Department of Mathematics
Permanent URI for this communityhttps://repository.cuilahore.edu.pk/handle/123456789/21
Browse
16 results
Search Results
Item Classifications of Determinantal Varieties(Library Information Services, COMSATS University, Lahore Campus, 2019) Sana Zahoor; , FA17-RMT-054; Dr. Imran Ahmed; LHR TP 5675Let Mns be a space of matrices of order n×s with complex enteries. The determinantal singularities are defined by vanishing of all the minors of a certain size of an n ×s matrix α : Ck → Mns. The class of determinantal singularities is a more general class than the class of complete intersection singularities. The G-finite deteminacy gives a special class of determinantal varieties known as essentially isolated determinantal singularities (EIDS), firstly introduced by Ebeling and Gusein-Zade in 2009. We give a computational method to find linear forms of EIDS by programming in CItem Investigation of Doped (III-V) Group Elements Emissive Layer for Visible LED Applications(Library Information Services, COMSATS University, Lahore Campus, 2019) Aqsa Hashmi,; FA17-RPH-043; Dr. Farah Alvi, Assistant Profesor [Supervisor]; LHR TP 5728This study Sb2S3 was prepared by applying hydrothermal technique with different concentration of Ag as a doping impurity to improve its optical and electrical properties to be used in optoelectronics for LED applications. FTIR spectra was used to analyze the vibrations of chemical bonds present in the different groups in the sample. The intensity of the peaks is reduced with the increase in doping concentration, this is because the strength of chemical bonds decreases because of intermolecular transition of groups present in the sample. Optical properties were studied by UV-Vis and PL spectroscopy. UV-vis spectra was used to calculate bandgap that comes out between 2.5-1.9 eV. The bandgap was reduced with the increase in doping concentration of Ag which indicate its good compatibility for LED applications. IV measurements were used to analyze IV characteristics of the samples and to find out the turn on voltage of the device. SEM results were helpful in analyzing the surface morphology of the samples and measuring the particle size. The device was characterized by electroluminescence spectra which confirmed the red emission from LEDs having emissive layers of undoped and doped Sb2S3. So the materials have bright future for visibe LED applications.Item Cordial Labelings of 𝐵𝑛 and Linear Phenylene Graphs(Library Information Services, COMSATS University, Lahore Campus, 2019) Yusra Amjad,; FA17-RMT-001; Dr. M. Faisal, Assistant Profesor; LHR TP 5641Cordial Labelings of Bn and Linear phenylene Graphs Graph theory is one of the important branch of mathematics. Mathematicians consider it useful in light of the fact that it has wide range of applications in different areas such as in computer science, sociology, engineering, communication networks, radar tracking and much more see [2, 3, 13].It has risen as the most important branch of mathematics. In graph theory there are different types of labeling. In this thesis our work is focused on cordial labelings of Bn graph and linear phenylene graph. First chapter includes introduction. In this chapter we basically discussed the basic definitions related to the graph and studied different types of graphs including Bn graph and linear phenylene graph. In second chapter we shed light on various types of labelings introduced by renowned scholars. We have discussed cordial labelings and its several types. In third chapter we have discussed some results for cordial labeling of Bn graph and linear phenylene graph. In chapter four we find the results for edge product cordial labeling of Bn graph and linear phenylene graph. In chapter five we find the results for total edge product cordial labeling of Bn graph and linear phenylene graphItem Warm Inflationary Dynamics of Chaplygin Gas Models with Constant Sound Speed(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) FA17-RMT-050; Azmat Rustam; Dr. Abdul Jawad, Assistant Profesor; LHR TP 5671This study investigates the warm inflationary dynamics of Chaplygin gas models under the assumption of a constant sound speed. Warm inflation, characterized by the simultaneous production of radiation during the inflationary phase, provides an alternative to the standard cold inflation scenario by eliminating the need for a separate reheating period. In this work, the Chaplygin gas—known for its unified description of dark energy and dark matter—is incorporated into the inflationary framework to explore its viability in describing the early universe. Assuming a constant sound speed simplifies the dynamical equations and allows for analytical treatment of the system. The evolution of key inflationary parameters, including the Hubble parameter, scalar field dynamics, and radiation energy density, is examined in detail. Slow-roll conditions are derived and analyzed within the context of dissipative effects inherent in warm inflation. Additionally, cosmological perturbations are studied to evaluate the scalar spectral index and tensor-to-scalar ratio, providing a means to compare theoretical predictions with observational data. The results demonstrate that Chaplygin gas models with constant sound speed can successfully support a sustained period of warm inflation while remaining consistent with current cosmological observations. This framework offers a promising avenue for connecting early universe inflation with late-time cosmic acceleration, contributing to a more unified cosmological model.Item Creeping Flow of Viscous Fluid through a Porous Permeable Slit with Exponential Reabsorption(Library Information Services, COMSATS University, Lahore Campus, 2019) Sadia Karamat,; FA17-RMT-048; Dr. Quart-Ul-Ain Azim, Assistant Profesor; LHR TP 5669Creeping flow across a porous channels occur in a diverse number of physical phenom ena like filtration plants in engineering and industry, glomerular tubule filtration, prox imal tubule reabsorption etc. There are a great many studies in literature that address the creeping flow of Newtonian liquid through porous cut, but corresponding studies for flow through porous media are unaccounted for. To address this space in ongoing research literature, we have done to execute the analytical study of creeping flow of viscous liquid through a slit with porous walls where the reabsorption function is ex ponential. The study is motivated by diseased proximal convoluted tubule in context, where the tubular space acts as a porous medium due to disease. Modeling is the first step of present work which interprets the physical problem into mathematical form. Then the resulting complex differential equations we solved to obtain exact solutions. Physical quantities like components of velocity, pressure distribution, leakage flux and fractional reabsorption are evaluated. Finally we present the graphical analysis of the obtained resultsItem Stationary Solutions And Optical Solitons For Nonl(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Insibat Afzal; FA17-RMT -012; Dr. Syed Tahir Raza Rizvi; LHR TP 5649Solitons are vastly growing field of research not only in the field of nonlinear optics but they also appear in applied mathematics, telecommunication industry and in various branches of physics and biology. Specially, optical solitons arises in many different f ields including nonlinear optics. They are the light pulses that do not diffract in the mediumthrough which they passes. These days, optical solitons play a significant role in many branches of modern telecommunication mediums including internet industry, twitter, Facebook and many more. Due to the property of not changing shape and path after collision, optical solitons are used to transfer data without using repeaters. A lot of work have been done in retrieving optical and exact solutions of the solitary waves in nonlinear optics. In this dissertation, we will obtain the stationary solutions of Gerdjikov-Ivanov (GI) equation, cubic-quintic NLSE and paraxial equation by using the help of Lie group analysis. And also, we will get chirped sub-pico bright, dark and dark singular combo optical soliton solutions for Triki-Biswas equation by using some constraints. To solve Triki-Biswas equation we will use two different integrating methods namely, sine Gordon method and modified extended direct algebraic method.Item Imex Methods For Ordinary Differential Equations(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Nida Khalid; FA17-RMT-053; Dr. Yousaf Habib; LHR TP 5674The aim of this thesis is to construct partitioned Runge-Kutta methods (PRK) for the numerical solution of non-separable system of ordinary differential equations y0 = f(y; z), z0 = g(y; z) as IMEX scheme (implicit explicit). The partitioned Runge-Kutta methods consist of two RK methods such that one method solve y0 = f(y; z), the non stiff differential equation, the other method solve z0 = g(y; z), the stiff differential equation. Explicit RK method is used for the solution of non stiff part and implicit RK method is used for the solution of stiff part. In order to construct PRK method, we have used the idea of effective order methods. The development of these methods require the solution of large number of order conditions, however, there exist simplifying assumptions which reduce the number of order conditions. In this thesis, simplifying assumptions for PRK method for non-separable differential equations are derived for the first time and applied successfully to reduce the effective order conditions, thus allowing us to construct effective order 3 PRK method with just two stages. This result in huge savings in terms of computational cost.Item Particle Creation with Adiabatic Transformation Through Thermodynamic Perspective in Modified Theories(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Mubashira Rasheed; FA17-RMT -014; Dr. Muhammad Zubair; LHR TP 5651Modified gravitational theories play significant role to discuss many con stituent of the accelerated phase of our universe for last few decades. A large numberofdifferent techniques in modified theories are proposed to sort out the cosmological problem. Weanalyzedopenirreversiblethermodynamicsinthescenarioofparticle cre ation for modified theory of gravity known as f(G,T) gravity theory, in which the generic function defines the coupling between GB invariant G and trace of the EMT with non-zero divergence. We discussed the generalized conser vation equation which involves additional contribution from matter geome try coupling for irreversible matter creation process with the help of general ized "second law of thermodynamics" in the light of the “Friedmann-Lematre Robertson-Walker" FLRW space time. Particle creation rate, number of particle creation, creation pressure, entropy production rate, and temperature for this theory have been formulated by choosing some particular model of f(G,T), which help us to explore the particle creation in a significant way. We also discussed non-minimal F(R,T,Q) theory of gravity where (R, T, Q are ricci scalar, trace of EMT and interaction of Ricci tensor and non-minimal coupling of Ricci scalar respectively, and Q = RαβTαβ) is the interaction of Ricci tensor and EMT. Due to the non-minimal coupling of gravity and geometry an extra force present which is perpendicular to four velocity. We also formulated some explicit results of created particle from gravitational field to the created ix matter such as particle creation rate, pressure of created particle and entropy with respect to time variation through irreversible thermodynamics interrelated with adiabatic transformation in the context of FLRW space time. We consid ered the dust universe i.e., P = 0 and the scale factor by power law a(t) = tm to precise our results. It is observed that in this procedure a large amount of co-moving entropy has been generatedItem Randic, Seidel And Laplacian Energy Of NEPS Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Yasir Ali; FA17-RMT-007; Dr. Sarfarz Ahmad; LHR TP 5645Let be the simple graph, then we can obtained the energy of a graph by taking the absolute sum of the eigenvalues of the adjacency matrix of . In this research we have computed different energy invariants of the Non-completed Extended P-Sum (NEPS) of graph . In particular we investigate the Randic, Seidel and Laplacian energies of the NEPS of path graph with any base . Here denotes number of vertices and denotes the number of copies of path graph . Our some of the results depend on the number of zeroes in base elements, for which we use the notation .Item Interaction Of Multi Nanoparticles In Flow(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Imran Latif Bhatti,; FA16-RMT-006; Dr. Mohsan Hassan,; LHR TP 5180Interaction of Multi Nanoparticles in Flow of Hybrid Nanofluid over Disk Nanofluid is an important chemical fluid that is used in industries due to high heat transfer rates. Lately, a new kind of nanofluid is called hybrid nanofluid is used for further enhancement in heat transfer rate and is produced by two or more dissimilar nanomaterials [1]. Hybrid nanofluid show amazing thermo-physical properties that are not existed in the convective heat transfer fluids (water, oil etc.) and the nanofluids containing single nanomaterial. The main purpose of hybrid nanofluids is to achieve great enhancement in thermal or rheological properties. Moreover, the hybrid nanofluid is expected to achieve more thermal conductivity as compared to a single material nanofluids. In a continuation of achieving better thermal conductivity and thermal performs through single nano-material, many studies have been done [2-4]. In an extension of nanofluid research, few papers have recently discussed the topic on thermal performance of hybrid nanofluids [5-7] and found a deficiency in agreement among their results. In addition, there is deficiency of theoretical models that can guess the exact thermal performance as well as fluid flow characteristic of these fluids. Thus, it is needed to be focused on theoretical modeling of hybrid nanofluid flow along with effective physical properties to measure better understanding of its heat and mass flow the behavior. In this study, to analyses theoretically heat and mass flow behavior, the physical problems will be modeled through equations of continuity, momentum and energy which base on different conservation laws of physics. For physical properties, we will product mathematical co-relational models by different theories. So, by solving these equations with effective physical properties, we will obtain results for velocity and temperature profiles. These results will be used also in further physical quantities of engineering. In addition, disk shaped bodies are often used in automobile and chemical industries etc. For examples, it is used for rotating heat exchangers, bio-fluids production applications and in tubular membrane system etc. So, it is also important to discuss about configuration of geometry when such fluid flow over it.