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Journal of Rare Earths 2021年第2期39卷 151-159页

作者： Irshad Ahmad muhammad shoaib Akhtar Ejaz Ahmed Mukhtar Ahmad Department of Physics Bahauddin Zakariya UniversityMultan60800Pakistan School of Computer and Communication Lanzhou University of TechnologyLanzhou 730000China

Facile combustion route synthesized Al and Ce co-doped ZnO nanoparticles photocatalysts were characterized using XRD,SEM,BET,EDS,UV-visible DRS,PL,photocurrent and EIS *** and SEM analyses identify that crystallite and particle size is reduced from 13.26 to 11.88 nm with introduction of Al and Ce into ZnO which assists inhibiting the recombination of photo generated charge *** DRS spectra indicate that optical assimilation of ZnO is significantly increased to visible region(-406 nm)and band gap reduces from 3.18 to 3.06 eV with introduction of Al and Ce *** impedance spectroscopy analysis under visible light illumination confirms the enhancement in visible light activity of Al and Ce co-doped ZnO nanoparticles as *** enhanced activity of Al and Ce co-doped ZnO photocatalyst can be ascribed to enhanced light assimilation,high surface area and efficient charge transfer *** results reveal that by incorporating precise amount of Al(~2%)and Ce(~2%)into ZnO,a highly efficient catalyst can be synthesized that have degraded almost 95%methyl orange(MO)dye in just 45 ***,the influence of various operational parameters such as solution pH,catalyst dose,dye concentration,airflow rate and light intensity on photodecomposition of MO was *** rmore,a possible mechanism for Al and Ce modified ZnO was proposed and designed photocatalysts demonstrates good stability in aqueous medium.

关键词： Nanoparticles ZnO Combustion MO decomposition PL Rare earths

Solution of Algebraic Lyapunov Equation on Positive-Definite Hermitian Matrices by Using Extended Hamiltonian Algorithm

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Computers, Materials & Continua 2018年第2期54卷 181-195页

作者： muhammad shoaib Arif Mairaj Bibi Adnan Jhangir Department of Mathematics Air UniversityPAF ComplexE-9IslamabadPakistan Department of Mathematics Comsats Institute of Information TechnologyPark RoadChak-ShahzadIslamabadPakistan Department of Mathematics Comsats Institute of Information TechnologyWah CanttPakistan

This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian *** choose the geodesic distance between􀀀AHX􀀀XA and P as the cost function,and put forward the Extended Hamiltonian algorithm(EHA)and Natural gradient algorithm(NGA)for the ***,several numerical experiments give you an idea about the effectiveness of the proposed *** also show the comparison between these two algorithms EHA and *** results are provided and analyzed *** also conclude that the extended Hamiltonian algorithm has better convergence speed than the natural gradient algorithm,whereas the trajectory of the solution matrix is optimal in case of Natural gradient algorithm(NGA)as compared to Extended Hamiltonian Algorithm(EHA).The aim of this paper is to show that the Extended Hamiltonian algorithm(EHA)has superior convergence properties as compared to Natural gradient algorithm(NGA).Upto the best of author’s knowledge,no approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices is found so far in the literature.

关键词： Information geometry algebraic lyapunov equation positive-definite hermitianmatrix manifold natural gradient algorithm extended hamiltonian algorithm

Computational Modeling of Reaction-Diffusion COVID-19 Model Having Isolated Compartment

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Computer Modeling in Engineering & Sciences 2023年第5期135卷 1719-1743页

作者： muhammad shoaib Arif Kamaleldin Abodayeh Asad Ejaz Department of Mathematics and Sciences College of Humanities and SciencesPrince Sultan UniversityRiyadh11586Saudi Arabia Department of Mathematics Air UniversityPAF Complex E-9Islamabad44000Pakistan

Cases of COVID-19 and its variant omicron are raised all across the *** most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous *** WHO(World health organization)records on 30 December 2021,the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266,active,recovered,and discharge were found to be 82,402 and 34,258,778,*** there were 160,989 active cases,33,614,434 cured cases,456,386 total deaths,and 605,885,769 total samples *** far,1,438,322,742 individuals have been *** coronavirus or COVID-19 is inciting panic for several *** is a new virus that has affected the whole *** have introduced certain ways to prevent the *** can lower the danger of infection by reducing the contact rate with other *** crowded places and social events withmany people reduces the chance of one being exposed to the *** deadly COVID-19 spreads *** is thought that the upcoming waves of this pandemicwill be evenmore *** have presented severalmathematical models to study the pandemic and predict future *** need of the hour is to restrict the mobility to control the infection from ***,separating affected individuals from healthy people is essential to control the *** consider the COVID-19 model in which the population is divided into five *** present model presents the population’s diffusion effects on all susceptible,exposed,infected,isolated,and recovered *** reproductive number,which has a key role in the infectious models,is *** equilibrium points and their stability is *** numerical simulations,finite difference(FD)schemes like nonstandard finite difference(NSFD),forward in time central in space(FTCS),and Crank Nicolson(CN)schemes are *** core characteristics

关键词： Reproductive number stability Routh Hurwitz criterion variational matrix NSFD scheme FTCS scheme Crank Nicolson scheme consistency

A Computational Analysis to Burgers Huxley Equation

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Computers, Materials & Continua 2021年第5期67卷 2161-2183页

作者： muhammad Saqib muhammad shoaib Arif Shahid Hasnain Daoud S.Mashat Department of Mathematics Numl UniversityIslamabad44000Pakistan Department of Mathematics Air UniversityIslamabad44000Pakistan Department of Mathematics Air UniversityMultan CampusMultan66000Pakistan Department of Mathematics King Abdulaziz UniversityJeddahSaudi Arabia

The efficiency of solving computationally partial differential equations can be profoundly highlighted by the creation of precise,higher-order compact numerical scheme that results in truly outstanding accuracy at a given *** objective of this article is to develop a highly accurate novel algorithm for two dimensional non-linear Burgers Huxley(BH)*** proposed compact numerical scheme is found to be free of superiors approximate oscillations across discontinuities,and in a smooth ow region,it efciently obtained a high-order *** particular,two classes of higherorder compact nite difference schemes are taken into account and compared based on their computational *** stability and accuracy show that the schemes are unconditionally stable and accurate up to a two-order in time and to six-order in ***,algorithms and data tables illustrate the scheme efciency and decisiveness for solving such non-linear coupled *** is scaled in terms of L_(2) and L_(∞) norms,which validate the approximated results with the corresponding analytical *** investigation of the stability requirements of the implicit method applied in the algorithm was carried *** agreement was constructed under indistinguishable computational *** proposed methods can be implemented for real-world problems,originating in engineering and science.

关键词： Burgers Huxley equation nite difference schemes HOC schemes Thomas algorithm Von-Neumann stability ana

Stochastic Numerical Analysis for Impact of Heavy Alcohol Consumption on Transmission Dynamics of Gonorrhoea Epidemic

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Computers, Materials & Continua 2020年第3期62卷 1125-1142页

作者： Kamaleldin Abodayeh Ali Raza muhammad shoaib Arif muhammad Rafiq Mairaj Bibi muhammad Mohsin Department of Mathematics and General Sciences Prince Sultan UniversityRiyadhSaudi Arabia Stochatic Analysis&Optimization Research Group Department of MathematicsAir UniversityPAF Complex E-9Islamabad44000Pakistan Faculty of Engineering University of Central Punjab LahorePakistan Department of Mathematics Comsats UniversityChak Shahzad Campus park roadIslamabadPakistan Department of Mathematics Uppsala UniversityUppsalaSweden

This paper aims to perform a comparison of deterministic and stochastic *** stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic ***,the deterministic solution is itself mean of the stochastic solution of the *** numerical analysis,first,we developed some explicit stochastic methods,but unfortunately,they do not remain consistent in certain *** we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic *** proposed method is independent of the choice of parameters and behaves well in all ***,some theorems and simulations are presented in support of the article.

关键词： Heavy alcohol model stochastic techniques stability analysis

Essential Features Preserving Dynamics of Stochastic Dengue Model

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Computer Modeling in Engineering & Sciences 2021年第1期126卷 201-215页

作者： Wasfi Shatanawi Ali Raza muhammad shoaib Arif muhammad Rafiq Mairaj Bibi muhammad Mohsin Department of Mathematics and General Sciences Prince Sultan UniversityRiyadhSaudi Arabia Department of Medical Research ChinaMedical University HospitalChina Medical UniversityTaichung40402Taiwan Department of Mathematics Hashemite UniversityZarqaJordan Stochastic Analysis&Optimization Research Group Department of MathematicsAir UniversityIslamabad44000Pakistan Department of Mathematics National College of Business Administration and EconomicsLahorePakistan Department of Mathematics Faculty of SciencesUniversity of Central PunjabLahore54500Pakistan Department of Mathematics Comsats University IslamabadIslamabadPakistan Department of Mathematics Uppsala UniversityUppsalaSweden

Nonlinear stochasticmodelling plays an important character in the different fields of sciences such as environmental,material,engineering,chemistry,physics,biomedical engineering,and many *** the current study,we studied the computational dynamics of the stochastic dengue model with the real material of the ***,boundedness,and dynamical consistency are essential features of stochastic *** focus is to design the computational method which preserves essential features of the *** stochastic non-standard finite difference technique is most efficient as compared to other techniques used in *** and comparison were explored in favour of ***,we address the comparison between the stochastic and deterministic models.

关键词： Dengue model stochastic ordinary differential equations numerical methods convergence of the proposed method

A Stochastic Numerical Analysis for Computer Virus Model with Vertical Transmission Over the Internet

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Computers, Materials & Continua 2019年第9期61卷 1025-1043页

作者： muhammad shoaib Arif Ali Raza Wasfi Shatanawi muhammad Rafiq Mairaj Bibi Department of Mathematics Stochastic Analysis&Optimization Research GroupAir UniversityPAF Complex E-9Islamabad44000Pakistan Department of Mathematics and General Courses Prince Sultan University Riyadh Saudi Arabia Department of Medical Research China Medical University HospitalChina Medical UniversityTaichung40402Taiwan Faculty of Engineering University of Central PunjabLahore54500Pakistan Department of Mathematics Comsats UniversityChak Shahzad CampusIslamabad44000Pakistan

We are presenting the numerical analysis for stochastic SLBR model of computer virus over the internet in this *** are going to present the results of stochastic and deterministic computer virus *** of the threshold number C∗hold in stochastic computer virus *** C∗1 shows virus spread in the computer ***,stochastic numerical techniques fail to cope with large step sizes of *** suggested structure of the stochastic non-standard finite difference scheme(SNSFD)maintains all diverse characteristics such as dynamical consistency,bounded-ness and positivity as well-defined by *** this basis,we can suggest a collection of plans for eradicating viruses spreading across the internet effectively.

关键词： Computer virus model stochastic modelling stochastic techniques stability

Ethnobotanical profiling and floristic diversity of Bana Valley, Kotli(Azad Jammu and Kashmir), Pakistan

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Asian Pacific Journal of Tropical Biomedicine 2015年第4期5卷 292-299页

作者： muhammad shoaib Amjad Department of Botany Women University of Azad Jammu and Kashmir Bagh Department of Botany PMAS-University of Arid Agriculture Rawalpindi Pakistan

Objective: To document the medicinal and other folk uses of native plants of the Bana Valley of district of Kotli-Azad Jammu Kashmir with a view to preserve the ethnobotanical knowledge of this area and to develop an ethnobotanical inventory of the species ***: The fieldwork was conducted during a period of one year. Data were collected through semi-structured questionnaire and interview of the informants including indigenous people, tribal people, and traditional health practitioners residing in the study ***: The present study documented etnobotanical uses of 86 plant species belonging to81 genera and 47 families. This study revealed that most of the species were used medicinally(74 spp; 42.29%). Leaves found to be the most frequently used part(56 spp., 36.13%) for preparation of indigenous recipes and fodder ***: The current research provides a huge lump of ethnobotanical knowledge and depicts strong human-plant interaction. It is an urgent need to document indigenous uses of plants for future domestication.

关键词： Ethnobotany Bana Valley Indigenous knowledge Conservation

Ethnobotanical inventory and medicinal uses of some important woody plant species of Kotli,Azad Kashmir,Pakistan

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Asian Pacific Journal of Tropical Biomedicine 2014年第12期4卷 952-958页

作者： muhammad shoaib Amjad muhammad Arshad Department of Botany PMAS-University of Arid Agriculture

Objective:To document ethnobotanical informations of useful woody plant species in the region of Kotli,Azad ***:An ethnobotanical survey was conducted in *** were collected by interview and semi structured questionnaire from selected local informants and traditional practitioners as well as by field ***:The present study documented the etnobotanical uses of 33 woody plant *** of the species have been used for dual *** 5 species are used for one *** revealed all species have medicinal value,among which 21 were used as fuel wood species,16 as fodder species,4 as timber wood species,12 as edible fruit species,6 as fence or hedge plant,7 as ornamental species and 12 species had other ***:Medicinal plants are still widely used for health care by locals of *** species of woodlands seem to be vulnerable to overcollection and *** the young generation is diverted toward allelopathic medicines,ethnobotanical knowledges of important medicinal plants are restricted to the old people *** is suggested to close the forest of district Kotli for next two to three decades for the conservation of plant biodiversity.

关键词： Ethnobotanical uses Kotli Hills Plant resources Human plant interaction Conservation

Mass Transfer of MHD Nanofluid in Presence of Chemical Reaction on A Permeable Rotating Disk with Convective Boundaries, Using Buongiorno’s Model

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Computer Modeling in Engineering & Sciences 2018年第7期116卷 31-49页

作者： muhammad shoaib Arif Yasir Nawaz Mairaj Bibi Zafar Ali Department of Mathematics Air UniversityPAF Complex E-9Islamabad44000Pakistan Department of Mathematics Comsats UniversityPark Road Chak Shahzad CampusIslamabad44000Pakistan

This communiquéis opted to study the flow of nanofluid because of heated disk rotation subjected to the convective boundaries with chemical reaction of first *** Buongiorno’s model for nanofluids is used due to its wide range of applications and the rotating disk under investigation is *** magneto Reynolds parameter and boundary layer assumptions are carried out to formulate the *** system of nonlinear partial differential equations governing the flow problem is converted into the set of ordinary differential equations by using particular relations known as Von Karman *** complicated set of coupled ordinary differential equations with complicated boundary conditions is set to solve by an analytical technique Homotopy Analysis Method(HAM).Whereby the results obtained by the aforementioned method are provided analytically and analyzed *** validation of the work is confirmed by providing comparison of previous works in tabular *** of chemical reaction parameter on mass transfer rate is also highlighted tabularly for its *** and Sherwood numbers calculated and compared to the like literature and found in good agreement.

关键词： Chemical reaction rotating disk nanoparticles velocity slip magnetic effect.