Browsing by Author "Sudhir Kumar Mishra"

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An error estimation of absolutely continuous signals and solution of Abel's integral equation using the first kind pseudo-Chebyshev wavelet technique
(Elsevier B.V., 2025) Susheel Kumar; A. K. AWASTHI; Sudhir Kumar Mishra; Harish Chandra Yadav; n. Abhilasha; Shyam N. Lal
This paper introduces a novel computational strategy for addressing challenges in approximation theory. It focuses on the use of first-kind pseudo-Chebyshev wavelet approximations and the methodology and evaluation of the error for a specific function are outlined, along with practical instances to showcase the method's effectiveness and efficiency. This approach is motivated by the need for highly efficient and precise methods for function representation and the error reduction in this domain. The paper also establishes the error of a function associated with the class of absolutely continuous functions using first-kind pseudo-Chebyshev wavelets via orthogonal projection operators, highlighting their precision and theoretical optimality within the domain of wavelet analysis. Additionally, the use of wavelet approximation to solve Abel's integral equation is demonstrated by computing the approximate solution using first kind pseudo-Chebyshev wavelet. © 2024 The Authors
Climate Change Impact on Flood Frequencies Using Geospatial Modeling
(Springer Science and Business Media Deutschland GmbH, 2025) Kanhu Charan Panda; Ramesh Mandir Singh; Pradosh Kumar Paramaguru; Uday Pratap Singh; Sudhir Kumar Mishra; Gaurav Singh Vishen
It is anticipated that climate change will significantly affect flood frequencies, with more frequent and intense floods likely to occur in many parts of the world. Geospatial modeling can be used to assess possible effects of climate change on flooding frequencies, providing valuable information for flood risk management and adaptation planning. The chapter depicts the current state of knowledge on the use of geospatial modeling to assess the climate change impact on flood frequencies. It discusses the key mechanisms through which climate change can affect floods, the range of geospatial modeling approaches that can be used to assess the impact of climate change on flood frequencies, and the challenges and limitations of using geospatial modeling for this purpose. A case study was included in the chapter to demonstrate the use of advanced geospatial technique to access the impact of climate change on flood frequencies. The chapter concludes by discussing the future directions for research on the use of geospatial modeling to assess the climate change impact on flood frequencies. This includes the development of more sophisticated modeling approaches, the use of ensemble modeling to account for uncertainty, and the integration of geospatial modeling with other risk assessment tools. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
PSEUDO CHEBYSHEV WAVELETS IN TWO DIMENSIONS AND THEIR APPLICATIONS IN THE THEORY OF APPROXIMATION OF FUNCTIONS BELONGING TO LIPSCHITZ CLASS
(RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2024) Susheel Kumar; Gaurav Kumar Mishra; Sudhir Kumar Mishra; Shyam Lal
In 2022, the concept of one-dimensional pseudo Chebyshev wavelets was introduced by the authors. Building upon this research, the present article extends the study to two-dimensional pseudo Chebyshev wavelets. It defines and verifies the two-dimensional pseudo Chebyshev wavelet expansion for a functions of two variables. The paper proposes a novel algorithm utilizing the two-dimensional pseudo Chebyshev wavelet method to address computation problems in approximation theory. To demonstrate the validity and applicability of the results, the methods are illustrated through an example and compared with well-known Chebyshev wavelet methods. The research includes error analysis and convergence analysis for signals f belonging to the Lip(α,β)Ω(ℝ), where Ω2 is a finite connected domain in ℝ2, classes using these wavelets. Furthermore, the paper estimates the error of approximation for a functions in the Lipschitz class using orthogonal projection operators of the two-dimensional pseudo Chebyshev wavelets. These findings represent significant advancements in wavelet analysis. © 2024, RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES. All rights reserved.
Two dimensional pseudo-Chebyshev wavelets and their application in the theory of approximation of functions belonging to Hölders class
(University of Nis, 2025) Susheel Kumar; Sudhir Kumar Mishra; Aditya Kumar Awasthi; Shyam N. Lal
For the first time in 2022, the authors introduced the notion of pseudo-Chebyshev wavelets in the context of one dimension. Continuing the study in advance sense, in this article, two dimensional pseudo Chebyshev wavelets are introduced. Two dimensional pseudo Chebyshev wavelet expansion of a function of two variable is defined and verified. This research paper introduces a novel algorithm based on the two dimensional pseudo Chebyshev wavelet method to address computation problems in approximation theory. The methods are illustrated by an example and compared with prominent Chebyshev wavelet methods to demonstrate the validity and applicability of the results. The error analysis and convergence analysis of a functions in the Hölder classes have been studied by this wavelets. More over the error of approximation of functions of Holder’s class have been estimated by an orthogonal projection operators of its two dimensional pseudo Chebyshev wavelets. The results of this paper are the significant developments in wavelet analysis. © 2020 Mathematics Subject Classification.