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TRIGONOMETRIC APPROXIMATION OF FUNCTIONS BY HAUSDORFF-MATRIX PRODUCT OPERATORS
Nigam Hare Krishna,Hadish Md. 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.4
In this paper, we obtain the error approximation of a function in weighted $W(L_r, xi(t), r>1$ class by Hausdorff-Matrix (^T) product means of its Fourier series. Our main theorems generalize the results of Nigam ([18], [19]), Nigam and Sharma [20], Singh and Srivastava [28] and Lal [14]. Thus, these results become the particular cases of our theorems. Some important corollaries are also deduced from our main theorems.
MAC layer based cross-layer solutions for VANET routing: A review
Nigam, Ujjwal,Silakari, Sanjay International Journal of Computer ScienceNetwork S 2021 International journal of computer science and netw Vol.21 No.spc12
Vehicular Ad hoc Networks (VANET's) are gaining popularity in research community with every passing year due to the key role they play in Intelligent Transportation System. Their primary objective is to provide safety, but their potential to offer a variety of user-oriented services makes them more attractive. The biggest challenge in providing all these services is the inherent characteristics of VANET itself such as highly dynamic topology due to which maintaining continuous communication among vehicles is extremely difficult. Here comes the importance of routing solutions which traditionally are designed using strict layered architecture but fail to address stringent QoS requirements. The paradigm of cross-layer design for routing has shown remarkable performance improvements. This paper aims to highlight routing challenges in VANET, limitations of single-layer solutions and presents a survey of cross-layer routing solutions that utilize the information from the MAC layer to improve routing performance in VANET.
Nigam, Hare Krishna,Sharm, Ajay Department of Mathematics 2010 Kyungpook mathematical journal Vol.50 No.4
A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.
MAC layer based cross-layer solutions for VANET routing: A review
Nigam, Ujjwal,Silakari, Sanjay International Journal of Computer ScienceNetwork S 2021 International journal of computer science and netw Vol.21 No.12
Vehicular Ad hoc Networks (VANET's) are gaining popularity in research community with every passing year due to the key role they play in Intelligent Transportation System. Their primary objective is to provide safety, but their potential to offer a variety of user-oriented services makes them more attractive. The biggest challenge in providing all these services is the inherent characteristics of VANET itself such as highly dynamic topology due to which maintaining continuous communication among vehicles is extremely difficult. Here comes the importance of routing solutions which traditionally are designed using strict layered architecture but fail to address stringent QoS requirements. The paradigm of cross-layer design for routing has shown remarkable performance improvements. This paper aims to highlight routing challenges in VANET, limitations of single-layer solutions and presents a survey of cross-layer routing solutions that utilize the information from the MAC layer to improve routing performance in VANET.
Review : Enzyme Based Biosensors for Detection of Environmental Pollutants- A Review
( Vinod Kumar Nigam ),( Pratyoosh Shukla ) 한국미생물 · 생명공학회 2015 Journal of microbiology and biotechnology Vol.25 No.11
Environmental security is one of the major concerns for the safety of living organisms from a number of harmful pollutants in the atmosphere. Different initiatives, legislative actions, as well as scientific and social concerns have been discussed and adopted to control and regulate the threats of environmental pollution, but it still remains a worldwide challenge. Therefore, there is a need for developing certain sensitive, rapid, and selective techniques that can detect and screen the pollutants for effective bioremediation processes. In this perspective, isolated enzymes or biological systems producing enzymes, as whole cells or in immobilized state, can be used as a source for detection, quantification, and degradation or transformation of pollutants to non-polluting compounds to restore the ecological balance. Biosensors are ideal for the detection and measurement of environmental pollution in a reliable, specific, and sensitive way. In this review, the current status of different types of microbial biosensors and mechanisms of detection of various environmental toxicants are discussed.
A STUDY ON APPROXIMATION OF A CONJUGATE FUNCTION USING CESARO-MATRIX PRODUCT OPERATOR
H. K. Nigam,Md Hadish 경남대학교 수학교육과 2020 Nonlinear Functional Analysis and Applications Vol.25 No.4
In this paper, we establish a new theorem to study the error approximation ofa function ~ conjugate of a function (2-periodic) in weighted Lipschitz class W(Lp; p1; (!)), by Cesaro-Matrix (CT) product means of its CFS, where CFS denotes conjugateFourier series. In fact, the results obtained in the paper provide the best approximation ofthe conjugate function ~ in W(Lp; p 1; (!)) class by CT product means of its ate CFSfor the cases p > 1 and p = 1. Our results generalize six previously known results. Thus,the results of [4], [11], [12], [13], [14], [15] become the particular cases of our results. Ourtheorems provide some important corollaries.
Varshney Shagun,Nigam Abhishek,Mishra Nidhi,Pawar S. J. 한국세라믹학회 2023 한국세라믹학회지 Vol.60 No.1
Global development of nanostructured bioceramics with enhanced functionalities has provided an insight into orthopedic, dental, and other biomedical applications. The present work reports a cost-effective and eco-friendly method for the green synthesis of magnesium oxide (MgO) nanoflakes (NFs) using Ficus Racemosa leaf extract. The NFs were subjected to different characterization techniques like X-ray diffraction, field emission scanning electron microscopy, energy-dispersive spectroscopy, Fourier-transform infrared spectroscopy, ultraviolet–visible, and photoluminescence spectroscopy to detect their structural, physical, chemical, and elemental characteristics. The powder X-ray diffraction of MgO NFs revealed the single phase with an average crystallite size of 24 nm. The Williamson–Hall plot also confirmed the crystallite size as 28 nm, nearly the same as obtained through Debye–Scherrer (24 nm) formula. Field emission scanning electron microscopy revealed the flake-like structure with an average thickness of 3 nm, and the average length was depicted as 280 nm. The ultraviolet–visible absorption spectra of MgO NFs showed a maximum wavelength of around 275 nm, and photoluminescence spectroscopy was used to observe the fluorescent properties. The antibacterial activity of MgO NFs against both S. aureus and E. coli bacteria demonstrated a significant reaction, making it a promising agent for several biomedical applications.