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FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

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Acta Mathematica Scientia 2016年第3期36卷 957-970页

作者： Dhananjay gopal Mujahid ABBAS Deepesh Kumar patel Calogero VETRO Department of Applied Mathematics&Humanities S.V.National Institute of TechnologySurat-395007GujaratIndia Department of Mathematics and Applied Mathematics University of PretoriaLynnwood RoadPretoria 0002South Africa Department of Mathematics King AbdulAziz UniversityP.O.Box 80203 Jeddah 21589Saudi Arabia Department of Mathematics Visvesvaraya National Institute of Technology Nagpur-440010MaharashtraIndia Universita degli Studi di Palermo Dipartimento di Matematica e InformaticaVia Archirafi34-90123 PalermoItaly

In this paper, we introduce new concepts of a-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from a-GF-contractions given in [8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an application to nonlinear fractional differential equation are given to illustrate the usability of the new theory.

关键词： fixed points nonlinear fractional differential equations periodic points

Manifestation of earthquake preparation zone in the ionosphere before 2021 Sonitpur,Assam earthquake revealed by GPS-TEC data

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Geodesy and Geodynamics 2022年第3期13卷 230-237页

作者： gopal Sharma North Eastern Space Applications Centre Umiam793103MeghalayaIndia

Global Positioning System(GPS)Continuously Operating Reference Station(CORS)data analysis shows that the ionosphere’s electron density variability is linked to the deformation and stress accumulation in the Earth’s *** in ionosphere total electron content(TEC)variability before 2021 M6.4 Sonitpur,Assam earthquake were detected using L1 and L2 GPS frequencies that showed three distinct abnormalities on April 3,9,10,***’s correlation coefficient(r)of TEC decreases in the CORS that lies away from the earthquake epicenter,indicating the possibilities of a positive relationship between TEC variability and earthquake *** concentration also decreases towards the epicenter within the earthquake preparation zone(EPZ).It is also observed that the Pearson’s correlation coefficient(r)of TEC decreases linearly near the *** study demonstrates the possibilities of determining the TEC anomalous zone in the ionosphere that coincides with the EPZ in the crustal *** research indicated the possibilities of magnitude estimation of an impending earthquake based on the TEC anomalous zone in the ionosphere using closely spaced dense CORS network data.

关键词： GPS TEC Sonitpur earthquake Ionosphere perturbation TEC anomaly Magnitude estimation

Approaches for enhancing the photocatalytic activities of barium titanate:A review

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Journal of Energy Chemistry 2022年第10期31卷 160-188,I0004页

作者： gopal Panthi Mira Park Carbon Composite Energy Nanomaterials Research Center Woosuk UniversityWanjuChonbuk 55338Republic of Korea Woosuk Institute of Smart Convergence Life Care(WSCLC)Woosuk UniversityWanjuChonbuk 55338Republic of Korea

Barium titanate(Ba TiO_(3)),a dielectric/ferroelectric semiconductor with perovskite structures is the most widely used photocatalyst in the field of environmental applications due to its low-cost,chemical stability,and *** types and forms of Ba TiO_(3)have shown their great potential toward the significant photocatalytic reactions owing to the several beneficial properties,including appropriate band positions,high oxygen vacancies,multiple crystal structures,the feasibility of size and morphology tailoring,spontaneous polarization,rapid migration of photogenerated charge carriers,and band ***,the large band gap and recombination of photogenerated charge carriers limit the overall photocatalytic efficiency of Ba TiO_(3).These difficulties can be further overcome by modifying the electronic band structure of Ba TiO_(3)to broaden its absorption to the visible region of the ***,this review encompasses various strategies,including modification of sizes and morphologies of particles by varying the reaction time and synthesis temperature,doping with non-metals/metals,loading with noble metals,and forming heterojunctions for enhancing the photocatalytic activities of Ba TiO_(3)-based photocatalysts possessing the effective capability of charge carrier separation,trapping and their transfer to the surface of ***,this review highlights the photocatalytic applications of Ba TiO_(3)-based photocatalysts along with the proposed mechanism in dyes/drugs degradation,H_(2)production,and bacteria killing.

关键词： Electrospinning BaTiO_(3)-photocatalyst Ferroelectricity Heterojunction Environmental remediation

Diagnosis of Helicobacter pylori : What should be the gold standard?

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World Journal of Gastroenterology 2014年第36期20卷 12847-12859页

作者： Saurabh Kumar patel Chandra Bhan Pratap Ashok Kumar Jain Anil Kumar Gulati gopal Nath Department of Microbiology Institut of Medical Sciences Banaras Hindu University Varanasi U221005 India Department of Gastroenterology Institute of Medical Sciences Banaras Hindu University Varanasi UP221005 India Department of Microbiology Institutof Medical Sciences Banaras Hindu University Varanasi U221005 India

Since the discovery of Helicobacter pylori (H. pylori) in 1983, numerous detection methods for the presence of the bacterium have been developed. Each one of them has been associated with advantages and disadvantages. Noninvasive tests such as serology, 13C urea breath test (UBT) and stool antigen tests are usually preferred by the clinicians. Serology has its own limitation especially in endemic areas while 13C UBT is technically very demanding. The stool antigen detection method, although specific, is usually associated with poor sensitivity. The 13C UBT is believed to be specific, but with present revelation of the fact that stomach is colonized by many other urease producing bacteria makes it questionable. Histology, culture, rapid urease test and polymerase chain reaction (PCR) are the tests which are carried out on antral biopsies collected by invasive means. Histology has been proposed to be very sensitive and specific but the question is how by simply looking the morphology of the bacteria in the microscope, one can claim that the curved bacterium is exclusively H. pylori. Rapid urease test (RUT), the doctor’s test, is also challenged because the presence of other urease producing bacteria in the stomach cannot be denied. Moreover, RUT has been reported with poor sensitivity specially, when density of the bacterium is low. Isolation of H. pylori is essential to investigate its growth requirements, antibiotic susceptibility testing, studying virulence factor to develop vaccine and many more explorations. It has also got several disadvantages i.e., special condition for transporting, media, incubation and few days waiting for the colonies to appear, apart from the speed essentially needed to process the specimens. Till date, majority of the microbiological laboratories in the world are not equipped and trained to isolate such fastidious bacterium. The option left is PCR methods to detect H. pylori’s DNA in gastr

关键词： Helicobacter pylori review Invasive tests Non-invasive tests Gold standard Polymerase chain reaction detection Nested polymerase chain reaction

Hydrothermal synthesis of Zn-Mg-based layered double hydroxide coatings for the corrosion protection of copper in chloride and hydroxide media

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International Journal of Minerals,Metallurgy and Materials 2021年第12期28卷 1991-2000页

作者： Nikhil gopal Ji Rajiv Prakash School of Materials Science and Technology Indian Institute of Technology(BHU)VaranasiVaranasi-221005Uttar PradeshIndia Centre for advanced studies Dr.APJAKTU LucknowU.P.-226031India

Layered double hydroxides(LDHs)hinder corrosive elements by forming a double layer and locking them between its ***,LDHs are interesting materials in corrosion *** this work,Zn-Mg-based LDHs are grown over a copper substrate by using a hydrothermal *** types of Zn-Mg-based LDH coating are prepared based on hydrothermal reaction *** types are characterized through Fourier transform infrared spectroscopy,Raman spectroscopy,high-resolution scanning electron microscopy,energy dispersive X-ray analysis,atomic force microscopy,and X-ray *** show that the two types of LDH coating are successfully grown on copper;however,they differ in thickness and structural *** testing of the LDH coatings is executed in 0.1 M Na Cl and 0.1 M Na OH through alternating current impedance measurements and Tafel polarization *** show that L48 gives more than 90%protection to copper,which is higher than the protection provided by ***,both LDH coatings(L24 and L48)are more effective corrosion inhibitors in Na Cl than in Na OH,suggesting that the LDH coatings can more efficiently exchange Cl ions than OH ions.

关键词： corrosion coating copper

Mysteries of R^ik=0： A novel paradigm in Einstein＇s theory of gravitation

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Frontiers of physics 2014年第1期9卷 98-112页

作者： Ram gopal Vishwakarma Unidad Academica de Matemdticas Universidad Autdnoma de Zacatecas C.P. 98068 Zacatecas ZAC Mexico

Despite a century-long effort, a proper energy-stress tensor of the gravitational field, could not have been discovered. Furthermore, it has been discovered recently that the standard formulation of the energy-stress tensor of matter, suffers from various inconsistencies and paradoxes, concluding that the tensor is not consistent with the geometric formulation of gravitation [Astrophys. Space Sci., 2009, 321： 151; Astrophys. Space Sei., 2012, 340： 373]. This perhaps hints that a consistent theory of gravitation should not have any bearing on the energy-stress tensor. It is shown here that the so-called ＂vacuum＂ field equations Rik = 0 do not represent an empty spacetime, and the energy, momenta and angular momenta of the gravitational and the matter fields are revealed through the geometry, without including any formulation thereof in the field equations. Though, this novel discovery appears baffling and orthogonal to the usual understanding, is consistent with the observations at all scales, without requiring the Moreover, the resulting theory circumvents the besides explaining some unexplained puzzles. hypothetical dark matter, dark energy or inflation long-standing problems of the standard cosmology

关键词： general relativity and gravitation - fundamental problems and general formalism cos-mological observations

Mysteries of the geometrization of gravitation

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Research in Astronomy and Astrophysics 2013年第12期13卷 1409-1422页

作者： Ram gopal Vishwakarma Unidad Acad'emica de Matem'aticas Universidad Aut'onoma de Zacatecas

As we now know, there are at least two major difficulties with general rel- ativity （GR）. The first one is related to its incompatibility with quantum mechanics, in the absence of a consistent, widely accepted theory that combines the two theo- ries. The second problem is related to the requirement of the dark sectors-inflaton, dark matter and dark energy by the energy-stress tensor, which are needed to explain a variety of astronomical and cosmological observations. Research has indicated that the dark sectors themselves do not have any non-gravitational or laboratory evidence. Moreover, the dark energy poses, in addition, a serious confrontation between funda- mental physics and cosmology. Guided by theoretical and observational evidences, we are led to an idea that the source of gravitation and its manifestation in GR should be modified. The result is in striking agreement with not only the theory, but also the ob- servations, without requiring the dark sectors of the standard approach. Additionally, it provides natural explanations to some unexplained puzzles.

关键词： general relativity and gravitation -- fundamental problems and generalformalism -- cosmology: observations

Pseudomonas fluorescens-like bacteria from the stomach:A microbiological and molecular study

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World Journal of Gastroenterology 2013年第7期19卷 1056-1067页

作者： Saurabh Kumar patel Chandra Bhan Pratap Ajay Kumar Verma Ashok Kumar Jain Vinod Kumar Dixit gopal Nath Department of Microbiology Institute of Medical SciencesBanaras Hindu UniversityVaranasi UP 221005India Department of Gastroenterology Institute of Medical SciencesBanaras Hindu UniversityVaranasi UP 221005India

AIM:To characterize oxidase-and urease-producing bacterial isolates,grown aerobically,that originated from antral biopsies of patients suffering from acid peptic ***:A total of 258 antral biopsy specimens were subjected to isolation of bacteria followed by tests for oxidase and urease production,acid tolerance and aerobic *** selected isolates were further characterized by molecular techniques *** for 16S rRNA using universal eubacterial and HSP60 gene specific *** amplicons were subjected to restriction analysis and partial sequencing.A phylogenetic tree was generated using unweighted pair group method with arithmetic mean(UPGMA) from evolutionary distance computed with bootstrap test of *** of acidity tolerance of bacteria isolated from antrum was performed using hydrochloric acid from 10-7 mol/L to 10-1 mol/***:Of the 258 antral biopsy specimens collected from patients,179(69.4%) were positive for urease production by rapid urease test and 31%(80/258) yielded typical Helicobacter pylori(***) after 5-7 d of incubation under a microaerophilic environment.A total of 240(93%) antral biopsies yielded homogeneous semi-translucent and small colonies after overnight *** partial 16S rRNA sequences revealed that the isolates had 99% similarity with Pseudomonas species.A phylogenetic tree on the basis of 16S rRNA sequences denoted that JQ927226 and JQ927227 were likely to be related to Pseudomonas fluorescens(***).On the basis ofHSP60 sequences applied to the UPGMA phylogenetic tree,it was observed that isolated strains in an aerobic environment were likely to be ***,and HSP60 sequences had more discriminatory potential rather than 16S rRNA ***,this bacterium was acid tolerant for hours at low ***,a total of 250(96.9%) genomic DNA samples of 258 biopsy specimens and DNA from 240 bacterial isolates were positive for the 613 bp amplicons by targetin

关键词： Antral biopsy Helicobacter pylori Pseudomonas fluorescens HSP60 Nested polymerase chain reaction Acid-tolerant bacteria

Nonlinear mixing-based terahertz emission in inclined rippled density plasmas

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Chinese Physics B 2023年第6期32卷 384-390页

作者： K gopal A P Singh S Divya Rajdhani College Department of Physics&ElectronicsUniversity of DelhiNew DelhiIndia Computational Plasma Dynamics Laboratory Rajdhani CollegeDepartment of Physics&ElectronicsUniversity of DelhiNew DelhiIndia

We propose to investigate the THz field generation using nonlinear mixing mechanism of laser beat wave with inclined rippled density *** laser pulses with frequencies(ω_(1),ω_(2)) and wave vectors(k_(1),k_(2)) co-propagate and resultant laser beat wave forms at beat frequency(ω_(1)-ω_(2)).Laser beat wave imparts a nonlinear force on the ambient electrons and pushes them outward with nonlinear velocity v_(NL).Coupling of induced density perturbation and nonlinear velocity v_(NL)generates nonlinear currents at laser beat frequency that further generates electromagnetic field E_((ω_(1)-ω_(2))) in terahertz(THz)*** the present scheme,density ripples are introduced at an angle with respect to laser propagation and flat Gaussian index(f) is introduced in laser field profile that transform curved top of Gaussian field envelope into flat top field *** combined effect of flat laser pulses with inclined density ripples in plasmas shows 10-fold enhancement in THz field amplitude when flat-Gaussian index(f) varies from 1 to ***,the THz field intensifies when density ripples inclination increases upto a certain angle and then decreases.

关键词： terahertz inclined ripple flat laser laser plasma interaction