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Power Generalized Weibull Distribution Based on Record Values and Associated Inferences with Bladder Cancer Data Example

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Communications in Mathematics and Statistics 2024年第2期12卷 213-238页

作者： devendra kumar Manoj kumar Jagdish Saran Department of statistics Central University of HaryanaJant-PaliMahendergarhIndia Department of Statistics University of DelhiDelhiIndia

The power generalized Weibull distribution has been proposed recently by[24]as an alternative to the gamma,Weibull and the exponentiated Weibull *** power generalized Weibull family is suitable for modeling data that indicate nonmonotone hazard rates and can be used in survival analysis and reliability *** andﬂexibility of the family are illustrated by reanalyzing Efron’s data pertaining to a head-and-neck cancer clinical *** data involve censoring and indicate unimodal hazard *** this distribution,some recurrence relations are established for the single and product moments of upper record ***,using these relations,we have obtained means,variances and covariances of upper record values from samples of sizes up to 10 for various values of the parameters and present them inﬁ*** data set is analyzed to illustrate theﬂexibility and importance of the model.

关键词： Record values Moments Characterization Power generalized Weibull distribution

Probing the degradation of pharmaceuticals in urine using MFC and studying their removal efficiency by UPLC-MS/MS

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Journal of Pharmaceutical Analysis 2021年第3期11卷 320-329页

作者： Priya Sharma devendra kumar Srikanth Mutnuri Applied Environmental Biotechnology Laboratory Birla Institute of Technology&Science(BITS)Pilani403726ZuarinagarIndia Central Sophisticated Instrumentation Facility Birla Institute of Technology&Science(BITS)Pilani403726ZuarinagarIndia Department of Pharmaceutical Sciences College of PharmacyUniversity of Nebraska Medical CenterOmahaNE68198-602USA

Nutrient recovery from source-separated human urine has attracted interest as it is rich in nitrogen and phosphorus that can be utilized as ***,urine also contains pharmaceuticals,steroid hormones,*** their removal is crucial as they have detrimental effects on the environment and human *** current study focuses on investigating the degradation of pharmaceuticals using a double-chamber microbial fuel cell(MFC).Urine was spiked with four pharmaceuticals(trimethoprim,lamivudine,levofloxacin,and estrone)at a concentration of 2 mg/*** MFC was operated for 7 months in batch mode with this spiked urine as *** degradation efficiency of the MFC was studied,for which a selective liquid chromatography-tandem mass-spectrometric method was developed for the quantitation of compounds used in the spiking experiments and was validated with a lower limit of quantification of 0.39 ng/*** maximum removal rate achieved was 96%±2%.The degradation mechanism involved processes like sorption and anoxic *** voltage curve obtained showed that the presence of pharmaceuticals had an initial negative impact on power generation along with increased organic content;however,after the reactor acclimatization,increased power output was achieved with maximum organics removal at 30 h of retention *** work opens a new perspective for the anoxic biodegradation of pharmaceuticals and can be useful in future bioremediation studies.

关键词： Pharmaceuticals Urine MFC Biodegradation Liquid chromatography mass spectroscopy

VARIABLE MESH FINITE DIFFERENCE METHOD FOR SELF-ADJOINT SINGULARLY PERTURBED TWO-POINT BOUNDARY VALUE PROBLEMS

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Journal of Computational Mathematics 2010年第5期28卷 711-724页

作者： Mohan K.Kadalbajoo devendra kumar Department of Mathematics & Statistics

A numerical method based on finite difference method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameter- uniform convergence, a variable mesh is constructed, which is dense in the boundary layer region and coarse in the outer region. The uniform convergence analysis of the method is discussed. The original problem is reduced to its normal form and the reduced problem is solved by finite difference method taking variable mesh. To support the efficiency of the method, several numerical examples have been considered.

关键词： Singularly perturbed boundary value problems Finite difference method,Boundary layer Parameter uniform-convergence Variable mesh.

Approximate analytical solution of fractional order biochemical reaction model and its stability analysis

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International Journal of Biomathematics 2019年第5期12卷 241-261页

作者： Ved Prakash Dubey Rajnesh kumar devendra kumar Faculty of Mathematical and Statistical Sciences Shri Ramswaroop Memorial University Lucknow-Deva Road Uttar Pradesh-225003India Department of Mathematics University of Rajasthan Jaipur-302004RajasthanIndia

Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to *** this paper,an effective and powerful mathematical technique,*** homotopy analysis transform method (FHATM),is employed to get the numerical solutions of biochemical reaction model with time fractional *** adopted scheme is the beautiful copulation of homotopy analysis technique and Laplace transform *** paper shows that the adopted scheme is quite easy as well as computationally attractive in the context of a solution *** Caputo-type fractional derivatives are considered in the present *** results of the probability density functions of the time fractional biochemical reaction model are computed for miscellaneous fractional Brownian motions as well as for classical motion and are presented *** time fractional biochemical reaction model with respect to stability analysis for various values of fractional order q is also *** the context of stability discussion,we have used the fractional Routh-Hurwitz stability criterion to establish the local stability of the biochemical reaction model of fractional order.

关键词： Biochemical reaction model FHATM Laplace transform homotopy stability analysis fractional order

Numerical solution of time-fractional three-species food chain model arising in the realm of mathematical ecology

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International Journal of Biomathematics 2020年第2期13卷 53-74页

作者： Ved Prakash Dubey Rajnesh kumar devendra kumar Faculty of Mathematical and Statistical Sciences Shri RamswaroopMemorial University Lucknow-Deva Road Barabanki 225003Uttar PradeshIndia Department of Mathematics University of Rajasthan Jaipur 302004RajasthanIndia

T'his research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional *** offered technique is a fantastic blend of homotopy analysis method(HAM)and Laplace transform(LT)operator and has been used fruitfully in the numerical computation of various fractional differential equations(FDEs).This paper involves the fractional derivatives of Caputo *** numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial *** is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only-a fact which authenticates the easiness and soundness of the suggested hybrid *** variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical *** outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate.

关键词： Three-species food chain model homotopy analysis transform method Laplace transform fractional order FDEs

An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves

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Journal of Ocean Engineering and Science 2021年第1期6卷 30-39页

作者： Ved Prakash Dubey Rajnesh kumar Jagdev Singh devendra kumar Faculty of Mathematical and Statistical Sciences Shri Ramswaroop Memorial UniversityLucknow-Deva RoadUttar Pradesh-225003India Department of Applied Science and Humanities Government Engineering CollegeNawadaDepartment of Science and TechnologyBihar-805122India Department of Mathematics JECRC UniversityJaipur-303905RajasthanIndia Department of Mathematics University of RajasthanJaipur-302004RajasthanIndia

In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)*** present study considers the Caputo fractional *** fractional order modified DP model is very important and plays a great role in study of ocean engineering and *** proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear *** offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series *** proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.

关键词： Fractional Degasperis-Procesi equation Nonlinear dispersive waves Analytical solution q-homotopy analysis method Sumudu transform

Statistical Inference of Exponentiated Moment Exponential Distribution Based on Lower Record Values

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Communications in Mathematics and Statistics 2017年第3期5卷 231-260页

作者： devendra kumar Tanujit Dey Sanku Dey Department of Statistics Central University of HaryanaJant-PaliMahendergarh 123031HaryanaIndia Department of Quantitative Health Sciences Cleveland ClinicClevelandOH 44121USA Department of Statistics St.Anthony’s CollegeShillongMeghalayaIndia

Based on lower record values,we first derive the exact explicit expressions as well as recurrence relations for the single and product moments of record values and then use these results to compute the means,variances and coefficient of skewness and kurtosis of exponentiated moment exponential distribution(EMED),a new extension of moment exponential distribution,recently introduced by Hasnain(Exponentiated moment exponential ***,2013).Next we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the ***,we consider Bayes estimation under the symmetric and asymmetric loss functions using gamma priors for both shape and scale *** have also derived the Bayes interval of this distribution and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record *** Carlo simulations are performed to compare the performances of the proposed methods,and a data set has been analyzed for illustrative purposes.

关键词： Lower record values Single and product moments Recurrence relations Bayes estimator General entropy loss function Maximum likelihood estimator

A new analysis of fractional fish farm model associated with Mittag-Leffler-type kernel

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International Journal of Biomathematics 2020年第2期13卷 35-51页

作者： Jagdev Singh devendra kumar Dumitru Baleanu Departmert of Maternatics JECRC UriversitgJaipur 303905RajasthanIrdia Departrruent of Matherratics Uriversitgy of Rajasthan Jaipur 302004RajzsthanIndia Department of Matheratics Facultg of Arts and Scierces arkaya UriwersitxEskischir Yolu 29.Km Yukarxgyurtcax Mahallesi Mimar Siran Caddesi No:406790 EtimesgutTurkey Institute of Space Sciences Migurele-BxucharestHowranria

In this paper,we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary *** rnodel is constituted with the group of non-linear differential equations having nutrients,fish and *** have included discrete kind gestational delay of *** solution of fish farm model is determined by employing homotopy analysis transforms method(HATM).Existence of and uniqueness of solution are studied through Picard-Lindelof *** influence of order of new non-integer order derivative on nutrients,fish and mussel is *** complete study reveals that the outer food supplies manage the behavior of the ***,to show the outcomes of the study,some numerical results are demonstrated through graphs.

关键词： Fish farm dynamical model Atangana-Baleanu fractional derivative Picard-Lindelof approach fixed point theorem stability analysis

FDTD based transition time dependent crosstalk analysis for coupled RLC interconnects

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Journal of Semiconductors 2014年第5期35卷 69-73页

作者： devendra kumar Sharma Brajesh kumar Kaushik R.K.Sharma Department of ECE Meerut Institute of Engineering and TechnologyMeerut India Department of Electronics & Computer Engineering Indian Institute of TechnologyRoorkee India Department of ECE National Institute of TechnologyKurukshetra Haryana India

The performance of high density chips operating in the GHz range is mostly affected by on-chip interconnects. The interconnect delay depends on many factors, a few of them are inputs toggling patterns, line ＆ coupling parasitics, input rise/fall time and source/load characteristics. The transition time of the input is of prime importance in high speed circuits. This paper addresses the FDTD based analysis of transition time effects on functional and dynamic crosstalk. The analysis is carried out for equal and unequal transition times of coupled inputs. The analysis of the effects of unequal rise time is equally important because practically, it is quite common to have mismatching in the rise time of the signals transmitting through different length wires. To demonstrate the effects, two distributed RLC lines coupled inductively and capacitively are taken into consideration. The FDTD technique is used because it gives accurate results and carries time domain analysis of coupled lines. The number of lumps in SPICE simulations is considered the same as those of spatial segments. To validate the FDTD computed results, SPICE simulations are run and results are compared. A good agreement of the computed results has been observed with respect to SPICE simulated results. An average error of less than 3.2% is observed in the computation of the performance parameters using the proposed method.

关键词： FDTD transition time crosstalk noise delay coupled interconnects