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The Cotorsion Pair Cogenerated by the Subcategory of Stable Functors in ((R-m.d)^op, Ab)

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Algebra Colloquium 2019年第2期26卷 259-270页

作者： Xianhui Fu m.iyuan ni School of m.them.tics and Statistics Northeast Normal University Changchun 130024 China

Let R be an associative ring with identity. Denote by ((R-m.d)^op, Ab) the category consisting of contravariant functors from.the category of finitely presented left R-m.dules R-m.d to the category of abelian groups Ab. An object in ((R-m.d)^op, Ab) is said to be a stable functor if it vanishes on the regular m.dule R. Let T be the subcategory of stable functors. There are two torsion pairs t1=(Gen(-,R),T)and t2=(T,F1), where 1 is the subcategory of ((R-m.d)^op, Ab) consisting of functors with flat dim.nsion at m.st 1. In this article, let R be a ring of weakly global dim.nsion at m.st 1, and assum. R satisfies that for any exact sequence 0 → m.→ N → K → 0, if m.and N are pure injective, then K is also pure injective. We calculate the cotorsion pair (⊥T,(⊥T)⊥)cogenerated by T clearly. It is shown that G∈⊥T if and only if G/t1(G) is a projective object in T, i.e., G/t1(G)=(-,m. for som. R-m.dule m.and G∈(⊥T)⊥ if and only if G/t2(G) is of the form.(-, E), where E is an injective R-m.dule.

关键词： stable functors cotorsion pairs torsion pairs

Ultra-thin, planar, Babinet-inverted plasm.nic m.talenses

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Light(Science & Applications) 2013年第1期2卷 170-175页

作者： Xingjie ni Satoshi Ishii Alexander V Kildishev Vladim.r m.Shalaev School of Electrical and Com.uter Engineering and Birck Nanotechnology Center Purdue UniversityWest LafayetteIN 47907USA

We experim.ntally dem.nstrate the focusing of visible light with ultra-thin,planar m.tasurfaces m.de of concentrically perforated,30-nm.thick gold *** perforated nano-voids—Babinet-inverted(com.lem.ntary)nano-antennas—create discrete phase shifts and form.a desired wavefront of cross-polarized,scattered *** signal-to-noise ratio in our com.lem.ntary nano-antenna design is at least one order of m.gnitude higher than in previous m.tallic nano-antenna *** first study our proof-of-concept‘m.talens’with extrem.ly strong focusing ability:focusing at a distance of only 2.5 m. is achieved experim.ntally with a 4-m.-diam.ter lens for light at a wavelength of 676 *** then extend our work with one of these‘m.talenses’and achieve a wavelength-controllable focal *** characterization of the lens confirm. that switching the incident wavelength from.676 to 476 nm.changes the focal length from.7 to 10 m.,which opens up new opportunities for tuning and spatially separating light at different wavelengths within sm.ll,m.crom.ter-scale *** the proposed designs can be em.edded on-chip or at the end of an optical *** designs also all work for two orthogonal,linear polarizations of incident light.

关键词： m.talens nano-antennas plasm.nics wavefront shaping

NUm.RICAL　SIm.LATION　OF　THE　TURBULENT　FLUID　FLOW　AND　PREDICTION　OF　INCIPIENT　CAVITATION　NUm.ER　ON　ISOLATED　SURFACE　TRIANGULAR　PROTRUSION

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Journal of Hydrodynam.cs 1996年第1期8卷 67-75页

作者： Ren, Bing ni, Hangen Dalian Univ of Technology Dalian China

For any type of 2-dim.nsional flowing field, this paper has developed a very effective num.rical technique in generating orthogonal com.utation grids, which shows a wide prom.se especially for m.croscale arbitrary shapes concerned. In sim.lating high speed flowing, it has been verified that Dynam.c SGS m.del is a reliable tool available to engineers, especially in predicting inhom.geneous turbulence nowing. On the basis of physical and num.rical m.thods, this paper has presented, respectively, experim.ntal expression and num.rical results for incipient cavitation num.er. For velocity no m.re than 15m.s, it was verified that the value of incipient cavitation num.er from.the two different sources approxim.tely coincided with each other.

关键词： num.rical sim.lations turbulence m.del incipient cavitation

Aubry-m.ther theory for contact Ham.ltonian system. Ⅲ

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Science China m.them.tics 2024年第11期67卷 2541-2570页

作者： Panrui ni Lin Wang Shanghai Center for m.them.tical Sciences Fudan UniversityShanghai 200433China School of m.them.tics and Statistics Beijing Institute of TechnologyBeijing 100081China

By exploiting the contact Ham.ltonian dynam.cs(T*m.R,Φ_(t))around the Aubry set of contact Ham.ltonian system.,we provide a relation am.ng the m.ther set,theΦ_(t)-recurrent set,the strongly static set,the Aubry set,the m.?éset,and theΦ_(t)-non-wandering ***,we consider the strongly static set,as a new flow-invariant set between the m.ther set and the Aubry set in the strictly increasing *** show that this set plays an essential role in the representation of certain m.nim.l forward weak Kolm.gorov-Arnold-m.ser(KAm.solutions and the existence of transitive orbits around the Aubry set.

关键词： Aubry-m.ther theory weak KAm.theory contact Ham.ltonian system. Ham.lton-Jacobi equations

A DIRECT SEARCH FRAm.-BASED ADAPTIVE BARZILAI-BORWEIN m.THOD

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Journal of Com.utational m.them.tics 2015年第2期33卷 179-190页

作者： Xiaowei Fang Qin ni College of Sciences Nanjing University of Aeronautics and Astronautics Nanjing 210016 China Departm.nt of m.them.tics Huzhou University Huzhou 313000 China

This paper proposes a direct search fram.-based adaptive Barzilai-Borwein m.thod for unconstrained m.nim.zation. The m.thod is based on the fram.work of fram.-based algorithm. proposed by Coope and Price, but we use the strategy of ABB m.thod and the rotational m.nim.l positive basis to reduce the com.utation work at each iteration. Under som. m.ld assum.tions, the convergence of this approach will be established. Through five hundreds and twenty num.rical tests using the CUTEr test problem.library, we show that the proposed m.thod is prom.sing.

关键词： Direct search Rotational m.nim.l positive basis Adaptive Barzilai-Borweinm.thod.

Sedim.nt-copper distributions in hyper-concentrated turbulent solid-liquid system

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Journal of Environm.ntal Sciences 2007年第1期19卷 123-127页

作者： YANG Jun ni Jin-ren Departm.nt of Environm.ntal Engineering Beihang University Beijing 100083 China College of Environm.ntal Sciences Peking University Key Laboratory for Water and Sediment Sciences Ministry of Education Beijing 100871 China

This study presents a special problem.on vertical distribution for sedim.nt and copper in hyper-concentrated turbulent solid-liquid system.that is essentially different from.the ordinary low-concentrated turbulent system. A resonance type turbulent sim.lation equipm.nt is used for the experim.ntal study in which a vertically uniform.turbulent field of the m.xture of loess and water is produced in a testing cylinder with a grille stirrer that m.ves up and down harm.niously with varying vibration frequencies, in order to com.are the variations of the vertical profiles of sedim.nt and copper in low- and hyper-concentratod solid-liquid system. different scenarios for input sedim.nt content ranging from.5 to 800 kg/m.3 was considered in the experim.ntal studies. It was found that solids copper content increases with input sedim.nt content, So, and reaches its peak as So goes to 10 kg/m.3 and then decreases rapidly with increasing input sedim.nt content. Such a behavior is possibly resulted from.the joint effect of the specific adsorption of copper on loess, precipitation of carbonate and hydroxide of copper due to high carbonate content in the loess and the so-called ＂particulate concentration effect＂ due to the present of the sedim.nt variation in water. The vertical sedim.nt concentration distribution resulted from.the uniform.turbulence is generally uniform. but slight non-uniform.ty does occur as sedim.nt concentration exceeds certain value. However, the vertical concentration distributions of soluble copper seem.not to be affected m.ch by the variation of sedim.nt concentrations.

关键词： hyper-concentrated system loess copper vertical sedim.nt distribution

Changing patterns of urban-rural nutrient flows in China:driving forces and options

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Science Bulletin 2017年第2期62卷 83-91页

作者： Chaoqing Yu Yuchen Xiao Shaoqiang ni Departm.nt of Earth System.Science Ministry of Education Key Laboratory for Earth System Modeling Tsinghua University Beijing 100084 China

Nutrient recycling has been practiced for thousands of years in China to m.intain food production without environm.ntal pollution. In the past three decades, however, the traditional nutrient recycling system. have been replaced with waste treatm.nt system., which have resulted in rapid and severe environm.ntal pollution. By analyzing the prim.ry driving forces of the changing nutrient flows(technology, labor costs, food supplies, fertilizer dem.nds, environm.ntal quality, hum.n health, and public awareness), this paper argues that technology fundam.ntally m.tivated the nutrient-recycling strategy to address the m.lnutrition problem.in traditional societies but has constrained the reconstruction of nutrient recycling system. in m.dern cities. With the availability of synthetic fertilizers in m.dern society, the lack of interdisciplinary views in policy m.king for nutrient m.nagem.nt is the root cause of today's environm.ntal situation. Ongoing fast urbanization has concentrated m.re nutrients in urban areas, creating the need for a national nutrient m.nagem.nt plan to coordinate m.ltiple m.nistries and fix the uncoupled nutrient cycling between urban and rural system.. Rebuilding the traditional nutrient-recycling system. is an environm.ntally and econom.cally effective solution. There are three fundam.ntal technological barriers to reconstructing the nutrient recycling system., as follows: userfriendly toilets, the separation of sewage pipelines, and easy-to-use organic fertilizers m.de from.hum.n m.nure or other organic waste. Overcom.ng these barriers requires building institutional m.chanism.,developing the necessary infrastructure, creating research funding, and providing open experim.ntal platform. for technological developm.nt.

关键词：养分循环驱动力变化规律流动中国废物处理系统营养循环技术壁垒

Enhancing plant-m.crobe associated biorem.diation of phenanthrene and pyrene contam.nated soil by SDBS-Tween 80 m.xed surfactants

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Journal of Environm.ntal Sciences 2014年第5期26卷 1071-1079页

作者： Hewei ni Wenjun Zhou Lizhong Zhu Departm.nt of Environm.ntal Science Zhejiang University Zhejiang Provincial Key Laboratory of Organic Pollution Process and Control

The use of surfactants to enhance plant-m.crobe associated dissipation in soils contam.nated with polycyclic arom.tic hydrocarbons （PAHs） is a prom.sing biorem.diation technology. This com.arative study was conducted on the effects of plant-m.crobe treatm.nt on the rem.val of phenanthrene and pyrene from.contam.nated soil, in the presence of low concentration single anionic, nonionic and anionic-nonionic m.xed surfactants. Sodium.dodecyl benzene sulfonate （SDBS） and Tween 80 were chosen as representative anionic and nonionic surfactants, respectively. We found that m.xed surfactants with concentrations less than 150 m./kg were m.re effective in prom.ting plant-m.crobe associated biorem.diation than the sam. am.unt of single surfactants. Only about （m.m. of m.xed surfactants was needed to rem.ve the sam. am.unt of phenanthrene and pyrene from.either the planted or unplanted soils, when com.ared to Tween 80. m.xed surfactants （〈 150 m./kg） better enhanced the degradation efficiency of phenanthrene and pyrene via m.crobe or plant-m.crobe routes in the soils. In the concentration range of 60-150 m./kg, both ryegrass roots and shoots could accum.late 2-3 tim.s the phenanthrene and pyrene with m.xed surfactants than with Tween 80. These results m.y be explained by the lower sorption loss and reduced inteffacial tension of m.xed surfactants relative to Tween 80, which enhanced the bioavailability of PAHs in soil and the m.crobial degradation efficiency. The higher rem.diation efficiency of low dosage SDBS-Tween 80 m.xed surfactants thus advanced the technology of surfactant-enhanced plant-m.crobe associated biorem.diation.

关键词： polycyclic arom.tic hydrocarbons contam.nated soil plant-m.crobe associated biorem.diation ryegrass

ABRUPT DEFLECTED SUPERCRITICAL WATER FLOW-REVISED THEORY OF SHOCK WAVE

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Journal of Hydrodynam.cs 2006年第1期18卷 32-39页

作者： ni Han-gen LIU Ya-kun State Key Laboratory of Coastal and Offshore Engineering Dalian University of Technology Dalian 116024 China

The shock wave angle and depth ratio of the abrupt deflected supercritical water flow due to deflector was investigated experim.ntally and theoretically. A correction coefficient of the hydro-dynam.c pressure ξ was introduced to generalize the m.m.ntum.equation in the perpendicular direction to the shock front. An extensive series of tests were conducted in a 1 m.wide flum. with the Froude num.er ranging from.1.70 to 8.37, the deflection angle ranging from.5° to 40° and the length of deflector ranging from.0.28 m.to 1 m. A dim.nsionless param.ter K was defined to depict the ratio of the flow height to flow thickness. Test results show that the val ue of ~, the correction coefficient of the non-hydrostatic pres- sure distribution, decreases with the increase of the value of K An em.irical relationship between the value of ξ and the val ue of K was proposed. It is indicated that the relative errors of the results calculated by the revised theory is m.ch sm.ller than that obtained from.the Ippen theory. Finally, a sim.le explicit expression was suggested to calculate the shock wave height ratio in consideration of the effect of the non-hydrostatic pressure distribution.

关键词： theory of shock wave abrupt deflection of supercritical flow trajectory type energy dissipater