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Totally Anisotropic Cosmological Models with Bulk Viscosity for Variable G and Λ

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Journal of Modern Physics 2012年第1期3卷 9-15页

作者： Shri Ram Manish K. Singh manoj K. verma 不详

Einstein's field equations with variable gravitational and cosmological constants are considered in the presence of bulk viscous fluid for the totally anisotropic Bianchi type II space-time in such a way as to preserve the energy momentum tensor. We have presented solutions of field equations which represent expanding, shearing and non-rotating cosmological models of the universe. The physical behaviours of the models are discussed .We observe that the results obtained match with recent observations of SNIa.

关键词： Bianchi II Cosmology Hubble Parameter Bulk Viscosity Variable G and Λ

Treatment Initiation among Patients with Multidrug Resistant Tuberculosis in Bhopal District, India

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Journal of Tuberculosis Research 2017年第4期5卷 237-242页

作者： Hemant Deepak Shewade Arun M. Kokane Akash Ranjan Singh manoj verma Malik Parmar Sanjay Singh Chahar manoj Tiwari Sheeba Naz Khan Mukesh Nagar Sanjai Kumar Singh Pradeep Kumar Mehra Ajay M. V. Kumar International Union against Tuberculosis and Lung Disease (The Union) South-East Asia Office New Delhi India Department of Community Medicine and Family Medicine All India Institute of Medical Sciences (AIIMS) Bhopal India State TB cell Department of Health and Family Welfare Bhopal India World Health Organization Country Office in India New Delhi India International Union against Tuberculosis and Lung Disease (The Union) Paris France

Revised national tuberculosis control programme in India has limited co-hort-wise information about what happens to patients diagnosed with multidrug resistant TB (MDR-TB). We determined the pre-treatment loss to follow-up (non-initiation of treatment by programme within 6 months of diagnosis) and time from diagnosis to treatment initiation in Bhopal district, central India (2014). Pre-treatment loss to follow-up was 13% (0.95 CI: 7%, 23%), not significantly different from the national estimates (18%) and median time to initiate treatment was seven days, lower than that reported elsewhere in the country. Bhopal was performing well with reference to time to treatment initiation in programmatic settings.

关键词： Multidrug-Resistant Tuberculosis Operational Research Pre-Treatment Attrition Diagnosis and Treatment Pathway Initial Loss to Follow-Up

An analytical solution of multi-dimensional space fractional diffusion equations with variable coefficients

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第1期12卷 229-255页

作者： Pratibha verma manoj Kumar Department of Mathematics Motilal Nehru National Institute of Technology Allahabad Prayagraj 211004 Uttar PradeshIndia

In this paper,we have considered the multi-dimensional space fractional diffusion equations with variable *** fractional operators(derivative/integral)are used based on the Caputo *** study provides an analytical approach to determine the analytical solution of the considered problems with the help of the two-step Adomian decomposition method(TSADM).Moreover,new results have been obtained for the existence and uniqueness of a solution by using the Banach contraction principle and a fixed point *** have extended the dimension of the space fractional diffusion equations with variable coefficients into ***,the generalized problems with two different types of the forcing term have been included demonstrating the applicability and high efficiency of the TSADM in comparison to other existing numerical *** diffusion coefficients do not require to satisfy any certain conditions/restrictions for using the *** are no restrictions imposed on the problems for diffusion coefficients,and a similar procedures of the TSADM has followed to the obtained analytical solution for the multi-dimensional space fractional diffusion equations with variable coefficients.

关键词： Caputo fractional operators space fractional diffusion equations Riesz derivative two-step Adomian decomposition method fixed point theorem

An analytical solution with existence and uniqueness conditions for fractional integro-differential equations

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International Journal of Modeling, Simulation, and Scientific Computing 2020年第5期11卷 147-169页

作者： Pratibha verma manoj Kumar Department of Mathematics Motilal Nehru National Institute of Technology AllahabadPrayagraj-211004Uttar PradeshIndia

This study aims to apply the two-step Adomian decomposition method(TSADM)to find an analytical solution of integro-differential equations for fractional order without discretization/approximation with less number of iterations and reduce the computational ***,we have established the results for the existence and uniqueness of a solution with the help of some fixed point theorems and the Banach contraction ***,the method is demonstrated on different test examples arising in real life *** is concluded that the TSADM provides exact solution of the fractional integro-differential equations in one *** the same time,the other existing methods furnish an approximate solution and require lots of computation to solve the problem applying discretization/approximation on fractional operators.

关键词： Caputo fractional derivative two-step Adomian decomposition method integro-differential equation fixed point theorem

Positive solutions and stability of fuzzy Atangana–Baleanu variable fractional differential equation model for a novel coronavirus (COVID-19)

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第6期12卷 205-229页

作者： Pratibha verma manoj Kumar Department of Mathematics Motilal Nehru National Institute of Technology Allahabad Prayagraj 211004 Uttar PradeshIndia

This work provides a new fuzzy variable fractional COVID-19 model and uses a variablefractional operator, namely, the fuzzy variable Atangana–Baleanu fractional derivativesin the Caputo sense. Next, we explore the proposed fuzzy variable fractional COVID-19 model using the fixed point theory approach and determine the solution’s existenceand uniqueness conditions. We choose an appropriate mapping and with the help ofthe upper/lower solutions method. We prove the existence of a positive solution for theproposed fuzzy variable fractional COVID-19 model and also obtain the result on theexistence of a unique positive solution. Moreover, we discuss the generalized Hyers–Ulam stability and generalized Hyers–Ulam–Rassias stability. Further, we investigate theresults on maximum and minimum solutions for the fuzzy variable fractional COVID-19model.

关键词： Novel coronavirus(COVID-19) variable Atangana–Baleanu fractional derivative Mittag–Leffler kernel existence and uniqueness fixed point theorems Hyers–Ulam stability

Analysis on Krasnoselskii’s fixed point theorem of fuzzy variable fractional differential equation for a novel coronavirus(COVID-19)model with singular operator

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第3期12卷 150-166页

作者： Pratibha verma manoj Kumar Anand Shukla Department of Mathematics Motilal Nehru National Institute of Technology Allahabad Prayagraj 211004 Uttar PradeshIndia Department of Mathematics Wollega UniversityEthiopia

The fuzzy variable fractional differential equations(FVFDEs)play a very important role in mathematical modeling of *** scientists are studying and developing several aspects of these COVID-19 *** existence and uniqueness of the solution,stability analysis are the most common and important study *** is no study in the literature to establish the existence,uniqueness,and UH stability for fuzzy variable fractional(FVF)order COVID-19 *** to high demand of this study,we investigate results for the existence,uniqueness,and UH stability for the considered COVID-19 model based on FVFDEs using a fixed point theory approach with the singular ***,discuss the maximal/minimal solution for the FVFDE of the COVID-19 model.

关键词： Novel coronavirus(COVID-19) variable Caputo fractional derivative fixed point theorem existence and uniqueness Ulam-Hyers stability

Ulam-Hyers stability and analytical approach for m-dimensional Caputo space-time variable fractional order advection-dispersion equation

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International Journal of Modeling, Simulation, and Scientific Computing 2022年第1期13卷 131-174页

作者： Pratibha verma manoj Kumar Anand Shukla Department of Mathematics Motilal Nehru National Institute of Technology Allahabad Prayagraj–211004 Uttar PradeshIndia†Department of Mathematics Wollega UniversityNekemteEthiopia

This article introduces the computational analytical approach to solve the m-dimensional space-time variable Caputo fractional order advection–dispersion equation with the Dirichlet boundary using the two-step Adomian decomposition method and obtain the exact solution in just one ***,with the help of fixed point theory,we study the existence and uniqueness conditions for the positive solution and prove some new ***,obtain the Ulam–Hyers stabilities for the proposed *** gen-eralized examples are considered to show the method’s applicability and compared with other existing numerical *** present method performs exceptionally well in terms of efficiency and ***,we solved both examples using the two most well-known numerical methods and compared them with the TSADM solution.

关键词： Fixed point theorems space-time variable Caputo’s fractional operators advection-dispersion equation Ulam-Hyers stability two-step Adomian decomposition method

Analyzing Effect of Demand Rate on Safety of Systems with Periodic Proof-tests

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International Journal of Automation and computing 2007年第4期4卷 335-341页

作者： manoj Kumar A.K.verma A.Srividya Control Instrumentation Division Bhabha Atomic Research CentreTrombayMumbai 400085India Reliability Engineering Group Indian Institute of Technology BombayPowaiMumbai 400076India

Quantitative safety assessment of safety systems plays an important role in decision making at all stages of system lifecycle, i.e., design, deployment and phase out. Most safety assessment methods consider only system parameters, such as configuration, hazard rate, coverage, repair rate, etc. along with periodic proof-tests （or inspection）. Not considering demand rate will give a pessimistic safety estimate for an application with low demand rate such as nuclear power plants, chemical plants, etc. In this paper, a basic model of IEC 61508 is used. The basic model is extended to incorporate process demand and behavior of electronic- and/or computer-based system following diagnosis or proof-test. A new safety index, probability of failure on actual demand （PFAD） based on extended model and demand rate is proposed. Periodic proof-test makes the model semi-Markovian, so a piece-wise continuous time Markov chain （CTMC） based method is used to derive mean state probabilities of elementary or aggregated state. Method to determine probability of failure on demand （PFD）（IEC 61508） and PFAD based on these state probabilities are described. In example, safety indices of PFD and PFAD are compared.

关键词： Probability of failure on demand fail safe Markov model continuous time Markov chain IEC 61508 diagnosis repair proof-test demand safety system.

HPTLC-MS as a Neoteric Hyphenated Technique for Separation and Forensic Identification of Drugs

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Journal of Analytical Sciences, Methods and Instrumentation 2018年第1期8卷 1-15页

作者： Kanak Lata verma manoj Kumar Amar Pal Singh Regional Forensic Science Laboratory Government of NCT of Delhi New Delhi India Forensic Science Post Graduate Course Department of Anthropology University of Delhi New Delhi India

Drugs are traditionally been identified on basis of chromatographic-spectroscopic hyphenated techniques in instrumental analysis. Gas chromatography (GC) and Liquid chromatography (LC) hyphenated with mass spectroscopy (MS) i.e. GC-MS and LC-MS give reliable and confirmatory results in drugs identification. In the present work the novel hyphenated technique High Performance Thin Layer Chromatography-Mass Spectroscopy (HPTLC-MS) has been used. This technique provides efficient, quick and simple method for identification and separation of Narcotic drugs and psychotropic substances. The drugs under study are Papaverine, Methadone, Cocaine, Ketamine, Caffeine, Codeine, Diazepam, Thebaine, Heroin, Methamphetamine, Carbamazepine, Morphine, Narcotine and Ephedrine. The present study comprising of sixteen drugs has been carried out on CAMAG HPTLC instrument with automatic sampling. Thin layer chromatography (TLC) plates were developed in various solvent systems, scanned under TLC scanner and the results in terms of Retention Factor (Rf value) and UV spectrum (λmax) are presented in the manuscript. Using hyphenated technique of HPTLC-MS (MS 2020 SHIMADZU) spots of these drugs from TLC plate was lifted with CAMAG TLC-MS interface and confirmed by the mass spectrum of the individual drugs by their m/z values thus delivering fast and accurate confirmatory result on the TLC plate.

关键词： Narcotic Drugs Psychotropic Substances HPTLC-MS Chromatography Mass Spectroscopy Hyphenated Techniques Forensic Science