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Item The application of the Sumudu transform to ordinary differential equations.(UMT Lahore, 2023-03) Manahil Maqsood; Ayesha Zaman; Maryam ShahidThe Laplace transform and Sumudu transform is widely used to solve ordinary differential equations. In this project, we discuss about the Laplace and Sumudu transforms by studying Modified Variational Iteration Method. We utilize MVIM to solve ordinary differential equations and to obtain solution to a few examples, demonstrating its effectiveness.Item Study of curvature and torsion with applications(UMT Lahore, 2023-04) Saba Tanveer; Hussain AhmadItem Exploring the impact of concentration(UMT Lahore, 2023-08) Muhammad Tayyab Ilyas; Syeda ZafeeraThis communication presents a theoretical framework for studying the behaviour of a tangent hyperbolic fluid with nano-biofilm. The fluid is subjected to an extending or shrinking sheet, resulting in a stagnation point flow. The framework also takes into account bioconvection induced by gyrotactic bacteria and chemical processes with activation energy. The research is made more novel by the fact that the study considers energetic thickness, thermal conductivity, nanoparticle mass permeability, and various transport properties of microbial organisms. Enhancing heat transport is the main objective of this effort. This is accomplished by formulating a system of partial differential equations with appropriate boundary conditions. The basic formulation is changed into a nonlinear differential equation by researchers using parallel transformation. Shooting method and R-K fourth categorize approach are used to collect observational data, and MATLAB script is used to generate numerical scheme. Through visual symbol, the property of various fluid move properties and various parameters on velocity, temperature, concentration, and dynamic density are assessed.Item Generating smooth cubic splines using antangana baleanu caputo derivative(UMT Lahore, 2023-07) Zohaib AkberWhen it comes to achieving flexibility in controlling the shape of a curve to create a smooth and continuous piecewise curve, the cubic spline method emerges as the optimal choice. Utilizing cubic splines is highly recommended to gain maximum control over the curve. In order to obtain the desired results for generating a smooth graph, the Atangna Baleno Caputo derivative is applied to the cubic spline. Other curve fitting methods, such as Lagrange interpolation, Hermit piecewise, and Bezier curves, also exist. However, these methods have a drawback: they require derivative schemes and introduce errors due to arithmetic or geometric conditions at both endpoints during the process of finding unknowns in the polynomial. As it is known that eight conditions are needed to solve for eight unknowns, Lagrange interpolation becomes increasingly laborious as the polynomial order and the number of points increase, necessitating the evaluation of approximate solutions for each point. In contrast, the Atangna Baleno Caputo derivative offers an ideal solution as it provides all eight necessary conditions, making it the perfect choice for users. The Atangna Baleno Caputo derivative employs a recursive relation to determine piecewise curves. This writing emphasizes that pleasing curves are achieved by utilizing their data points, and mathematical examples are provided to demonstrate the quality of this approach.Item Twin paradox and special relativity(UMT Lahore, 2023) Muhammad Jamil; Faisal Rehan KhanThe twin paradox is a thought experiment in special relativity that explores the difference in aging between two twins, one of whom goes on a round-trip journey into space in a high-speed spacecraft, while the other remains on Earth. According to special relativity, time passes more slowly in a reference frame that is moving relative to an observer. In the context of the twin paradox, this means that the twin who travels into space will experience time dilation, or a slower passage of time, compared to the twin who remains on Earth. When the traveling twin returns to Earth, both twins will have aged differently, with the twin who traveled into space appearing younger. This paradoxical result arises because the traveling twin experiences time dilation only during the portion of the trip where he is moving away from Earth and toward the destination and back. During the portions of the trip where he is accelerating and returning to Earth, he experiences a different type of time dilation due to gravity. The twin paradox is a key example of how special relativity can lead to seemingly paradoxical results, and it has been the subject of much debate and discussion among physicists and philosophers. However, it is important to note that the paradox is only apparent and can be resolved by taking into account the differences in reference frames experienced by the two twins during the journey. The twin paradox highlights the fundamental nature of time and the importance of considering the relative motion of different observers in special relativity.Item Analysis and applications of subdivision surfaces(UMT Lahore, 2023-07) Samer Iqbal; Talha NaveedThe subdivision surface is a convenient way to model objects with arbitrary topologies. Using non-uniformly sampled data points, we reconstruct objects using a piecewise smooth subdivision scheme that we analyze in this dissertation. Subdivision surfaces are well-defined, smooth tangent plane surfaces (G1) that result from repeated refinement of a mesh of 3D control points. A great deal of attention has been paid to the analysis of smooth surface schemes with symmetrical rules around each vertex and edge in the scheme. Surfaces with sharp features, however, can be created in a scheme that does not exhibit this symmetry. By using eigen analysis and characteristic maps for quartic triangular B-spline surfaces, a piecewise smooth subdivision scheme is analyzed for such surfaces. Objects have been reconstructed from 3D data using subdivision surfaces as optimized surface fittings. Dense and uniform samples of data have been used to create accurate representations of objects in the past. As a practical low-cost alternative to the construction of subdivision surfaces by hand, we propose an algorithm that computes subdivision surfaces from data.Item Sumudu transform method and its applications(UMT Lahore, 2023) Maha Ahmed; Amina ArshadOrdinary differential equations (ODE’s) can be solved accurately with the Sumudu transform method. In this study, we investigate the abilities provided by the Sumudu transform method, including its applications to four different scenarios. The primary objectives of this research are to show how the Sumudu transform method works for solving ODE’s and to look at how it might be used in real-world scenarios. First, we give a brief overview of the Sumudu transform technique by highlighting its basic ideas and mathematical foundation. Then we use this approach for modeling each of the selected applications. These equations’ transformed expressions can be used to carry out operations in the modified domain once we apply the Sumudu transform. Once the results have been interpreted, we skillfully use the inverse Sumudu transform to them in order to get exact solutions in the domain that originally existed. The Sumudu transform approach produces findings that are very accurate and consistent with assumptions derived from theory. This method’s effectiveness confirms the Sumudu transform method’s promise as a useful analytical tool for resolving differential equations that can arise in a variety of scientific and engineering domains.Item Curvature, torsion and its application(UMT Lahore, 2023-06) Rao Muhammad Ibrar; Hafiz Shahzaib; Muhmmad Shoaib Akhtar; Kashif AliThe twin paradox is a thought experiment in special relativity that explores the difference in aging between two twins, one of whom goes on a round-trip journey into space in a high-speed spacecraft, while the other remains on Earth. According to special relativity, time passes more slowly in a reference frame that is moving relative to an observer. In the context of the twin paradox, this means that the twin who travels into space will experience time dilation, or a slower passage of time, compared to the twin who remains on Earth. When the traveling twin returns to Earth, both twins will have aged differently, with the twin who traveled into space appearing younger. This paradoxical result arises because the traveling twin experiences time dilation only during the portion of the trip where he is moving away from Earth and toward the destination and back. During the portions of the trip where he is accelerating and returning to Earth, he experiences a different type of time dilation due to gravity. The twin paradox is a key example of how special relativity can lead to seemingly paradoxical results, and it has been the subject of much debate and discussion among physicists and philosophers. However, it is important to note that the paradox is only apparent and can be resolved by taking into account the differences in reference frames experienced by the two twins during the journey. The twin paradox highlights the fundamental nature of time and the importance of considering the relative motion of different observers in special relativity.Item Computer aided geometric design in animation using 3D graphic software(UMT Lahore, 2023-06) Irfan Sharif; Ali HaiderComputer aided geometric design plays a crucial role in the field of animation, enabling the creation of realistic and visually captivating 3D graphics. This paper explores the application of computer aided geometric design techniques in animation using 3D graphic software. An overview of computer aided geometric design and its significance in the animation industry is presented. It highlights the fundamental principles and mathematical concepts that form the basis of computer aided geometric design, including spline curves and surfaces. It also explores the benefits of using computer aided geometric design in animation, highlighting how computer aided geometric design techniques facilitate efficient and precise control over geometric shapes, allowing animators to manipulate objects with greater flexibility and accuracy. The use of computer aided geometric design also enhances the realism of animations, as it enables the creation of smooth and organic motion, realistic deformations, and lifelike character models.Item Computation of SEIR model of outbreak virus using RK4 method(UMT Lahore, 2023-08) Zahrah Fatima; Kinza ShahzadiIn this study, we formulate the mathematical model of COVID-19 with the effects of partially and fully vaccinated individuals. Here, the purpose of formulating the model is to study these models numerically. It is very complex to solve the four equations of the SEIR model, so we use the fourth-order Runge-Kutta method to solve those equations. This method is very efficient and practically suited for solving initial value problems. That’s why we formulated the SEIR model with the incorporation of fully and partially vaccinated parameters. Then we try to solve our equations by converting them into the fourth-order Runge-Kutta method. Moreover, to make the model more realistic, we assume the outbreak of COVID-19 in Bangladesh. We used Python for simulation purposes.Item Fixed points, completeness, and quasi-metric spaces(UMT Lahore, 2023) Hammad AliIn order to generalize classical Banach contraction principle in the setup of quasi metric spaces, we introduce Suzuki-type f (f 1)-contractions of quasi metric spaces and prove some fixed point results. Examples have been furnished to make sure that generalizations we obtain are the proper ones. Moreover, we consider the existence of fixed points of generalized Suzuki type contractions of (so-called)-symmetric quasi-metric spaces.Item Applications of the Sumudu transform to fractional differential equations(UMT Lahore, 2023-08) Maria Jabeen; Sadia BatoolThe Sumudu transform's use with fractional differential equations is covered in this paper. A relatively advanced integral transform with a broad range of applications, the Sumudu transform has become more well-known in recent years. In this study, we embellish the efficiency of the Sumudu transform in solving differential equations with fractions by applying it to various kinds of problems. We provide various examples to demonstrate the use of the Sumudu transform and contrast its outcomes with those attained using alternative techniques. Our findings show that this Sumudu transform is capable of being used as an instrument for solving differential equations with fractions.Item Prevalance of tech neck syndrome and its association with chest expansion in university students(UMT Lahore, 2023) Asad Baig; Ahmad Ilyas; Ali Hassan Bukhari; Usama Sarwar; Numan Arif; M. MushtaqObjectives: To find the prevalence of tech neck syndrome among university students who are on screen users and to find the significant association between tech neck syndrome and reduced chest expansion. Materials and Methods: 100 confirmed cases of tech neck syndrome are taken who use on-screen devices on an average of about 4 or more hours and have significant forward head posture. Costovertebral angle was measured with a goniometer, while chest expansion was measured with an inch tape during the respiration and inspiration phases, and the difference between them was recorded. Results: 54 participants out of 100 confirmed cases of tech neck syndrome have significantly reduced chest expansion, which is the final result of this study, while 46 participants have greater chest expansion, showing that they are normal but still have tech neck syndrome.Item Applications of RK method in physics and computer science.(UMT Lahore, 2023-06-07) Qasim RazaIn unique research, the Runge-Kutta is the most popular technique with a large number of stages computed using the order method. The RK technique is the more generalized concept employed in the modified Euler approach. By using the RK approach to solve numerical solutions of ordinary equations like explicit, delay, and partial differential equations in modern concepts today. The current study indicates a review of modern computational approaches for more favorable solving large-scale differential equations employing the RK algorithm of many orders. We also used the RK method in C language with output. Additionally, running this process on Turbo C and available versions and other platforms must obtain a few modification steps to the modern code. Finally, comparisons of approaches with their precarious comments as remarks have been also included.Item Modelling and simulation of quarter car suspension system.(UMT Lahore, 2023-02-09) Arfa Barira