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A SPECTRAL METHOD FOR PANTOGRAPH-TYPE DELAY DIFFERENTIAL EQUATIONS AND ITS CONVERGENCE ANALYSIS

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Journal of Computational Mathematics 2009年第2期27卷 254-265页

作者： ishtiaq ali Hermann Brunner Institute of Computational Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Mathematics COMSA TS Institute of Information Technology IslamabadPakistan Hermann Brunner Department of Mathematics and Statistics Memorial University of NewfoundlandSt.John’sCanada Department of Mathematics Hong Kong Baptist UniversityHong KongChina

We propose a novel numerical approach for delay differential equations with vanishing proportional delays based on spectral methods. A Legendre-collocation method is employed to obtain highly accurate numerical approximations to the exact solution. It is proved theoretically and demonstrated numerically that the proposed method converges exponentially provided that the data in the are smooth. given pantograph delay differential equation

关键词： Spectral methods Legendre quadrature formula Pantograph-type delay differential equations Error analysis Exponential convergence

Numerical simulations of reaction-diffusion equations modeling prey-predator interaction with delay

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International Journal of Biomathematics 2018年第4期11卷 179-195页

作者： ishtiaq ali Ghulam Rasool Saleh Alrashed Department of Mathematics COMSATS Institute of Information TechnologyPark Road Chak Shahzad 44000 Islamabad Pakistan College of Computer Science and Information Technology Imam Abdulrahman Bin Faisal University KSA

To model biological systems one often uses ordinary and partial differential equations. These equations can be quite good at approximating observed behavior, but they suffer from the downfall of containing many parameters, often signifying quantities which cannot be determined experimentally. For the better understanding of complicated phe- nomena, the delay differential equation approach to model such phenomena is becoming more and more essential to capture the rich variety of dynamics observed in natural systems. In this study, we investigated numerically the influence of delay on the dynam- ics of nonlinear reaction-diffusion equations modeling prey-predator interaction using finite difference scheme subject to appropriate initial and boundary conditions. We first consider the prey-predator with Holling type II functional response where the growth of prey is assumed to be logistic in the sense of predator in one-dimensional space. The effect of delay was investigated with the help of simulations and is compared with the model equation without delay. The proposed method is then extended to two-dimensional space.

关键词： Reaction-diffusion equations with delay prey-predator interactions Hollingtype II functional response finite difference scheme.

The Space-Time CE/SE Method for Solving Reduced Two-Fluid Flow Model

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Communications in Computational Physics 2012年第9期12卷 1070-1095页

作者： Shamsul Qamar Munshoor Ahmed ishtiaq ali Department of Mathematics COMSATS Institute of Information TechnologyPark RoadChak Shahzad IslamabadPakistan Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr.139106 MagdeburgGermany

The space-time conservation element and solution element(CE/SE)method is proposed for solving a conservative interface-capturing reducedmodel of compressible two-fluid *** flow equations are the bulk equations,combined with mass and energy equations for one of the two *** latter equation contains a source term for accounting the energy *** one and two-dimensional flow models are numerically investigated in this *** CE/SE method is capable to accurately capture the sharp propagating wavefronts of the fluids without excessive numerical diffusion or spurious *** contrast to the existing upwind finite volume schemes,the Riemann solver and reconstruction procedure are not the building block of the suggested *** method differs from the previous techniques because of global and local flux conservation in a space-time domain without resorting to interpolation or *** order to reveal the efficiency and performance of the approach,several numerical test cases are *** validation,the results of the current method are compared with other finite volume schemes.

关键词： Reduced model space-time CE/SE method central schemes conservation laws hyperbolic systems shock solutions

Influences of double diffusion upon radiative flow of thin film Maxwell fluid through a stretching channel

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Chinese Physics B 2023年第8期32卷 327-335页

作者： Arshad Khan ishtiaq ali Musawa Yahya Almusawa Taza Gul Wajdi Alghamdi College of Aeronautical Engineering National University of Sciences and Technology(NUST)Sector H-12Islamabad 44000Pakistan Department of Mathematics and Statistics College of ScienceKing Faisal UniversityAl-Ahsa 31982Saudi Arabia Department of Mathematics Faculty of ScienceJazan UniversityJazanSaudi Arabia Department of Mathematics City University of Science and Information TechnologyPeshawar 25000Pakistan Department of Information Technology Faculty of Computing and Information TechnologyKing Abdulaziz UniversityJeddah 80261Saudi Arabia

This work explores the influence of double diffusion over thermally radiative flow of thin film hybrid nanofluid and irreversibility generation through a stretching *** nanoparticles of silver and alumina have mixed in the Maxwell fluid(base fluid).Magnetic field influence has been employed to channel in normal *** that are going to administer the fluid flow have been converted to dimension-free notations by using appropriate *** analysis method is used for the solution of the resultant *** this investigation it has pointed out that motion of fluid has declined with growth in magnetic effects,thin film thickness,and unsteadiness *** of fluid has grown up with upsurge in Brownian motion,radiation factor,and thermophoresis effects,while it has declined with greater values of thermal Maxwell factor and thickness factor of the thin *** distribution has grown up with higher values of thermophoresis effects and has declined for augmentation in Brownian motion.

关键词： Maxwell fluid flow magnetohydrodynamic(MHD) hybrid nano fluid flow stretching channel double diffusion entropy generation HAM technique

On the Numerical Solutions of One and Two-Stage Model of Carcinogenesis Mutations with Time Delay and Diffusion

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Applied Mathematics 2013年第10期4卷 118-124页

作者： ishtiaq ali Department of Mathematics COMSATS Institute of Information Technology Islamabad Pakistan

In this paper, we focused on numerical solutions of carcinogenesis mutations models that are based on reaction-diffusion systems and Lotka-Volterra food chains. We consider the case with one and two-stages of mutations with appropriate initial conditions and the zero-flux boundary conditions. The main purpose is to construct a stable discretization scheme, which allows much accuracy than those of a standard approach. To this end, we use the spectral method to postprocess numerical solutions for the proposed model by using some classical methods for solving differential equations. The implementation of the algorithm is simple and it does not need to solve the linear or nonlinear system (in case the model is nonlinear). We simulate the one and two-stage carcinogenesis mutations model and compared the results with previously published ones.

关键词： Carcinogenesis Mutations Delay and Diffusion Spectral Postprocessing Numerical Simulations

中国贸易对环境恶化的影响 ——来自“一带一路”国家的证据

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中国贸易对环境恶化的影响 ——来自“一带一路”国家的证据

作者： ishtiaq ali 东南大学

学位级别：硕士

20世纪80年代,尽管有关双边和多边贸易的多哈回合谈判没有产生丰硕的谈判成果,却促使世界不同地区达成许多贸易协定。事实上,这些谈判影响到不同国家的收入增长和出口潜力,但是,谈判者却完全忽略了未来可能引致的贸易路线过剩,以及可能... 详细信息

20世纪80年代,尽管有关双边和多边贸易的多哈回合谈判没有产生丰硕的谈判成果,却促使世界不同地区达成许多贸易协定。事实上,这些谈判影响到不同国家的收入增长和出口潜力,但是,谈判者却完全忽略了未来可能引致的贸易路线过剩,以及可能造成的环境问题。新的贸易路线和新兴经济体的快速工业化将消耗大量的自然资源和能源,从而在自然界释放出更多的环境污染物。贸易过程也会释放许多温室气体,而二氧化碳被认为是温室效应的主要来源。众所周知,工业化过程主要消耗石油、天然气和煤炭等化石燃料,成为二氧化碳排放的主要原因之一。与此同时,相关实证研究进一步探讨了对外贸易对环境恶化的显著影响。有研究认为经济增长会对环境产生影响,直到达到一定的阈值水平,但一些学者认为贸易与环境关系的问题仍未有效解决,还有待进一步探讨。20世纪90年代初期,世界贸易组织的成立以及联合国环境与发展会议的重大事件影响了全世界。各地区的环境保护和贸易自由化政策及其对环境的影响引起了争议性的辩论。许多研究人员试图探索贸易、增长、能源和环境之间的联系现象。早期研究将贸易可能带来的环境影响效应分为的三个组成部分,这三个核心组成部分和影响渠道分别是规模、结构和技术效应。在规模效应中,GDP越高,污染则越严重;在构成效应中,贸易改变了部门的结构,进而对环境产生了消极或积极的影响;在技术效应中,当我们使用清洁生产技术时,贸易对环境产生了积极的影响。另外,负规模效应则意味着,经济增长将长期以环境恶化作为代价。但是,自由贸易偏好者认为,贸易自由化对经济增长产生了积极的技术效应和结构效应,这两种效应能够补偿负的规模效应。贸易对环境的直接影响在实证研究中得到了广泛的检验,但对于贸易与环境之间的正负相关关系,一直未达成共识,贸易增长对环境质量既可以是威胁也可以是机遇。中国的“一带一路”倡议是与亚洲、非洲和欧洲部分地区经济一体化的重要战略。它以国际合作为目标,以贸易为核心领域,达成面向未来的新共识。“一带一路”倡议在实施大型项目方面加强了广泛的全球化协同和国际合作,其中包括对能源、基础设施和矿业的各种投资。自2013年以来,“一带一路”倡议取得了巨大成就,引起了全球关注。“一带一路”政策对中国的国际贸易产生了重大影响。有研究发现,在“一带一路”政策宣布之前,中国与“一带一路”国家的贸易能力低于非“一带一路”国家,但在政策实施之后,贸易规模显著增加,尤其是2014年之后,出口量有所增加。许多研究表明,由于碳排放,贸易和收入与环境质量之间有关系,可能会对不同经济发展水平的不同地区产生影响。众所周知,“一带一路”倡议涉及到的沿线国家大多处于低收入并且相较于中国仍欠发达,“一带一路”倡议可能会给这些国家的环境质量带来变化。因此,考虑这些变化并估测中国与“一带一路”国家的贸易对环境和资源的持续影响是非常重要的。以往的研究更多考虑的是孤立的国家而忽略了“一带一路”倡议国家在双边或者多边贸易,尤其是与中国的贸易快速增长的情况下的环境问题。目前有关环境问题辩论的核心是,一个特定国家的贸易和收入增长是否对其环境造成压力?为了突出贸易-能源和收入对环境的影响问题,有必要在上述领域进行进一步研究。自20世纪90年代以来,中国迅速开始了贸易自由化并提高了其出口潜力,因此,揭示贸易、能源和收入与环境的联系将是非常重要和有意义的。本论文旨在评估“一带一路”国家及其子区域与中国进行贸易对环境的影响,考虑了能源消耗、收入增长和其他控制变量。本文选择二氧化碳排放作为经济发展、能源消耗、贸易和人口增长的替代变量来衡量“一带一路”国家的环境恶化程度。此外,二氧化碳的排放包含了一个叫做环境库兹涅茨曲线(EKC)的假说,EKC假说提出,在经济增长的初期,工业化和经济增长的增加会导致二氧化碳的高排放,在达到一定的阈值水平后,经济增长的进一步增加会减少二氧化碳的排放,该假说从理论上讨论了收入增长与环境之间的关系。本文也将在EKC的框架内进行分析。本研究有两方面的目标。首先,探讨通过一带一路的国际贸易造成污染上的区域差异,进一步强调能源消耗、国内收入对环境恶化的作用。其次,本研究的主要主题是突出与中国的贸易对“一带一路”国家区域环境的不同影响,试图检验对外贸易对环境恶化的区域和区域内的影响。文章采用了1992年至2018年期间,60个“一带一路”倡议的国家及其子区域的全面板数据,重点考察了中国贸易、二氧化碳排放、能源消费、人口增长、GDP和GDP平方之间的长期联系。中国与“一带一路”国家的贸易数据以固定美元为单位,而GDP数据以十亿美元为单位。能源消耗产生的二氧化碳排放量以百万公吨为单位,而能源消耗量则以百万英热单位为单位。不同“一带一路”倡议国家与中国的贸易数据来自“联合国商品贸易数据库”,而GDP、人口增长、二氧化碳排放和能源消耗则来自WDI。本文以二氧

关键词： “一带一路”沿线国家库茨涅茨曲线二氧化碳排放中国贸易

Removal of heavy metals through adsorption using sand

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Journal of Environmental Sciences 2003年第3期15卷 413-416页

作者： M. ali Awan ishtiaq A. Qazi Imran Khalid Institute of Environmental Science and Engineering (IESE) National University of Sciences & Technology (NUST) Rawalpindi PakistanPakistan Council of Renewable Energy TechnologiesInstitute of Environmental Science and Engineering (IESE) National University of Sciences & Technology (NUST) Rawalpindi Pakistan Islamabad Pakistan

The removal of four heavy metals i.e. Pb, Cr, Cu, and Zn from their aqueous solutions, using ordinary sand as an adsorbent, was studied at 20℃. The amount of metal adsorbed to form monolayer on sand(a_m), obtained from Langmuir isotherm, exhibited the preference of metals for sand in the order Pb>Cr>Cu>Zn. The heavy metal-sand adsorption phenomena can be illustrated on the basis of the interaction between surface functional group of silicates (sand) and the metal ions. It is deduced that sand can be used as a low cost adsorbent for the removal of heavy metal from wastewater (containing low conc. of metals), especially in the developing countries.

关键词： sand heavy metals adsorption

Development of thermochromic strips as a water pasteurization indicator

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Journal of Environmental Sciences 2003年第6期15卷 863-864页

作者： ishtiaq A. Qazi M. ali Awan M. Anwar Baig Pakistan Council of Renewable Energy Technologies(PCRET) Institute of Environmental Science and Engineering(IESE) National University of Sciences & Technology (NUST)Institute of Environmental Science and Engineering(IESE) National University of Sciences & Technology (NUST) Islamabad PakistanRawalpindi PakistanRawalpindi Pakistan

Boiling of water, for purification, commonly practiced in the world, has many problems associated with it like danger of scalding, scaling in the vessels, removal of useful minerals and blandness of taste etc. Water can be made safe for drinking simply by heating at 65℃ for 6 minutes. A colour indicating strip was developed which changes colour from red to purple at 67℃. Use of this strip can help in pasteurizing water without the above problems and with considerable energy saving.

关键词： thermochromic strips pasteurization indicator Pakistan

Unordered rule discovery using Ant Colony Optimization

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Science China(Information Sciences) 2014年第9期57卷 189-203页

作者： KHAN Salabat BAIG Abdul Rauf ali Armughan HAIDER Bilal KHAN Farman ali DURRANI Mehr Yahya ishtiaq Muhammad Department of Computer Science COMSATS Institute of Information TechnologyAttock CampusPakistan Department of Computer Science National University of Computer and Emerging SciencesIslamabadPakistan Al Imam Mohammad Ibn Saud Islamic University (IMSIU) College of Computer and Information SciencesRiyadhSaudi Arabia

In this article,a novel unordered classification rule list discovery algorithm is presented based on Ant Colony Optimization(ACO).The proposed classifier is compared empirically with two other ACO-based classification techniques on 26 data sets,selected from miscellaneous domains,based on several performance *** opposed to its ancestors,our technique has the flexibility of generating a list of IF-THEN rules with unrestricted *** makes the generated classification model more comprehensible and easily *** results indicate that the performance of the proposed method is statistically significantly better as compared with previous versions of AntMiner based on predictive accuracy and comprehensibility of the classification model.

关键词： classification ant colony optimization data mining unordered rule set comprehensibility pattern recognition