http://localhost:8081/jspui/handle/123456789/33 2026-10-16T22:22:39Z 2026-10-16T22:22:39Z Meena, Rohitash Kumar http://localhost:8081/jspui/handle/123456789/21140 2026-06-15T10:28:09Z 2022-05-01T00:00:00Z

Title: Maximal Density of M-sets and its applications Authors: Meena, Rohitash Kumar Abstract: Suppose 𝑀 is any given set of positive integers and we have to find the maximal density of 𝑀-sets which is denoted by 𝜇(𝑀), where 𝑀-sets are defined as the set of non–negative integers in which the difference of any two elements of 𝑀, does not lie in 𝑀. Maximal density for 𝜇(𝑀) will be given for |𝑀| ≤ 2 and some partial results are known for the case |𝑀| ≥ 3 including when 𝑀 is infinite. This number theory problem of getting maximal density will be further associated in various coloring problem of distance graphs generated by 𝑀 in Graph Theory. It is known that the reciprocal of fractional chromatic number of distance graph generated by 𝑀 is equal to the maximal density of 𝑀-sets given 𝑀 is finite. Some special family of finite sets known as almost difference Closed Sets and some infinite sets can be discussed further for which value of 𝜇(𝑀) will be find. For some of these, exact value of 𝜇(𝑀) will be known and for some we can get the bounds on 𝜇(𝑀) which will further help in finding the fractional chromatic number of the distance graph generated by that 𝑀-set. Using all the methods elucidated here to find 𝜇(𝑀) can be used further to get fractional chromatic number of distance graphs generated by these special family of sets as both are indeed the same problem.

2022-05-01T00:00:00Z Singh, Praveendra http://localhost:8081/jspui/handle/123456789/20498 2026-04-24T06:33:32Z 2024-09-01T00:00:00Z

Title: NATURE- INSPIRED OPTIMIZATION FOR INVENTORY CONTROL OF NON-INSTANTANEOUSLY DETERIORATING ITEMS Authors: Singh, Praveendra Abstract: Deterioration is a natural process for many products such as food, chemicals, fruits, vegetables, flowers, etc. This study investigates some inventory control policies pertaining to non instantaneously degradable items (NDIs). The prime aim of our research is to model inventory control problems under realistic assumptions, such as preservation technology investments, mutual spoilage reduction through inspection, demand functions sensitive to selling price, stock and advertisement frequency, time-sensitive holding cost functions, trade credit, advance payment policies, carbon reduction measures, product freshness, etc. Memory-based inventory control models via fractional calculus approaches are also explored. Due to the complexity and nonlinearity of the profit maximization problems, various nature inspired optimization techniques, viz., real coded genetic algorithm (RCGA), particle swarm optimization (PSO), differential evolution (DE), etc., are implemented to obtain optimal inventory control policies. A dimensional learning-based metaheuristic framework is developed to improve the search performance of the existing metaheuristic algorithms. The applicability of the suggested inventory control models is examined through a number of numerical illustrations. The optimal design and variability of the different inventory control descriptors have been investigated through optimization and sensitivity analysis. The investigation done on inventory control policies for NDIs is arranged into ten chapters. Chapter 1 provides an overview of the basic concepts along with methodological aspects used in inventory control of NDIs. Nature-inspired optimization approaches, viz., GA, PSO, QPSO, DE, and GWO, are described to deal with complex optimization problems of inventory systems. A review of the literature pertaining to the research conducted in this thesis is also included. In Chapter 2, the product’s freshness-sensitive demand and shelf-life dependent deterioration rate are taken into account to develop an inventory policy. Promotional efforts and price sensitivity factors are also included in the demand function. In order to reduce carbon emissions and achieve sustainable objectives, a carbon cap and trade scheme is used. The concerned inventory optimization issues are handled by using PSO, QPSO and DE metaheuristics. Chapter 3 focuses on a two-level partial trade credit policy for a finite horizon inventory problem for NDIs by considering shelf-time sensitive degradation and inflation effect. A preservation investment strategy is developed to control the deterioration. The demand is assumed to vary with inflated selling price, advertisement frequency, and downstream credit period. Due to the non-linear characteristic of the proposed optimization problem, metaheuristics, viz., PSO, DE, and grey wolf optimizer (GWO) are employed.

2024-09-01T00:00:00Z Kumar, Ankit http://localhost:8081/jspui/handle/123456789/20497 2026-04-24T06:33:12Z 2024-05-01T00:00:00Z

Title: WELL-POSEDNESS AND ASYMPTOTIC ANALYSIS OF A CLASS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS Authors: Kumar, Ankit Abstract: The literature has devoted a great deal of attention to the analysis of stochastic partial differential equations (SPDEs) since the turn of the century. The models/general frame work we consider in this thesis have various applications in the fluid dynamics models, namely, describing the interaction between reaction mechanisms, convection effects, hy drodynamics models, etc. Aside from applications, the primary objective of phenomena in f luid dynamics models is to comprehend how random perturbations to an equation might affect its properties. Recent years have seen a shift away from the confines of classical f luid mechanics in studying of fluids and their turbulent behavior. Because of the sub ject’s many significant mathematical challenges and scientific/engineering applications, researchers from various fields of mathematics, such as nonlinear partial differential equa tions, functional analysis, harmonic analysis, stochastic analysis, ergodic theory, large deviations theory, and control filtering theory, are working together to advance the field. This thesis is the outcome of the following three projects: 1. We consider a stochastic generalized Burger-Huxley (SGBH) equation under differ ent types of noises. Existence and uniqueness of solutions and invariant measures, large deviation principle (LDP), uniform large deviation principle (UDLP), and ab solute continuity of the law of the solution are discussed to understand the behavior of various properties of solutions. 2. We consider 2D-stochastic Navier-Stokes equations (SNSE) in the vorticity form driven by infinite-dimensional noise (additive) and finite-dimensional multiplicative noise. Well-posedness of 2D-SNSE in the vorticity form driven by finite-dimensional noise has been explored. Furthermore, ULDP for 2D-SNSE in the vorticity form driven by two types of noises have established. i ii 3. Well-posedness of a class of SPDEs driven by L´evy noise has been established. Furthermore, an LDP for the laws of the solutions to a class of SPDEs driven by L´evy noise has been demonstrated. This class covers a large number of fluid dynamics models. The main goal of the thesis is to explore the well-posedness of different types of SPDEs and to analyze the large time behavior of the solutions. The random forcing may differ; that is, we consider both additive and multiplicative noises (with bounded or linear growth coefficients), which can be white in time and colored in space or space-time white noise. Moreover, the thesis deals with the following questions arising in stochastic analysis: • What about the existence and uniqueness of solutions to SGBH equation, 2D-SNSE in vorticity form, and a class of SPDEs perturbed by random forcing? • What about the absolute continuity of the law of the solution to SGBH equation with respect to the Lebesgue measure and the existence of the density? • What about the LDP (Wentzell-Friedlin type) as well as ULDP for the laws of the solutions to SGBH equation and 2D-SNSE in vorticity form? • What about the LDP (Wentzell-Friedlin type) for the law of the solutions to a class of SPDEs with fully monotone coefficients driven by L´evy noise? • WhatabouttheLDP(Donsker-Varadhantype) for the occupation measure of SGBH equation, which expresses the exact rate of exponential convergence? Our procedure to tackle this question includes the knowledges about the irreducibility and strong Feller properties of the associated Markovian semigroup. • Whatabout the existence and uniqueness of invariant measures of solution to SGBH equations and their ergodic behavior?

2024-05-01T00:00:00Z Singh, Km Neeraj http://localhost:8081/jspui/handle/123456789/20496 2026-04-24T06:32:56Z 2024-07-01T00:00:00Z

Title: NEW VARIANTS OF STOCKWELL TRANSFORM WITH APPLICATION IN IMAGE PROCESSING Authors: Singh, Km Neeraj Abstract: This thesis deals with many new variants of the Stockwell transform (S-transform) in signal and image processing for solving mathematical problems. We study mathematical formulas and theorems for signal processing applications, i.e., Parseval’s formula, the inversion formula, the reproduction property, the convolution theorem, and the cross-correlation theorem. Additionally, signal reconstruction harnesses the concept of reconstructing phase from the magnitude of a signal transform. The proposed work also demonstrates the application of signal reconstruction, denoising, and compression in signal analysis. The later part of the thesis dedicates a significant amount of effort to designing various new variants of Stockwell transforms (continuous anddiscrete forms), drawinginspiration fromsome existing integral transforms. Thethesispresentsseveralmathematicalformulasforthe proposed transforms. The thesis begins with a general introduction of the proposed work and a brief motivation. A brief inspection and literature review of the existing integral transforms and their relevant mathematical results are summarized in the f irst chapter. The next chapter deals with proposing a relationship between the phase and the log-magnitude of the S-transform. These relations can be utilized for reconstructing the phase from themagnitudeoftheS-transformofanysignalandcan also be used to overcome the computational cost of the S-transform. The work also includes a relationship between partial derivatives of the real and imaginary parts of the wavelet and the S-transform for a couple of window functions. The third chapter of the thesis focuses ondesigning another transform, say, the spectral graph fractional Stockwell transform (SGFrST), to identify the structure of signals on weighted graphs with the help of SGFrWT. We propose the transform by defining a distinct form of the Laplacian matrix. First, we propose the spectral graph Stockwell transform by modulation in the graph wavelet transform and the corresponding approximation results of Stockwell coefficients. Furthermore, we present the inversion form of the proposed transform with the window function’s admissibility condition. This study also derives the ’Inner product theorem’ for a fixed window function in the vertex domain. Next, we introduce a transform for non-stationary signals named the non-isotropic angular fractional Stockwell transform (NIAFrST). Additionally, we derived important mathematical properties such as linearity, anti-linearity, translation, scaling, parity, and the conjugation property NIAFrST.

2024-07-01T00:00:00Z