http://localhost:8081/jspui/handle/123456789/19062 2026-04-26T01:39:47Z 2026-04-26T01:39:47Z Nandita http://localhost:8081/jspui/handle/123456789/20504 2026-04-24T06:35:51Z 2024-07-01T00:00:00Z

Title: PROPAGATION OF SHOCK WAVES IN GASEOUS MEDIA GOVERNED BY QUASI-LINEAR HYPERBOLIC SYSTEMS OF PDES Authors: Nandita Abstract: This thesis addresses the detailed analytical and numerical investigation of the so lutions of selected hyperbolic systems of quasi-linear partial differential equations. Chapter 1 is introductory, providing an overview of the subject matter that has evolved over time. Chapter 2 The purpose of this study is to obtain the solutions using the Lie group of symmetry method for the problem of propagating magnetogasdynamic strong cylindrical shock wave in a self-gravitating non-ideal gas with the axial mag netic field. Here, isothermal flow is considered. In the undisturbed medium, varying magnetic field and density are taken. Out of four different cases, only three cases yield the similarity solutions. Numerical computations have been performed for the cases of power-law and exponential-law shock paths, to find out the behavior of flow variables in the flow field immediately behind the shock. Similarity solutions are obtained by taking arbitrary constants in the expressions of infinitesimals of the Lie group of transformations. Also, the study of this work provides a clear picture of whether and how the variations in the non-ideal parameter of the gas, Alfven-Mach number, adiabatic exponent, ambient magnetic field variation index, and gravita tional parameter affect the propagation of shock and the flow behind it. Chapter 3 is focused on studying the shock waves propagation through an ideal radiating gas containing solid dust particles of arbitrary strength. To analyze the shock front kinematics, an infinite set of transport equations determining shock strength and induced discontinuities is obtained. A truncation approach of the in f inite system of transport equations yields an efficient shock propagation system of f inite ordinary differential equations. The analysis appropriately reflects the nonlin ear steepening effects of the flow behind shock fronts due to the dynamic interaction between shock fronts and the flow behind them. The effects due to dust param eters and radiation on shock propagation are discussed with the help of graphical representations. The decay laws for weak shocks in a non-radiating gas are pre cisely recovered by the second-order truncation approximation. The characteristic rule, the first- and second-order approximations, are compared for shock waves of arbitrary strength.

2024-07-01T00:00:00Z Yadav, Akshay Kumar http://localhost:8081/jspui/handle/123456789/20469 2026-04-20T10:36:15Z 2024-05-01T00:00:00Z

Title: SOFTWARE RELIABILITY GROWTH MODELS BASED ON NHPP FOR MULTIPLE TYPES OF FAILURES Authors: Yadav, Akshay Kumar Abstract: With the progression of software innovation, it has been observed that one of the most important parameters which controls the software reliability enhancement is the testing Effort function (TEF). In this paper, effects of testing efforts on NHPP based software reliability model has been studied. The sensitivity analysis has been provided to examine the effect of system parameters of the developed model on the reliability of the software, mean value function and on cost function. The maximum likelihood method has been used for estimating the parameters of the model. A warranty cost model is also framed for evaluating the optimal release policy. The analytical results obtained are supported by numerical illustration. Innovative advancements are quick in an industry, to stay aware of the bit by bit expanding race and to get upper hand, the product advancement associations need to acquire the right information about software, use it competently and pass it to the next generation. Since software reliability is a key component of good programming, it is possible to decouple quantitative measures for the reliability of programming frameworks from models of software reliability. Software reliability is commonly understood to be the likelihood that a software system will successfully fulfil the task that has been assigned to it in a specific environment for a predetermined number of inputs, assuming that the hardware and the input are both error-free. One of the primary factors contributing to the software quality is its reliability. The three-phase software reliability growth model discussed in this research includes test coverage in an adequately debugged environment. We construct two models for the growth of software reliability that take complete debugging and testing coverage into account. The findings of the sensitivity analysis show that the parameters of the formulated models affect both mean value function (MVF) and the reliability of the software. GA, and PSO methods has been used to optimize the cost of the software. The stability or life of a software system with different capacities is referred to as software reliability. The software quality is the most important consideration while designing a software system. Software quality is determined by a variety of criteria, including software reliability, efficiency, testing abilities and cost considerations. In this paper, we deal with two different SRGMs (software reliability growth models) based on NHPP (Non-homogeneous Poisson process). We develop the models for inflection S-shaped context by considering time independent fault content factor for perfect debugging environment whereas another model v differs in an imperfect debugging environment by involving time dependent total fault content factor. We suppose that once a software problem is identified (removed), immediate debugging begins, and that either the total number of faults is detected (removed) with probability p1(p2) or the total number of faults remains constant with probability (1−p1)(1−p2), i.e., p1 % of the faults can be identified successfully and p2 % of the faults may be removed as well during the software testing phase. The intended SRGMs' results are used to assess the software's reliability. We further compare the performance of both the software reliability growth models. The findings show that the model can perform better in terms of fitting and prediction. In the current era of modern technology, a human cannot think to survive without software as such key area of attention of software manufacturer is to produce bug-free software and maintain the reliability and compatibility with human activities dependent upon software embedded devices. The manner in which the software will perform in a random field environment is a very major issue to study. Taking effects of random field environment into account, in this paper we develop a generalized software reliability growth model (G-SRGM) with generalized fault coverage function. For demonstrating the better performance of the proposed model, two data sets are taken and computational results of proposed models are compared with the existing models using Least Square Estimation (LSE) technique in MATLAB software. The three goodness-of-fit criteria such as the sum of square error, R-square, and root mean square error are also used for comparison. Chapter 1 is an introductory in nature and provides the basic definitions, background and motivation of the work presented in this thesis, along with basic definitions and preliminary concepts of software reliability growth models. Chapter 2 provides the literature survey on the application of Software reliability growth models (SRGMs) incorporating various factors for assessment of the software’s reliability. Chapter 3 explores a generalized software reliability prediction model for module-based software incorporating testing effort with cost model. Chapter 4 proposes a generalized two and three phase software reliability growth model incorporating testing coverage with cost model in a perfect debugging environment. vi vii Chapter 5 presents a software reliability growth model in perfect and imperfect debugging environment. Chapter 6 explores a generalized software reliability growth model for Software System Operating in Random Environment. Chapter 7 summarizes the work, present important conclusions, and discusses the future research endeavors. The major contributions of this thesis along with concluding remarks in theoretical and application facets are presented in this chapter. The results obtained in all the chapters indicate that the performance of SRGMs can be improved significantly by integrating it with either random field environment, test-coverage function or imperfect debugging process. The maintenance cost of the software can be minimized by using the soft computing techniques like- nature inspired algorithms for optimization.

2024-05-01T00:00:00Z Chauhan, Swati http://localhost:8081/jspui/handle/123456789/19902 2026-03-24T07:00:56Z 2022-09-01T00:00:00Z

Title: STUDY ON SHOCK WAVES PROPAGATION IN GASEOUS MEDIA AND SYMMETRY ANALYSIS OF COUPLED EQUAL WIDTH WAVE EQUATION Authors: Chauhan, Swati Abstract: Gasdynamics is a sub eld of hydrodynamics, which is the study of uids, liquids, and gases. It emerged at the tail end of the nineteenth century as a consequence of e orts to comprehend the fundamentals of high-speed compressible ow theories. The equations of gasdynamics have traditionally been used to study shock wave propagation. The phenomenon of shock waves is mathematically and physically interesting, and study into them has been extremely important over the past few decades. One of the primary reasons for this is that it can be applied in a wide variety of domains. In brief, a shock wave is a non-linear wave that travels faster than the speed of sound in the medium. Shock waves occur frequently in everyday life, although they go unnoticed the majority of the time. Physically, the emergence of a shock wave in a uid ow is always characterized by instant changes in the ow velocity, pressure and temperature. This change is not reversible; inside the shock wave, dissipation of energy occurs and the entropy increases. Shock waves have gained much importance due to instantaneous changes in velocity and pressure, and are being investigated for potential applications in a variety of elds. In the eld of aerodynamics, when designing the optimal geometry of objects moving faster than the speed of sound, such as supersonic aircraft or spacecraft re-entering the atmospheres of planets, having an understanding of shock waves is extremely important. A shock wave can promote the transition of graphite into diamond, which is a classic example of this phenomenon. In the eld of astrophysics, two common scenarios that involve shock waves are the explosions of supernovae and the collisions of clouds. Numerous applications of shock waves may be found in the realm of medical science. One such application is the removal of kidney stones from the human body using a technique known as \Extracorporeal Shock Wave Lithotripsy (ESWL)", which involves the use of relatively modest shock waves. To begin, we will conduct a quick review of shock waves. In this type vii viii of wave, the shock that is associated with hyperbolic systems of conservation laws can be identi ed by its front. This front is a moving surface that divides the space into two subspaces in which a continuous solution exists but there is a jump in the eld variables across the shock front. The existence of shock waves was predicted by considering certain waves traveling in a uid governed by the Euler equations.

2022-09-01T00:00:00Z Singh, Meenu http://localhost:8081/jspui/handle/123456789/19667 2026-03-16T10:50:34Z 2022-09-01T00:00:00Z

Title: HYBRID DECISION-MAKING MODELS FOR MULTI-CRITERIA OPTIMIZATION PROBLEMS Authors: Singh, Meenu Abstract: Most of the real-world problems are dependent on a set of criteria rather than a single criterion, which are usually tangible and their corresponding information is merely impossible to get in quantitative form. Hence, this increases difficulties for a method to handle such complexities and provide a feasible solution. If the Decision Makers (DMs) are involved too, it can worsen the decision output. Thus, the development of efficient Hybrid Decision-making (HDM) models is a need of the hour that can provide the optimal solutions to the DMs. The main focus of this thesis is to develop efficient Hybrid Multi-Criteria Decision Making (HMCDM) models for handling fuzzy environment, sustainability issues, rankability issues, multi-dimension data and incomplete data. The HMCDM models are developed by integrating the different Multi-Criteria Decision Making (MCDM) methods, followed by the sensitivity analysis and correlation analysis for validation purposes in different chapters. The application of the proposed integrated model is demonstrated on a set of three problems taken from different Indian industries, including the pulp and papermaking industry, packaging industry, and paper mills. Four types of HMCDM models are considered (I) integration of MCDM methods with MCDM methods, (II) integration of MCDM with Fuzzy Set Theory, (III) integration of MCDM with MODM method, and (IV) integration of MCDM with a sports ranking method (D-matrix). The entire work done for this research is organized into six chapters of the thesis. Chapter 1 defines multicriteria decision-making in the context of decision analysis in general and draws the distinction between single and multicriteria decision-making. It provides a classification of MCDM methods into those based on multi-attribute utility theory, outranking methods and hierarchical approaches. It further provides elementary decisions and distinguishes between multi-objective decision making and multi-attribute decision making and illustrates their historical development along with a brief literature review of some selected weighting methods. An analysis of published literature provides some insights into recent trends. Chapter two provides a brief summary of the main MADM and MODM methods used in this thesis. This includes mathematical formulations and brief descriptions of the steps required for application of a method.Chapters 3 to 5 contain the main contributions of the thesis. Each of them develops one or two HMCDM methods and applies them to a particular industrial application. Third chapter deal with the selection problem while considering the fuzziness in the DMs’ opinions and information collected. In this chapter, two different HMCDM models are proposed for both the selection problems of the pulp and papermaking industry and the packaging industry in India. The fourth chapter draws the attention towards another ranking problem in MCDM. Here, MCDM method is integrated with a minimization model to overcome the drawback of MCDM methods of providing conflicting rankings. An example of Pulp and paper industry in context to India is considered to demonstrate the proposed framework. Here, the performance of twenty-two Indian paper mills is measured by seven MCDM methods and finally, an optimal aggregated rank is acquired. The fifth chapter covers the issue of incomplete information in the MCDM problem by discussing the various imputation in the past and then proposes a method Modified D-Matrix (MoDM) method. This method can handle biased and bias free evaluations in both result-separating and result-merging contexts. The proposed method is applied to the supplier selection data, and the results were found to be in accordance with experts. Finally, the major contributions of this thesis along with concluding remarks in theoretical and application facets are presented in Chapter six. The results obtained in all the chapters indicate that the performance of MCDM can be improved significantly by integrating it with either classical MCDM or artificial intelligence techniques like Fuzzy set theory, Genetic Algorithm.

2022-09-01T00:00:00Z