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Group Analysis, Fractional Explicit Solutions and Conservation Laws of Time Fractional Generalized Burgers Equation

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Communications in Theoretical Physics 2018年第1期69卷 5-8页

作者：王岗伟 A.H.kara School of Mathematics and Statistics Hebei University of Economics and Business School of Mathematics University of the Witwatersrand

The generalized fractional Burgers equation is studied in this paper. Using the classical Lie symmetry method, all of the vector fields and symmetry reduction of the equation with nonlinearity are constructed. In particular,an exact solution is provided by using the ansatz method. In addition, other types of exact solution are obtained via the invariant subspace method. Finally, conservation laws for this equation are derived.

关键词：能量守恒定律汉堡包方程组分时间 ansatz 对称方法非线性

An Analysis of the Invariance and Conservation Laws of Some Classes of Nonlinear Ostrovsky Equations and Related Systems

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Chinese Physics Letters 2011年第1期28卷 1-4页

作者： K. Fakhar A. H. kara Department of Mathematics Faculty of Science Universiti Teknologi Malaysia 81310 UTM Skudai Johor Malaysia School of Mathematics and Centre for Differential Equations Continuum Mechanics and Applications University of the Witwatersrand Johannesburg P Bag 3 Wits 2050 South Africa

A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ＇multipliers＇ associated with the conservation laws with a stronger emphasis on the ＇higher-order＇ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers.

关键词： Mathematical physics Statistical physics and nonlinear systems

An angle-insensitive electromagnetic absorber enabling a wideband absorption

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Journal of Materials Science & Technology 2022年第18期113卷 33-39页

作者： Zhichao Lou Qiuyi Wang Xiaodi Zhou Ufuoma I.kara Rajdeep S.Mamtani Hualiang Lv Meng Zhang Zhihong Yang Yanjun Li Chenxuan Wang Solomon Adera Xiaoguang Wang Jiangsu Co-Innovation Center of Efficient Processing and Utilization of Forest Resources Nanjing Forestry UniversityNanjing 210037China Willian G.Lowrie Department of Chemical and Biomolecular Engineering The Ohio State UniversityColumbusOH43210United States of America Institute of Materials Research and Engineering Agency for SciencesTechnology and ResearchSingapore State Key Laboratory of Medical Molecular Biology Institute of Basic Medical Sciences Chinese Academy of Medical SciencesSchool of Basic Medicine Peking Union Medical CollegeBeijing 100005China Department of Mechanical Engineering University of MichiganAnn ArborMI48109United States of America Sustainability Institute The Ohio State UniversityColumbusOH43210United States of America School of Materials Science and Engineering Henan University of Science and TechnologyLuoyang 471023China

Electromagnetic(EM)wave absorbers with wideband absorption capability are proposed as a strategy to mitigate environmental pollution by EM ***,designing an EM absorber with its performance capacity independent of the EM wave incident angle remains elusive to *** this challenge requires development of EM absorbers whose EM absorption performance is insensitive to the EM wave incident ***,we synthesized EM absorbers with a variety of structures with different symme-tries(including micro-/nanospheres,nanoflakes and nanotubes)to study the effect of the EM absorbers’structure and the EM wave incident angle on the EM absorption *** analysis reveals that non-magnetic EM absorbers with spatially symmetric nanostructures exhibit excellent EM wave incident ***,we demonstrate that a class of non-magnetic EM absorbers made from bam-boo derived-carbon nanospheres exhibit EM incident angle-insensitivity and wideband EM absorption performance with an effective absorption band up to 3.5 GHz when the thickness is 1.4 mm,a signif-icant improvement from prior studies which used thicknesses as high as 3-4 mm for comparable EM absorption performance.

关键词： Nanostructure Angle-insensitive EM absorption Biomass derived carbon Wideband

A Galerkin-Type Fractional Approach for Solutions of Bagley-Torvik Equations

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Computer Modeling in Engineering & Sciences 2020年第6期123卷 941-956页

作者： Şuayip Yüzbaşı Murat karaçayır Department of Mathematics Akdeniz UniversityAntalya07070Turkey

In this study,we present a numerical scheme similar to the Galerkin method in order to obtain numerical solutions of the Bagley Torvik equation of fractional order 3/*** this approach,the approximate solution is assumed to have the form of a polynomial in the variable t=xα,whereαis a positive real parameter of our *** problem is firstly expressed in vectoral form via substituting the matrix counterparts of the terms present in the *** taking inner product of this vector with nonnegative integer powers of t up to a selected positive parameter N,a set of linear algebraic equations is *** incorporation of the boundary conditions,the approximate solution of the problem is then computed from the solution of this linear *** present method is illustrated with two examples.

关键词： Bagley-Torvik equation fractional derivative Galerkin method numerical solutions.

Impacts of urban headwater disturbances on downstream sediment loading where streamside management zones for forest harvesting activities are present downstream

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International Journal of Sediment Research 2017年第4期32卷 555-563页

作者： Ilkim Cavus Latif Kalin Ferhat kara Ministry of Forestry and Water Affairs.General Directorate of Combating Desertification and Erosion Auburn University School of Forestry and Wildlife Sciences Kastamonu University Faculty of Forestry

Watershed disturbances caused by land use/land cover(LU/LC) change, intensive forestry practices, and other forms of watershed disturbance are known to negatively affect water quality, if best management practices(BMPs) are not present. Disturbances near or around headwaters where BMPs are absent or are inadequate may impact downstream water quality and stream ecology regardless of the presence of downstream BMPs. In this study, the recovery of two small forest-dominated watersheds(Ww and Ew) in Auburn, Alabama, USA, was monitored 6-years after a partial clearcut was done. The streamside management zone(SMZ) in Ww was also partially harvested shortly after the partial clearcut to improve its sediment trapping effectiveness over the long-term. The hydrology and sediment transport in these watersheds were expected to stabilize over this period, however, new disturbances in the headwaters of both watersheds changed the watershed dynamics. Streamflow and sediment load were examined over a15-month period from February 2014 to May 2015. The clearcut in Ww and Ew, and the partially harvested SMZ in Ww seemed to have recovered; however, substantial amount of sediment load were measured across all monitoring sites in both watersheds as a result of upstream disturbances. This study emphasizes the necessity of watershed management as a whole, and the importance of BMP applications within the entire watershed. It also highlights the fact that watershed management and BMP implementation is a dynamic process, thus, strategies and techniques need to be continuously adapted in response to environmental changes.

关键词： Headwater disturbances Best management practices Sediment load Southeast USA

Management of Barrett’s esophagus with dysplasia refractory to radiofrequency ablation

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World Journal of Gastroenterology 2020年第17期26卷 2030-2039页

作者： kara L Raphael Arvind J Trindade Division of Gastroenterology Long Island Jewish Medical CenterZucker School of Medicine at Hofstra/NorthwellNorthwell Health SystemNew Hyde ParkNY 11040United States

Radiofrequency ablation(RFA)is very effective for eradication of flat Barrett’s mucosa in dysplastic Barrett’s esophagus after endoscopic resection of raised ***,in a minority of the time,RFA may be ineffective at eradication of the Barrett’s *** complete eradication of intestinal metaplasia can be challenging in these *** review article focuses on the management of patients with dysplastic Barrett’s esophagus refractory to RFA *** strategies discussed in this review include optimizing the RFA procedure,optimizing acid suppression(with medical,endoscopic,and surgical management),cryotherapy,hybrid argon plasma coagulation,and EndoRotor resection.

关键词： Low-grade dysplasia High-grade dysplasia Radiofrequency ablation Cryotherapy EndoRotor Hybrid argon plasma coagulation Argon plasma coagulation

The Fictitious Domain Method with Sharp Interface for Elasticity Systems with General Jump Embedded Boundary Conditions

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Advances in Applied Mathematics and Mechanics 2021年第1期13卷 119-139页

作者： Mohamed kara Salim Mesbahi Philippe Angot Applied Mathematics Laboratory Department of MathematicsFaculty of SciencesFerhat Abbas UniversitySetifAlgeria Fundamental and Numerical Mathematics Laboratory Department of MathematicsFaculty of SciencesFerhat Abbas UniversitySetifAlgeria Aix-Marseille Universit´e Institut de Math´ematiques de MarseilleCNRS UMR 7373MarseilleFrance

In framework of the fictitious domain methods with immersed interfaces for the elasticity problem,the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp interface for the vector elasticity system discretized by a proposed finite volume *** main idea of the fictitious domain approach consists in embedding the original domain of study into a geometrically larger and simpler one called the fictitious ***,we present a cell-centered finite volume method to discretize the fictitious domain *** proposed method is numerically validated for different test *** work can be considered as a first step before more challenging problems such as fluid-structure interactions or moving interface problems.

关键词： Fictitious domain method sharp interface elasticity system jump embedded boundary conditions finite volume method

A Note on the Invariance Properties and Conservation Laws of the Kadomstev–Petviashvili Equation with Power Law Nonlinearity

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Chinese Physics Letters 2011年第9期28卷 10-11页

作者： A H Bokhari F D Zaman K Fakhar A H kara Department of Mathematical Sciences King Fahd University of Petroleum and MineralsDhahran 31261Saudi Arabia Department of Mathematics Faculty of ScienceUniversiti Teknologi Malaysia81310 UTM SkudaiJohorMalaysia Ibnu Sina Institute for Fundamental Science Studies Universiti Teknologi Malaysia81310 UTM SkudaiJohorMalaysia School of Mathematics University of the WitwatersrandJohannesburgWits 2050South Africa

First,we studied the invariance properties of the Kadomstev–Petviashvili equation with power law ***,we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the *** point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved flows.

关键词： equation conserved equation

Phytochromes and Phytohormones： The Shrinking Degree of Separation

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Molecular Plant 2013年第1期6卷 5-7页

作者： Qin wang Ziqiang Zhu kara Ozkardesh Chentao Lin College of Biology Hunan University Changsha 410082 China Department of Molecular Cell and Developmental Biology University of California Los Angeles CA 90095 USA

Any two people on Earth may be connected by a chain of ＇a friend of a friend＇ in six steps or less, dubbed as the ＇six degrees of separation＇. In the world of plant systems, the degree of separation between the signaling ＇pathways＇ of photoreceptor phytochromes and growth regulator phyto- hormones is smaller than previously expected, according to the recent studies.

关键词： Degree of separation Plant hormone Phytochrome Growth regulator Plant system Link chain Photosensitive element photosensitive