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AN EFFICIENT AND STABLE ALGORITHM FOR NUMERICAL EVALUATION OF HANKEL TRANSFORMS
Singh, Om P.,Singh, Vineet K.,Pandey, Rajesh K. The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.5
Recently, a number of algorithms have been proposed for numerical evaluation of Hankel transforms as these transforms arise naturally in many areas of science and technology. All these algorithms depend on separating the integrand $rf(r)J_{\upsilon}(pr)$ into two components; the slowly varying component rf(r) and the rapidly oscillating component $J_{\upsilon}(pr)$. Then the slowly varying component rf(r) is expanded either into a Fourier Bessel series or various wavelet series using different orthonormal bases like Haar wavelets, rationalized Haar wavelets, linear Legendre multiwavelets, Legendre wavelets and truncating the series at an optimal level; or approximating rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. The purpose of this communication is to take a different approach and replace rapidly oscillating component $J_{\upsilon}(pr)$ in the integrand by its Bernstein series approximation, thus avoiding the complexity of evaluating integrals involving Bessel functions. This leads to a very simple efficient and stable algorithm for numerical evaluation of Hankel transform.
AN EFFICIENT AND STABLE ALGORITHM FOR NUMERICAL EVALUATION OF HANKEL TRANSFORMS
Om P. Singh,V. K. Singh,R. K. Pandey 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.5
Recently, a number of algorithms have been proposed for nu-merical evaluation of Hankel transforms as these transforms arise natu-rally in many areas of science and technology. All these algorithms depend on separating the integrand rf(r)Ju(pr) into two components; the slowly varying component rf(r) and the rapidly oscillating component Ju(pr). Then the slowly varying component rf(r) is expanded either into a Fourier Bessel series or various wavelet series using di®erent orthonormal bases like Haar wavelets, rationalized Haar wavelets, linear Legendre multiwavelets,Legendre wavelets and truncating the series at an optimal level; or approxi-mating rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. The purpose of this communication is to take a different approach and replace rapidly oscillating component Ju(pr) in the integrand by its Bernstein series approximation, thus avoiding the complexity of evaluating integrals involving Bessel functions. This leads to a very simple effcient and stable algorithm for numerical evaluation of Hankel transform.
Pramod K. Rajak,Vijay K. Singh,Asha L. Singh,Narendra Kumar,Om P. Kumar,Vishvajeet Singh,Aniruddha Kumar,Rai Ankita,Shweta Rai,Amiya S. Naik,Prakash K. Singh 한국지질과학협의회 2020 Geosciences Journal Vol.24 No.4
The present study is an attempt to know the temporal and spatial distribution of geochemical components in the lignite deposit of Kapurdi, Barmer Basin (Rajasthan). Lignite samples have been subjected to proximate, ultimate and elemental analyses, and determination of mineral carbon (MINC%). Besides, various minerals and functional groups have been analyzed through X-ray diffraction (XRD) and Fourier transforms infrared spectroscopy (FTIR). Selected environmentally sensitive and potential hazardous elements like Cu, Cd, Zn, Ni, Cr, Pb, Mn, Al, Fe and Co are determined using atomic absorption spectrophotometer (AAS). To know the association of minerals with organic matter, scanning electron microscopy-energy dispersive spectroscopy (SEM-EDS) has also been carried out. The concentration of Co, Ni, Cd, Pb, Na, and K is high when compared with world average and is main concern for the environmental and health hazards. The elements like Fe, Ca, Mg, Zn, and Pb have shown increasing trend from top to bottom of the lignite seam with some fluctuations in the values in few bands whereas others do not follow a definite trend of variation along the seam profile.
Study of a novel phenolic-ester as antioxidant additive in lube, biodiesel and blended diesel
Raj K. Singh,Aruna Kukrety,Om P. Sharma,Siddharth Baranwal,Neeraj Atray,Siddharth S. Ray 한국공업화학회 2016 Journal of Industrial and Engineering Chemistry Vol.37 No.-
A novel phenolic-ester denoted as Bz–4–tBz was synthesized by esterification reaction between the1,2,4,5-benzenetetracarboxylic acid and 3,5-di-tert-butyl-4-hydroxybenyl alcohol in N,N0-dimethyla-cetamide using N,N0-dicyclohexylcarbodiimide as catalyst. The Bz–4–tBz was evaluated as antioxidantin polyol by the rotatory bomb oxidation test while the Rancimat test were also done for evaluating theantioxidant potential in the biodiesel (B100) and blended diesel (B20). The RBOT time of polyol wasobserved to be increased from 6.72 min to 17.42 min when blended 2000 mg/kg Bz–4–tBz in it. Theoxidation stability of biodiesel (B100) and blended diesel (B20) was also found to be increased.
Raj K. Singh,Piyush Gupta,Om P. Sharma,Siddharth S. Ray 한국공업화학회 2015 Journal of Industrial and Engineering Chemistry Vol.24 No.-
Cellulose fatty esters with different fatty acids as lauric, myristic, palmitic, stearic and oleic acid having same degrees of substitution (DS 2.0) were prepared homogeneously using 1-butyl-3-methylimida- zolium chloride ([C4mim]+Cl). All samples were characterized by IR and NMR. The triboevaluation in terms of average friction coefficient was done by nanotribometer using 3000 ppm solution of each ester in polyol (pentaerythritol tetraoleate) which is taken as biolube reference fluid. The cellulose esters are found to show antifriction character in the order as myristate > palmitate > laurate > stearate > oleate.