Browsing by Author "Krishna Kumar Singh"

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A Newton-Like method for generalized operator equations in Banach spaces
(Kluwer Academic Publishers, 2014) D.R. Sahu; Krishna Kumar Singh; Vipin Kumar Singh
In this paper, we are concerned with the semilocal convergence analysis of a Newton-like method discussed by Bartle (Amer Math Soc 6: 827–831, 1955) to solve the generalized operator equations containing nondifferentiatble term in Banach spaces. This method has also been studied by Rheinboldt (SIAM J Numer Anal 5: 42–63, 1968). The aim of the paper is to discuss the convergence analysis under local Lipschitz condition our results extend and improve the previous ones in the sense of local Lipschitz conditions. We apply our results to solve the Fredholm-type operator equations. © 2014, Springer Science+Business Media New York.
An experimental evidence of non-ducted propagation during daytime from the ESD whistler observations at low latitude ground station Jammu
(Springer Netherlands, 1999) Lalmani; Madhu Kaul Babu; Rajou Kumar; Rajesh Singh; Krishna Kumar Singh
The propagation mechanism of low latitude daytime whistlers is investigated on the basis of ground measurements made continuously during daytime in North India at Jammu (geomag. lat. 22°26′ N; L = 1.17). On February 14, 1998 extremely small dispersion (ESD) whistlers with dispersion varying from 5-10 sec1/2 in surprisingly large numbers were recorded at Jammu during daytime in the late afternoon. The results of a study of the characteristics of ESD whistlers are presented and the discussion indicates that ESD whistlers recorded are the VLF waves radiated from the return stroke of the lightning discharge launched at the ionosphere with different initial wave normal angles, propagated upwards under either quasi-longitudinal conditions or pro-longitudinal whistler mode, turned around at different heights due to quasi-transverse propagation and received at Jammu with the dispersion of the order of 5-10 sec1/2. The validity of this suggestion has been tested by performing actual ray-tracing computations in the presence of equatorial anomaly model.
Astrophysics with compact objects: An Indian perspective, present status and future vision
(Springer, 2025) Manjari Bagchi; Prasanta Bera; Aru Beri; Dipankar Bhattacharya; Bhaswati Bhattacharyya; Sudip Bhattacharyya; Manoneeta Chakraborty; Debarati Chatterjee; Sourav Chatterjee; Indranil Chattopadhyay; Santabrata Das; Sushan Konar; Pratik Majumdar; Ranjeev Misra; Arunava Mukherjee; Banibrata Mukhopadhyay; Mayukh Pahari; Krishna Kumar Singh; Mayuresh P. Surnis; Firoza K. Sutaria; Shriharsh P. Tendulkar
Astrophysical compact objects, viz., white dwarfs, neutron stars and black holes, are the remnants of stellar deaths at the end of their life cycles. They are ideal testbeds for various fundamental physical processes under extreme conditions that are unique in nature. Observational radio astronomy with uGMRT and OORT facilities has led to several important breakthroughs in studies of different kinds of pulsars and their emission mechanisms. On the other hand, accretion processes around compact objects are at the core of Indian astronomy research. In this context, AstroSat mission revolutionized spectro-temporal observations and measurements of accretion phenomena, quasi-periodic oscillations, and jet behaviour in binary systems hosting compact objects. Moreover, recently launched XPoSat mission is set to provide an impetus to these high-energy phenomena around compact objects by enabling us to conduct polarization measurements in the X-ray band. Further, during the past decade, numerous gravitational wave signals have been observed from coalescing black holes and neutron stars in binary systems. Recent simultaneous observation of GW170817 event in both gravitational waves and electromagnetic channels has ushered in the era of multi-messenger astronomy. In the future, synergistic efforts among several world-class observational facilities, e.g., LIGO-India, SKA, TMT, etc., within the Indian astrophysics community will provide a significant boost to achieve several key science goals that have been delineated here. In general, this paper plans to highlight scientific projects being pursued across Indian institutions in this field, the scientific challenges that this community would be focusing, and the opportunities available in the coming decade. Finally, we have also mentioned the required resources, both in the form of infrastructural and human resources. © Indian Academy of Sciences 2025.
Estimation of magnetospheric electron densities from low latitude whistlers
(2008) Krishna Kumar Singh; Shubha Singh; R.P. Patel; Jaipal Singh; A.K. Singh; Ashok K. Singh; R.P. Singh; Lalmani
Dispersion analysis of whistler waves recorded at the low latitude stations have been used to estimate electron density in the equatorial region and electron contents in the flux tube aligned along the dipolar geomagnetic fields lines. This is possible only when waves have propagated along the field lines. In this paper, we report some examples of whistler waves recorded at the ground station Jammu (geom. lat. 220 26′ N, L = 1.17), India, whose analysis yield path of propagation in the range 1.62≤ L ≤ 4.39. The matched filtering and parameter estimation technique has been used to analyze these whistlers and the error in estimating the path of propagation is less than 3%. However, the computed electron densities and electron tube contents based on the analysis of these whistlers are found to be one order of magnitude smaller than the values reported by the other workers. This shows that the matching of simulated and observed dynamic spectra need not necessarily yield correct path of propagation and hence correct value of electron density. As a result either the propagation mechanism at low latitude or the analysis method of whistlers recorded at low latitudes has to be reconsidered. © 2008 IACS.
Hisslers observed during daytime in a low latitude ground station
(2009) Krishna Kumar Singh; Ravindra Pratap Patel; Balraj Kumar; Mohamad Altaf; Prince Ahmad Ganai; Abhay Kumar Singh; Ram Pal Singh; Lalmani
The observation of hisslers during daytime at low latitude station Jammu, India, is reported. The hissler elements are quasi-periodic falling tones observed during the period of hiss activity and appear in minutelong sequences with average spacing between individual elements of the order of 0.15 s. Hissler elements exhibit almost no dispersion and no complex internal structure in slope and intensity, and successive hissler elements do not overlap in time. It seems that the reported hisslers might have propagated in prolongitudinal mode. © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2009.
Hisslers: Quasi-periodic VLF noise forms observed at low latitude ground station Jammu (L = 1.17)
(2004) Krishna Kumar Singh; Rajesh Singh; R.P. Singh; A. Shyampati
This paper reports the observation of hisslers at a low latitude ground station Jammu (geomag. lat., 22°26′N), which are falling tone noises during the period of hiss activity and appear in minute-long sequences with average spacing between individual bursts of the order of 0.2 seconds and falling tones do not overlap intime. Generation and propagation mechanisms are briefly discussed. Copyright 2004 by the American Geophysical Union.
On generalized Newton method for solving operator inclusions
(2012) D.R. Sahu; Krishna Kumar Singh
In this paper, we study the existence and uniqueness theorem for solving the generalized operator equation of the form F(x) + G(x) + T(x) ∋ 0, where F is a Fréechet differentiable operator, G is a maximal monotone operator and T is a Lipschitzian operator defined on an open convex subset of a Hilbert space. Our results are improvements upon corresponding results of Uko [Generalized equations and the generalized Newton method, Math. Programming 73 (1996) 251-268].
On the convergence analysis of a newton-like method under weak smoothness assumptions
(Yokohama Publications, 2015) D.R. Sahu; Krishna Kumar Singh; Xiaopeng Zhao
The aim of the paper is to discuss the semilocal convergence analysis of a Newton-like method for solving the generalized operator equations containing nondifferentiable term in Iianach spaces under ω-type conditions. Our result extends and generalizes the corresponding result discussed by Argyros and Hiloul [Improved generalized differentiability conditions for Newton-like methods, J. Complexity, 26 (2010), 316-333]. A numerical example is discussed in support of our main result. © 2015.
Some Newton-like methods with sharper error estimates for solving operator equations in Banach spaces
(2012) D.R. Sahu; Krishna Kumar Singh; Vipin Kumar Singh
It is well known that the rate of convergence of 5-iteration process introduced by Agarwal et al. (pp. 61-79) is faster than Picard iteration process for contraction operators. Following the ideas of 5-iteration process, we introduce some Newton-like algorithms to solve the non-linear operator equation in Banach space setting. We study the semi-local as well as local convergence analysis of our algorithms. The rate of convergence of our algorithms are faster than the modified Newton method. © 2012 Sahu et al.