the 1 to 9 numbers in each row or column to avoid the occurrence of a number more than once and a numeral inside any of the 3 blocks provided. When someone tries to respond to a Sudoku puzzle, a series of questions arise without even realizing what it is. Several instances are provided: Can I find out how to solve this problem if the problem exists? Is the solution unique, provided it exists? How many options may I choose if the answer is not unique? Furthermore, are all potential reactions to a problem that can systematically be followed? Having a definite solution, how many issues do you know? When a puzzle is constructed to ensure that every issue is answered in a unique manner, what is the very minimal number of entries possible? In order to respond to these exciting and thought-provoking issues, this project has been created.Item Einstein field equations(UMT Lahore, 2022-07-06) Saba YousafWe examine the kinematical structure of the common theory of relativity and the result of gravitational fields on bodily systems. The solid center of the theory, however, consists of Einstein’s field equations, which relate the metric field to matter. After a discussion of the objective sense of the curve tensor, we shall first give a simple physical inspiration for the field equations and will then show that they are strong-minded by only a few natural requirements.Item Resolvability in certain classes of homogeneous hypergraphs(UMT Lahore, 2022-04) Tuba NawazItem Cluster Project(UMT Lahore, 2022-07) MahnoorItem Bezier curve in 3D(UMT Lahore, 2022) Zara Jamil; Khola AftabThe objective of this undertaking was to make a 3D model of a certifiable model and prepare it into an import resource for be utilized for games and other displaying programming. Throughout recent years another industry has developed and created as the world's innovation turned out to be quicker, more remarkable and reasonable. This industry is 3D computer animation. Whether you watch motion pictures or TV, read magazines or papers, it is an interesting day when you don't see 3D PC pictures of some kind. 3D movement permitted the movies to look more reasonable and this innovation was embraced regardless of the way that making such a film is more enthusiastically. Character drawing is the initial step of 3D movement. To make a 3-deck model, the craftsman makes photos of characters according to however many viewpoints as could reasonably be expected. Almost similarly the person modeler involves earth or stone for making a genuine figure, he picks various strategies for cutting the cut model. The primary distinction is that on a virtual organization this is accomplished. The made undertaking for additional improvement of the model and study how this present reality can be moved to a game climate. Toward the end there ought to be a functioning 3D model resource for be utilized in ongoing tasks for game turn of events or further clean the model in a 3D displaying program. Animations is significant on the grounds that it empowers us to recount stories and express feelings and thoughts in a manner that is extraordinary to youngsters and grown-ups. It has basically been a method for making a wet, insightful story. Surprisingly realistic movies urge individuals to make biased focuses in light of a person entertainer's appearance and genuine character. Be that as it may, the person seems to be its own being as an enlivened person. The apparatuses utilized in this venture is Blender 3D displaying programming. The scene is created and the characters are moved by the illustrator who utilizes Blender to deliver the development deception by giving the underlying and the last places of the ideal moves. Along these lines, individuals need to see a daily existence like film. Obviously, it's one of the most widely recognized filmmaking modes.Item On convex multi-fuzzy sets and convex multi-fuzzy soft sets(UMT Lahore, 2022-08-04) Nabiha Hassan SamraIn this study, after given some fundamental definitions of multi-fuzzy sets and multi-fuzzy soft sets, we firstly define convex and concave multi-fuzzy sets. Then, by investigating their properties, we give some relations between convex and concave multi-fuzzy sets. Moreover, we define convex and concave multi-fuzzy soft sets and give some properties for the sets.Item Lorentz transformation and its application(UMT Lahore, 2022-07-01) Zubair Ikram; Saqlain Akram; Raazia Bushra; UsmanTreatments of the Lorentz transformation of special relativity at an undergraduate level usually assume that the motion of one observer is along the x-axis of another observer, resulting in the 2-4 dimensional Lorentz transformation group. The (1+n) dimensional Lorentz group for n=2 or n=3 is unknown to many physics students because of the simplified (1+1) dimensional treatments found in most texts. The aim of this article is to simplify the presentation of the Lorentz group to the point where the (1+n) dimensional Lorentz group can readily be presented to physics students in n space dimensions, where n is finite or infinite. The study of the Lorentz transformation group is simplified and generalized in this article, thus obtaining an elegant formalism to deal with the Lorentz group.Item Solution of Fractional Differential Equations via Fixed Point Theory(UMT Lahore, 2022) Shazia MuzaffarIn the existing study, we will define the criteria of existence of solution for relatively new variants of Caputo fractional differential equations and inclusion problems. In this work, we are given a boundary value problem involving Riemann–Liouville fractional differential equation of given specific order. We aim to explore the existence aspect of solutions related to a novel structure of integro-differential equation in Caputo sense equipped with integral boundary conditions in the Riemann–Liouville sense. To seek the results, we are using contractive mappings in the given boundary value problem. In this thesis, we are proving the inclusion boundary value problem in different definite orders to establish the result. The results that are used to prove and extend the new study are given for completeness. All the examples are provided regarding the results used in the manuscript. Moreover, numerical examples are given in order to confirm the final findings and are also illustrated.Item Solution of 𝜐 fractional differential equation with non local boundary values via fixed point theory(UMT Lahore, 2022) Fariha IrshadFractional calculus is a meaning of derivative to an integer of any order. The concept of fractional calculus caught the attention of many mathematicians who work on it. Fractional calculus is also known as fractional derivatives. Riemann and Caputo were the famous mathematicians who worked extensively on fractional derivatives. Riemann and Caputo are kinds of fractional derivatives. In 2018, E. Karapinar blended the Kannan fixed point theorem and interpolative theory. The idea was actually the rate of meeting to find fixed point results. In recent years, there have been many developments in finding fixed point results for the contraction used in set-valued mapping with some order. This work is introduced for the study of fractional derivatives of boundary value problems (BVPs), which consist of Riemann–Liouville and Caputo integro-differential equations with multiple nonlinear terms. In this work, we investigate the criteria of existence of solutions for Caputo fractional equations and inclusion problems with nonlocal integral boundary conditions. In order to achieve the solution, we have to use contractive mapping and the theory of endpoints. For each theorem in our work, we provide an example based on the required assumptions to support the new results.Item Study of reverse and hyper-reverse topological indices of Sierpinski networks and of its line graphs.(UMT Lahore, 2022-06-22) Hammad AhmadIn this thesis, we will compute the closed expression of total reverse vertex degree index, first reverse Zagreb alpha index, first and second reverse Zagreb and hyper-reverse Zagreb indices, reverse atom bond connectivity index, reverse geometric arithmetic index, sum connectivity reverse index, product connectivity reverse index, first and second reverse Zagreb polynomials and reverse hyper-Zagreb polynomials of generalized Sierpinski networks denoted as S(k,t) for k,t ≥ 1. We will repeat the same calculations for its line graph.Item Some operations on hesitant fuzzy graph structures(UMT Lahore, 2022-09-23) Maheen UsmanDuring this work, we introduce the concept of hesitant fuzzy graph structure and explain it with an example. Some operations on hesitant fuzzy graph structures will be defined, that is, Cartesian product, composition, normal product, and tensor product. Further, we present the vertex degree in the products of hesitant fuzzy graph structure. Moreover, the connection is established between the vertex degree of hesitant fuzzy graph structures and the vertex degree of hesitant fuzzy graph structure attained by their distinct products.Item Computation of reverse and hyper-reverse topological indices and polynomials of subdivision graphs of Sierpinski networks(UMT Lahore, 2022-07-14) Muhammad NoumanItem Applications of certain fuzzy clustering algorithms on cyclic networks(UMT Lahore, 2022-08-23) Inayat KarimThe fuzzy c-medoids algorithm (FCMdd) and robust fuzzy c-medoid algorithm (RFCMdd) [16] are used in clustering relational data. In this paper, we have modified FCMdd (mFCMdd) and also modified RFCMdd (mRFCMdd) by introducing a similarity relation comparing with the Cn graph to make FCMdd and RFCMdd algorithms useful for cluster cyclic networks. These algorithms are based on the graph distance of object to object, where the number of edges in the shortest path between two objects is considered as a measure of dissimilarity. We have also added applications to mFCMdd and mRFCMdd.Item 3D geometric designing using linear algebra.(UMT Lahore, 2022-07-22) Roshi Anwar; Hafiza Arooj Azeem; Syeda Tayyiba Zamir; Rimsha ShahidInterest in systems with a free license has grown over the past several years. The Blender is a robust system for 3D design that comes with a free license. A growing number of people are becoming interested in the Blender 3D graphic system because of its compact volume, lack of significant high hardware system needs, numerous benefits, and advancements. The adoption of the open-source Blender system in design practice is justified as being reasonable and correct given this trend's quick, nonlinear positive evolution. It is well known that a large range of software programs are available in the field of 3D graphic design. The makers of 3D software always work to add new features and improve the packages they provide. In actuality, some users may not be able to afford the costs of some of the premium 3D graphics tools. The right 3D system must also take into account its large data capacity and demanding hardware requirements. In recent years, the standards for the quality of the finished result have increased in relation to the computing power of software packages, the design methodologies used during computer design, and particularly the finished visualizations of static and animated models. Given these elements, selecting the best 3D graphics system is a crucial requirement for the design process. This supports the incorporation of a Blender into suggested design practice. Blender is a current technology program that many users like because of its free licensing, open source, easy interface, multilateral design characteristics, and light hardware needs.Item Application of regression and correlation in real life(UMT Lahore, 2022) Majid AliThe regression and the correlation is frequently used statistical methods to inspect the relationship between any two or more than two variables. In our life there are many problems in which the correlation and regression help us to solve the problem. Here in this project we have discussed some of the real-life problems and their solutions using correlation and regression. By using these methods, we can solve many different problems of different fields. It is also very helpful in finding the relationship between the stocks of the markets.Item Numerical analysis of modified SIR epidemic model(UMT Lahore, 2022) Abdul Manan SalamatItem Application of topsis for real life mcdm problem of motor bike selection(UMT Lahore, 2022) Hassan NaveedIn real life, multi criteria decision making is very important. Multi criteria decision making techniques are used for the best selection given the attributes. First of all, a universal set (∪), (𝐴) is the subset of 𝑈, (𝐴) is the set of bikes under consideration. ⊆𝑈 and (𝐸) is the set of attribute of (𝐴). The generalized results of TOPSIS on soft set from TOPSIS on fuzzy-soft-set. In this problem, we select a best bike for use in our daily life. Bike is a basic need of almost every person in Pakistan. Due to its increasing demand and the competition in the Pakistani market, all companies claim that their bike is the best. We use the fuzzy, soft set and fuzzy soft set on TOPSIS method for the selection of a bike by using data and scrutinize the relative ranking of the best motor bikes according to chosen parameters.Item Solution of Partial Differential Equations Using Integration(UMT Lahore, 2022) HAFSA MUSHTAQThis thesis deals with partial differential equations (PDEs). It overlooks the most important PDEs with boundary conditions: the Laplace, heat, uniform transmission line, and wave equations. The method of separation of variables is discussed for spherical and cylindrical coordinates. Examples of both problem types have been discussed in detail. The solution of the uniform transmission line has been examined in detail.