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Item Cracking of charged compact star admitting conformal motion(UMT Lahore, 2022) Adnan AminThe cracking of charged spherically symmetric compact star admitting conformal motion is examined in this thesis. It is supposed that the stellar structure’s interior is going through great pressure and has a powerful gravitational field. An integral interaction between the metric variables is produced by the conformal symmetry requirement. The Einstein-Maxwell field equations are developed, that are further used to construct hydrostatic equilibrium equation. In order to find instabilities in the system when it departs from equilibrium, density dependent perturbation scheme is applied on hydrostatic equilibrium equation. It has been observed that cracking occurs in compact star at some points in force distribution from center towards boundary.Item Numerical analysis of Covid-19 disease with two susceptible classes.(UMT Lahore, 2022) Mamoona AhmadThis research uses a layout non-standard finite difference technique to investigate a susceptible infected treatment recovered (SITR) dynamical model of coronavirus 2019 (Covid-19) with bi-model pathogen transmission in a susceptible population. This model is solved numerically with three different numerical schemes, forward Euler, RK-4 and the proposed non-standard finite difference (NSFD) techniques respectively. The proposed (NSFD) technique becomes a more efficient and reliable numerical technique than forward Euler and RK-4 techniques. NSFD technique retains all essential characteristics of the continuous bi-model Covid-19 SITR model like positivity, stability of equilibria, while well-known forward Euler and RK-4 techniques cannot sustain these characteristics. Furthermore, the proposed technique is independent of the time step size while forward Euler and RK-4 depend on the step size. The numerical simulations with the aid of a numerical test are presented for the validation of the results.Item Studies of Sudoku graphs via connection number based topological indices(UMT Lahore, 2022) Muhammad Basit AliLet κ = (V(κ), E(κ)) be a simple, undirected and connected graph with vertex set V(κ) and edge set E ⊆ V(κ) × V(κ). A topological index is a function from the class of graph to the set of real number that associates a unique number to each member (graph) of this class. In this thesis, we compute the different connection number-based TIs such as first and second Zagreb connection, modified first, second, third and fourth Zagreb connection, first, second, third and fourth multiplicative Zagreb connection and modified first, second and third multiplicative Zagreb connection indices for Sudoku graphs (SKn×n) for n ≥ 3.Item Stability analysis of physically viable anisotropic strange star models through cracking technique.(UMT Lahore, 2022) Rizwan ArshadThis dissertation is devoted to the explorations related to the cracking of physically viable anisotropic strange star models using concept of local density perturbation for equation of hydrostatic equilibrium and on all physical parameters. Karmarkar condition is applied on the onset of field equation corresponding to anisotropic matter distribution. In order to find cracking of spherical symmetric anisotropic star, the compact star model developed in [15] is considered. Graphical representation of force distribution identifies cracking points and refines stability region.Item Numerical modeling of SEIR on two-dose vaccination of rubella virus(UMT Lahore, 2022) Awais AhmadThis thesis determines non-linear terminologies under the modulation of dynamic transmission in childhood diseases is analyzed to explore the effect of Rubella virus with two-dose vaccination strategy. We have to find the equilibria of susceptible, exposed, infectious and recovered individuals. This model was shown to have two equilibria: a disease-free equilibrium and an endemic equilibrium, and their local stability was defined using the computed effective reproduction number R0, as well as the sensitivity of variables. This model is solved numerically with three different numerical techniques, forward Euler, RK-4 and the proposed nonstandard finite difference NSFD technique. The proposed NSFD technique is more efficient and reliable than the forward Euler and the RK-4 techniques. NSFD technique retains all essential characteristics of the continuous SEIR vaccine epidemic model like positivity and stability of equilibria. While the well-known forward Euler and RK-4 techniques do not sustain these characteristics.Item Zagreb indices of dendrimer nanostars using connection numbers(UMT Lahore, 2022) Nageen FatimaNumerical invariants or topological indices (TIs) are the graph descriptors that assist us in preserving physicochemical characteristics like boiling point, temperature, pressure, melting point, freezing point, and stability of different chemical compounds. To evaluate the physical and chemical properties of molecules, numerous TIs have been studied in the literature. Among all the investigated indices in the literature, the Zagreb connection indices (ZCIs) are examined to be more valuable to evaluate the chemical and physical attributes of molecular substances. In this thesis, we calculate ZCIs, known as first ZCI (FsZCI), second ZCI (SZCI), modified FsZCI, modified SZCI, and modified third ZCI (TZCI). Moreover, we compute multiplicative ZCI (MZCI), named as first MZCI (FsMZCI), second MZCI (SMZCI), third MZCI (TMZCI), fourth MZCI (FrMZCI), modified FsMZCI, modified SMZCI, and modified TMZCI of dendrimer nanostars. Moreover, we compare our computed results with each other to check their authenticity and superiority.Item Computational analysis for bioconvection of motile microorganisms in prandtle nanofluid flow across an inclined sheet(UMT Lahore, 2022) Muhammad AjmalIn the existence of an aligned magnetic Öeld across the inclined stretching shrinking sheet in non-darcy permeable medium,the two dimensional boundary layer áow of prandtl nanoáuid is analyzed. The formulation of partial di§eren- tial equation, which manage the distinctive properties of heat and áow transfer is converted into ordinary di§erential equation by using the appropriate similarity variables. The governing equations are resolved numerically by using the Runge- Kutta method along shooting technique is coded in MATLAB platform.This pro- cedure is widely used for the solution of such problems as it is e¢ cient with cost- e§ectiveness and Öfth order accuracy. The signiÖcance of immerse parameters on the velocity,temperature,concentration and bioconvection are dispose through Ög- ures.Also physical parameters skin friction coe¢ cient and nusselet numbers are demonstrated in table.The declining behavior of the áow velocity against the áuid parameter 1 and the porosity parameter KP and the local inertia coe¢ cient F r these two parameters of Darcy resistance and Darcy forchiemer resistance are responsible for slowing the áuid speed .The áuid temperature is increases with pa- rameters of Brownian motion N b and thermophoresis N t. The increasing values of Brownian motion N b and the Lewis numberLe decreases the concentration of nanoparticles. The ináated inputs of Lewis numberLb and the Peclet number P e declined the bioconvection distributionItem Some results on maximal strong lexical product of fuzzy graph structures.(UMT Lahore, 2022) Danial HameedIn this thesis, we establish the novel idea of maximal strong lexical product of two fuzzy graphs structures. Also, we gave an idea to how calculate the degree of vertex and total degree of a vertex in the maximal strong lexical product by taking different scenarios. This products are apply on different theorems along with numerical examples. As an application, we apply our results in detecting of marine crimes by using maximal strong lexical productItem Exact traveling wave solutions possessing beta derivative of the fractional generalized reaction duffing model and the density dependent fractional diffusion reaction equation(UMT Lahore, 2022) Kausar ShahzadiIn this dissertation, we study the two important nonlinear fractional differential equations, beta derivative the generalized reaction duffing model and density dependent m- fractional diffusion reaction equation by using three dependent, generalized tanh method method, generalized bernoulli sub-ode method and generalized Bernoulli sub-ode method. A wave transformation in the fractional form via the beta derivative is applied to transform the differential equations into ordinary differential models. These methods contribute a variety of exact solutions. As a result, a series of exact traveling wave solutions are obtained by using the software mathematica. The numerical simulation of obtaining solutions depicts that the suggested approaches are simple and efficient to produce rapid results as compared to many other methods.Item Stability of isotropic massive stellar object in f(R) gravity(UMT Lahore, 2022-09-07) KausarIn this thesis for spherically symmetric collapsing we inspect the (in)stability conditions of the pressure of condition of isotropy dissipative distribution of fluid including exotic matter. For scenario of evolution and to presume terms which are exotic we used f(R) theory. The cluster features like density homogeneity, anisotropic pressure and dissipation as well as shear is directly affected due to the dark matter's presence. It is discovered that inhomogeneities of energy density, and/or dissipative fluxes and/or the shear presence in the flow of fluid in the dark matter's presence, initially force any configuration of isotropic to give up completely in such a condition, giving rise to anisotropy in pressure.Item Prevalence of tech neck syndrome and its association with chest expansion in university students.(UMT Lahore, 2022) 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 uses on screen devices on an average of about 4 or more than 4 hours and having significant forward head posture. Costovertebral angle measured with the goniometer while the chest expansion has been measured with the inches’ tape during respiration and inspiration phases and recorded the difference between them. Results: 54 participants out of 100 confirmed cases of tech neck syndrome have significant reduced chest expansion which is the final result of this study while the 46 participants are having greater chest expansion and showing that they are normal but they have tech neck syndrome.Item Interval-valued(UMT Lahore, 2022-08) Faisal Rehium AkhtarUsually in decision-making (DM) a huge use of the fuzzy sets is observed to undertake the uncertainty by its property of membership grades. Also neutrosophic set is used to undertake the uncertainty by truth, indeterminacy and falsity membership grades, in decision-making. However, in certain cases it is hard to define the fuzzy membership grade with a specific value in real life problems, specially in social science where data is not discrete. The research discussed below, is an introduction of interval-valued neutrosophic fuzzy set that is the combination of FS and I-VNS. Its use in DM leads to overcome the issue of the specific value of fuzzy membership grades in social science. The application of I-VNFS is presented with an example to undertake some difficulties and uncertainties xi in statistical data form real life problems due to the nonstandard interval of neutrosophic components. We introduce I-VNFS which is considered as much reliable and give accurate results than S-VNFS.Item On sum degree based topological indices of some connected graphs(UMT Lahore, 2022) Navid IqbalIn mathematical chemistry, molecular structure of any chemical substance can be ex- pressed by a numeric number or polynomial or sequence of numbers which represents the whole graph is called topological index. An important branch of graph theory is the chemical graph theory. As a consequence of their worldwide uses, chemical networks have inspired researchers since their development. Determination of the expressions for topological indices of different derived graphs of graphs is a new and interesting problem in graph theory. In this article, some graphs which are derived from honeycomb structure are studied, and obtained their exact results for sum degree-based indices. Additionally, a comparison is shown graphically among all the indices.Item On local fractional metric dimensions of Mycielski's graphs(UMT Lahore, 2022) Hira ManzoorMetric dimension is an effective tool to study different distance based problems in the field of telecommunication, robotics, computer networking, integer programming, chemistry and electrical networking. the fractional metric dimension is the latest developed form of the metric dimension that is frequently used for the non-integral linear programming problems. in this thesis we will compute local fractional metric dimension (lfmd) for two different classes of mycielski's graphs called by path mycielski and cycle mycielski in the form of lower and upper bounds.the bounded and unboundedness of the obtained results is also discussed.we developed the general formulas of upper and lower bounds of local fractional metric dimension of mycielski's path graph for n≤10 , n ≡ 0(mod4) and mycielski's cycle graph. all the obtained results are illustrated by the examples of particular graphs belonging to the understudied families of graphs.Item Conformal compact model of massive stellar object in 𝒇𝒇(𝑹𝑹, 𝑻𝑻) gravity(UMT Lahore, 2022-07-19) Ghulam FatimaThe present analysis explores exact solutions of a massive compact stellar object in f (r, t ) gravity using conformal motion. here r is ricci scalar and t is trace of energy momentum. we presume that the substance inside the stellar structure has high pressure and density as well as strong gravitational fields. the integral relationship between metric functions is due to conformal motion. we apply the conformal motion to obtain an anisotropic solution of the f (r, t ) field equations. for relativistic compact stars, this approach is very useful. for the stellar object p srj1614 − 2230 we discuss radius, mass, density, pressures, energy conditions and stability criteria. our solutions have been seen to be physically acceptable in f (r, t ) using conformal motion.Item Best proximity points of generalized contractions in ordered b-quasi metric spaces(UMT Lahore, 2022-12-29) Hira YousafThe motive of this dissertation is to explore the existence of best proximity points for more general contraction conditions in the context of b-quasi metric spaces. Czerwik introduced b-metric space which is more general than metric space. Many authors generalized metric space and quasi metric space. A quasi metric space is a distance function which is asymmetric unlike the metric which is symmetric. Apart from generalization of metric space, quasi metric space induce a partial order, which is an important tool for mathematics and related discipline. In this study, the first part consists of a review of some ordered rational proximal contraction type results for the sake of completeness. In the second part we introduced generalized rational proximal contraction in the frame of references of b-quasi metric space. Results presented in this thesis generalized and extended many results in existing literature. Our results extend many best proximity point theorems on partially ordered b-quasi space including the well known banach contraction principal. We present some examples to manifest the generality of our conclusion.Item Intuitionistic fuzzy soft positiveimplicative hyper bck-ideals(UMT Lahore, 2022) Ayshah RehmanIn this study, we institute the idea of IntFSPIH BCK-I of kind (≪, ≪, ⊆), (≪, ⊆, ⊆) and (⊆, ≪, ⊆). some related properties are considered. relation of IntFSH BCK- I, IntFSSH BCK-I and IntFSPIH BCK-I of kind (≪, ≪, ⊆), (≪, ⊆, ⊆) and (⊆, ≪, ⊆) are introduced. additionally, we demonstrate that the L-set of IntFSPIH BCK-I of kind (≪, ≪, ⊆), (≪, ⊆, ⊆) and (⊆, ≪, ⊆) are PIH BCK-I of kind (≪, ≪, ⊆), (≪, ⊆, ⊆) and (⊆, ≪, ⊆) apart. the order for an IntFSset to be IntFSPIH BCK-I of kind (≪, ≪, ⊆), (≪, ⊆, ⊆) and (⊆, ≪, ⊆) are begin apart and the situation for an IntFS-set to be an IntFSWH BCK- I is also review.Item On local fractional metric dimension of harary graphs(UMT Lahore, 2022) Komal AzamLet g = ( v(g),e(g) ) be a finite connected graph. We will compute local fractional metric dimension (lfmd) of harary graphs by generating four classes n ≡ 0(mod4), n ≡ 1(mod4), n ≡ 2(mod4), n ≡ 3(mod4). The bounded and unboundedness also discussed for lfmd of that graph. We developed the general formulas of upper and lower bounds of local fractional metric dimension of harary graphs in the form of m and n where m is even and n may be odd or even. All the obtained results are illustrated by the examples of particular graphs belonging to the understudied families of graphs.Item Synthesis and characterization of Ni-Co doped zinc ferrites and their photocatalytic activity(UMT Lahore, 2022) Mehwish NazarIn this project hydrothermal method used for the synthesis of zinc ferrites and doped with nickel-cobalt by using different percentage such as (1, 2, 3, 4 and 5 %) in zinc ferrites were synthesized. The prepared doped zinc ferrites were subjected to characterization using various analytical techniques such as ftir, scanning electron microscopy, x-ray diffraction, and uv-visible spectroscopy. The results proved that successful mixture of target zinc ferrites. The nickel-cobalt doped zinc ferrites were applied for the photocatalytic degradation of a model dye ‘methylene blue’. Methylene blue used as a standard pollutant to analyze photocatalytic activity of all the synthesized nps and compared. Various percentage of doped nikel-cobalt (1, 2, 3 ,4 and 5 %) were employed for the process of degradation. It was noted that 79 % degradation of mb was shown by 5 % nikel-cobalt doped zinc ferrites and lowest activity 18 % of 1% of ni-co doped zinc ferrites. The photocatalytic activity of zinc ferrites depend upon the concentration of nikel-cobalt as increasing the amount of nanoparticles up-to 50 % and further decrease in the degradation. It degrades the methylene blue 0.012 g/l aqueous solution of 78 % which may be improved further in future research.Item Preparation and characterizations of molybdenum oxide and reduced molybdenum oxide thin films for hydrogen generation(UMT Lahore, 2022-08-01) Abdul WahaabSolar driven hydrogen production, also known as photovoltaic hydrogen production, is a promising technology that harnesses the power of sunlight to produce hydrogen gas through water splitting. The produced hydrogen can be used as a clean energy source. In this work, MoO3 thin films were prepared on glass and FTO substrates at 400°C, 500°C, 600°C temperatures under vacuum and oxygen environment, using the chemical vapor deposition technique as photo electrodes for water splitting. It is noticed that the band gap of MoO3 thin film was decreased by increasing the annealing temperature. SEM results depict that the nanorods and nanoneedles like structures are formed by annealing in oxygen and vacuum environment. The photo electrochemical showed that the annealed films have better photocurrent response as compared to pristine MoO3. The solar to hydrogen conversion STH% of MoO3 vacuum-annealed MoO3-500°C is 9 times higher than pure MoO3.