Browsing by Author "Susheel Kumar"

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A computational study of binary eutectic system with convection under volumetric freezing: A Moving Boundary Problem
(Elsevier Ltd, 2024) Susheel Kumar; Vikas Chaurasiya; Jitendra Singh
A reduction in the operating time during the solidification of an eutectic alloy is one of the prime demands in front of the investigators. The classical theory of solidification was not able to offer rapid solidification of an alloy due to not account the structural property of the material. To account convection and external heat sink effect, an external volumetric heat sink is considered and it depends on the distance and time. The thermal conductivity, density, and specific heat of the mushy zone are assumed to be the linear combination of solid and liquid regions properties with a solid fraction distribution. The mathematical model accounts for the solid fraction distribution, which has a linear relationship with the temperature of the mushy zone. The analytical solution of the problem has been determined via similarity transformation. To explore the current study, numerical data of the Copper-Aluminum alloy with 5% Copper is presented. It has been found that with a volumetric heat sink, the rate of solidification becomes faster than usual. Further, the rate of heat removal from the surface accelerates. Convection enhances the rate of freezing of the eutectic alloy. The temperature of the mushy region is going up for the increasing value of the solid fraction in mushy zone, which is lying in [0,1] and when we increase the strength of volumetric heat, then the temperature profile decreases and, the first-interface and second-interface increase gradually in the whole medium. We compared the current result with Tien and Geiger's result, and it is found in good compliance. It is expected that the current study will improve the fundamental understanding of the solidification of an eutectic alloy and reduce the time for freezing, which is useful to design industrial freezing devices for alloys. © 2024 Elsevier Ltd
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
Best wavelet approximation of functions belonging to generalized lipschitz class using Haar scaling function
(Chiang Mai University, 2017) Shyam Lal; Susheel Kumar
In this paper, four new theorem on best wavelet approximation of the functions f ∈ Lipα, 0 < α < 1, f ∈ Lip(ξ, p), 1 ≤ p < ∞, have been estimated. © 2017 by the Mathematical Association of Thailand. All rights reserved.
First record of Pressastarte zakharov and Pinguiastarte kelly (mollusca: Bivalvia) from the turonian (upper cretaceous) of the bagh beds, central India
(Palaeontological Society Of India, 2015) Anand K. Jaitly; Susheel Kumar; B. Pandey
The genus Pressastarte Zakharov, 1970 and the subgenus Pinguiastarte Kelly, 1992 (Family Astardiae) have been recorded from the Turonian (Upper Cretaceous) of the Bagh Beds, central India for the first time. The Pressastarte Zakharov is represented by two species: Pressastarte (Pressastarte) lincolnshirensis Kelly 1992 and Pressastarte (Pressastarte) var. clavertensis Duff, 1978 in the Bagh Beds. Pressastarte (Pinguiastarte) senecta (Woods, 1906) and Pressastarte (Pinguiastarte) var. pressula Zakharov 1970 are the two recorded species of the subgenus Pinguiastarte. On the basis of the present record, henceforth the Pressastarte (Pinguiastarte) ranges from the Middle Jurassic (Middle Bathonian) to the Late Cretaceous (Turonian).
Fungal and mycotoxin contamination of herbal raw materials and their protection by nanoencapsulated essential oils: An overview
(Elsevier Ltd, 2022) Bijendra Kumar Singh; Shikha Tiwari; Akash Maurya; Susheel Kumar; Nawal Kishore Dubey
Presently, consumption of herbal raw materials (HRMs) has been an emerging concern owing to therapeutic potential against broad range of human diseases. However, there are various cases available reporting the fungal and mycotoxin contaminations. These HRMs after collection undergo severe extent of deterioration, leading to degradation of their active principles. Different chemical preservatives have been frequently used to protect HRMs from fungal and mycotoxin contamination, however, their indiscriminate use could lead to adverse effects on human health and environment due to residual toxicity. The use of essential oils (EOs) based formulations has been recommended as a green alternative of synthetic preservatives having greater safety profile and biodegradable nature. Nanoencapsulation maintains the stability of EOs and facilitate the controlled delivery with improvement in maintenance of bioactive principles of HRMs against fungal and mycotoxin mediated biodeterioration to boost pharmaceutical sectors. This review summarizes the pharmacological properties of some HRMs, the extent of degradation by fungal and mycotoxin contamination, preservation through nanoencapsulated EOs, mode of action, patenting of EOs as preservatives, and finally future opportunities to mitigate the associated problems. © 2021 Elsevier Ltd
Mechanistic investigations on antifungal and antiaflatoxigenic activities of chemically characterised Carum carvi L. essential oil against fungal infestation and aflatoxin contamination of herbal raw materials
(Taylor and Francis Ltd., 2022) Akash Maurya; Susheel Kumar; Bijendra Kumar Singh; Anand Kumar Chaudhari; Abhishek Kumar Dwivedy; Bhanu Prakash; Nawal Kishore Dubey
This study aimed to investigate the efficiency of chemically characterised Carum carvi essential oil (CcEO) against aflatoxin B1 (AFB1) producing strain of Aspergillus flavus (AF-LHP-WS-4) causing deterioration of herbal raw materials (HRM). GC-MS analysis of the EO revealed the presence of carvone (69.85%) as a dominant component. CcEO caused complete suppression of A. flavus growth and AFB1 secretion at 0.7 and 0.6 µL/mL, respectively. The investigation on antifungal mode of action showed that CcEO inhibited fungal growth via abrogating ergosterol biosynthesis and triggered efflux of vital cellular ions. The inhibition of AFB1 biosynthesis was attributed to the inhibition of cellular methylglyoxal (MG) biosynthesis. In addition, CcEO showed remarkable antioxidant activity (IC50 = 10.564 µL/mL) against DPPH (2,2-diphenyl-1-picrylhydrazyl) radicals. Based on overall results, it can be concluded that the CcEO may be recommended as potential antifungal agent for protection of HRM from fungal infestation and AFB1 contamination. © 2021 Informa UK Limited, trading as Taylor & Francis Group.
On generalized carleson operator with application in walsh type wavelet packet expansions
(Chiang Mai University, 2021) Shyam Lal; Susheel Kumar
In this paper, two new theorems on generalized Carleson operator for a Walsh type wavelet packet system and for periodic Walsh type wavelet packet expansion of a function f ∈ Lp [0, 1), 1 < p < ∞, have been established. © 2021 by TJM. All rights reserved.
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.
Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation
(Hindawi Limited, 2016) Shyam Lal; Susheel Kumar
A sufficient literature is available for the wavelet error of approximation of certain functions in the L2-norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a function f belonging to Lipα[a,b] class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a function f belonging to Lipα, 0 < α ≤ 1 class using the projection Pmf of its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis. © 2016 Shyam Lal and Susheel Kumar.
The age of the Nodular Limestone Formation (Late Cretaceous), Narmada Basin, central India
(Springer, 2018) Susheel Kumar; Deo Brat Pathak; Bindhyachal Pandey; Anand Kumar Jaitly; Jai Prakash Gautam
The age of the marine Nodular Limestone Formation of the Bagh Group is refined at Substage level through ammonoid and inoceramid index taxa. The study is based on the fresh collections from three well-defined successive intervals (Lower Karondia, Upper Karondia and Chirakhan members) of this formation having excellent exposures in different localities of the Narmada Basin, central India. The first record of the widely distributed Turonian ammonoid genera Spathites Kummel and Decker and Collignoniceras Breistroffer from the Nodular Limestone Formation constrained its age exclusively to Turonian. The Early Turonian species Spathites (Jeanrogericeras) aff. revelieranus (Courtiller) and Mytiloides labiatus (Sclotheim) occur in the lower part, while the Middle Turonian marker Collignoniceras cf. carolinum (d’Obrbigny) and Inoceramus hobetsensis (Nagao and Matsumoto) occurs in the upper part of the Karondia Member. The record of the index species Inoceramus teshioensis (Nagao and Matsumoto) in association with Placenticeras mintoi Vredenburg from Chirakhan Member allows a definite Late Turonian age. The present contribution is an attempt to resolve the controversies in the age of the Nodular Limestone Formation and also demarcation of the three divisions (Early, Middle and Late) of the Turonian Stage in the Narmada Basin, central India. © 2018, Indian Academy of Sciences.
Turonian (Late Cretaceous) Heterodont Subfamilies: Lucininae, Eriphylinae and Opinae (Bivalvia: Veneroida) from the Narmada Basin, central India
(Palaeontological Society Of India, 2021) A.K. Jaitly; Susheel Kumar; Bindhyachal Pandey; J.P. Gautam; Deep Narayan Tiwari
Eight species belonging to the genera/subgenera Lucina, Parvilucina (Microloripes), Callucina, Eriphyla (Lyapinella), Crassatellina and Opis of the three subfamilies Lucininae, Eriphylinae and Opinae have been reported here from the Turonian (Late Cretaceous) of Narmada Basin, India. Out of these, the two species Crassatellina minuta and Opis reticulata have been newly created. The overall characters of the subfamily Opinae, the genus Callucina and the subgenus Eriphyla (Lyapinella) have also been reviewed here. © 2021 Palaeontological Society Of India. 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.