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Least Energy Solutions for the Fractional Schrodinger–Poisson System with General Potential and Nonlinearity
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作者 ZHU Shaojuan HUANG Xianjiu 《数学进展》 北大核心 2025年第5期1031-1058,共28页
In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Und... In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Under some assumptions on V(x)and f,using Nehari–Pohozaev identity and the arguments of Brezis–Nirenberg,the monotonic trick and global compactness lemma,we prove the existence of a nontrivial least energy solution. 展开更多
关键词 fractional Schrodinger-Poisson system variational method Nehari-Pohozaev identity least energy solution
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Advancements in hydrogen storage technologies:Integrating with renewable energy and innovative solutions for a sustainable future
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作者 Yasin Khalili Sara Yasemi +1 位作者 Mohammadreza Bagheri Ali Sanati 《Energy Geoscience》 2025年第2期24-48,共25页
Hydrogen storage plays a crucial role in achieving net-zero emissions by enabling large-scale energy storage,balancing renewable energy fluctuations,and ensuring a stable supply for various applications.This study pro... Hydrogen storage plays a crucial role in achieving net-zero emissions by enabling large-scale energy storage,balancing renewable energy fluctuations,and ensuring a stable supply for various applications.This study provides a comprehensive analysis of hydrogen storage technologies,with a particular focus on underground storage in geological formations such as salt caverns,depleted gas reservoirs,and aquifers.These formations offer high-capacity storage solutions,with salt caverns capable of holding up to 6 TWh of hydrogen and depleted gas reservoirs exceeding 1 TWh per site.Case studies from leading projects demonstrate the feasibility of underground hydrogen storage(UHS)in reducing energy intermittency and enhancing supply security.Challenges such as hydrogen leakage,groundwater contamination,induced seismicity,and economic constraints remain critical concerns.Our findings highlight the technical,economic,and regulatory considerations for integrating UHS into the oil and gas industry,emphasizing its role in sustainable energy transition and decarbonization strategies. 展开更多
关键词 Hydrogen storage Oil and gas industry Enhanced oil recovery(EOR) Greenhouse gas emission reduction Sustainable energy solution
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High Energy Normalized Solutions for the Schrodinger Equations with Exponential Critical Growth
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作者 ZHANG Xiao-cang XULi-ping 《Chinese Quarterly Journal of Mathematics》 2025年第1期1-19,共19页
In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 rep... In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 represents a trapping potential,and f has an exponential critical growth.Under the appropriate assumptions of f,we have obtained the existence of normalized solutions to the above Schr?dinger equation by introducing a variational method.And these solutions are also high energy solutions with positive energy. 展开更多
关键词 High energy normalized solutions Schrodinger equation Trapping potential Exponential critical growth Variational method
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Artificial Suns:A New Energy Solution
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作者 Lan Xinzhen 《Beijing Review》 2025年第50期33-33,共1页
On November 24,the Chinese Academy of Sciences(CAS)launched an international science program for research on burning plasma and released its research plan for the Burning Plasma Experimental Superconducting Tokamak(BE... On November 24,the Chinese Academy of Sciences(CAS)launched an international science program for research on burning plasma and released its research plan for the Burning Plasma Experimental Superconducting Tokamak(BEST),also known as an“artificial sun.” 展开更多
关键词 burning plasma energy solution tokamak artificial suns BEST
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Industrial Untapped Rotational Kinetic Energy Assessment for Sustainable Energy Recycling 被引量:1
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作者 See Wei Jing Md Tanjil Sarker +2 位作者 Gobbi Ramasamy Siva Priya Thiagarajah Fazlul Aman 《Energy Engineering》 2025年第3期905-927,共23页
Electrical energy can be harvested from the rotational kinetic energy of moving bodies,consisting of both mechanical and kinetic energy as a potential power source through electromagnetic induction,similar to wind ene... Electrical energy can be harvested from the rotational kinetic energy of moving bodies,consisting of both mechanical and kinetic energy as a potential power source through electromagnetic induction,similar to wind energy applications.In industries,rotational bodies are commonly present in operations,yet this kinetic energy remains untapped.This research explores the energy generation characteristics of two rotational body types,disk-shaped and cylinder-shaped under specific experimental setups.The hardware setup included a direct current(DC)motor driver,power supply,DC generator,mechanical support,and load resistance,while the software setup involved automation testing tools and data logging.Electromagnetic induction was used to harvest energy,and experiments were conducted at room temperature(25℃)with controlled variables like speed and friction.Results showed the disk-shaped body exhibited higher energy efficiency than the cylinder-shaped body,largely due to lower mechanical losses.The disk required only two bearings,while the cylinder required four,resulting in lower bearing losses for the disk.Additionally,the disk experienced only air friction,whereas the cylinder encountered friction from a soft,uneven rubber material,increasing surface contact losses.Under a 40 W resistive load,the disk demonstrated a 17.1%energy loss due to mechanical friction,achieving up to 15.55 J of recycled energy.Conversely,the cylinder body experienced a 48.05%energy loss,delivering only 51.95%of energy to the load.These insights suggest significant potential for designing efficient energy recycling systems in industrial settings,particularly in manufacturing and processing industries where rotational machinery is prevalent.Despite its lower energy density,this system could be beneficially integrated with energy storage solutions,enhancing sustainability in industrial practices. 展开更多
关键词 Rotational kinetic energy electromagnetic induction energy harvesting disk-shaped body cylinder-shaped body energy efficiency mechanical loss industrial energy recycling sustainable energy solutions
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Energy Recycling System for Harnessing Industrial Rotational Kinetic Energy
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作者 Md Tanjil Sarker See Wei Jing +2 位作者 Gobbi Ramasamy Siva Priya Thiagarajah Md.Golam Sadeque 《Energy Engineering》 2025年第7期2891-2909,共19页
Industrial processes often involve rotating machinery that generates substantial kinetic energy,much of which remains untapped.Harvesting rotational kinetic energy offers a promising solution to reduce energy waste an... Industrial processes often involve rotating machinery that generates substantial kinetic energy,much of which remains untapped.Harvesting rotational kinetic energy offers a promising solution to reduce energy waste and improve energy efficiency in industrial applications.This research investigates the potential of electromagnetic induction for harvesting rotational kinetic energy from industrial machinery.A comparative study was conducted between disk and cylinder-shaped rotational bodies to evaluate their energy efficiency under various load conditions.Experimental results demonstrated that the disk body exhibited higher energy efficiency,primarily due to lower mechanical losses compared to the cylinder body.A power management circuit was developed to regulate and store the harvested energy,integrating voltage,current,and speed sensors along with a charge controller for battery storage.The experimental setup successfully converted rotational kinetic energy into usable electrical power,with the disk achieving up to 16.33 J of recycled energy,outperforming the cylinder.The disk body demonstrated higher energy recovery efficiency compared to the cylinder,particularly under the 40 W resistive load condition.These findings demonstrate the feasibility of implementing energy recycling systems in industrial settings to enhance sustainability,reduce energy consumption,and minimize waste.Future research should focus on optimizing power management systems and improving energy harvesting efficiency to enable wider adoption of energy recycling technologies in various industrial applications. 展开更多
关键词 Rotational kinetic energy electromagnetic induction energy harvesting energy efficiency mechanical loss industrial energy recycling sustainable energy solutions
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A Focus on the Water-Energy Nexus for Sustainable Development
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作者 Jiuhui Qu Gang Liu 《Engineering》 2025年第7期1-2,共2页
The water-energy nexus is a key area of focus in efforts to achieve the United Nation’s Sustainable Development Goals.As population growth and climate change continue to strain both water and energy systems,innovativ... The water-energy nexus is a key area of focus in efforts to achieve the United Nation’s Sustainable Development Goals.As population growth and climate change continue to strain both water and energy systems,innovative and integrated solutions are required that take into account the inextricable interdependen-cies of these systems.Optimizing resource use,reducing carbon emissions,and increasing system resilience are no longer optional;they are critical imperatives for a sustainable future.This special issue of Engineering presents groundbreaking research exploring the synergies and tradeoffs within the water-energy nexus,offer-ing invaluable insights for policymakers,engineers,and researchers. 展开更多
关键词 innovative solutions increasing system resilience carbon emissionsand water energy nexus climate change population growth sustainable development water energy systemsinnovative integrated solutions
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Least energy solutions for semilinear Schrdinger equation with electromagnetic fields and critical growth 被引量:2
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作者 TANG ZhongWei WANG YanLi 《Science China Mathematics》 SCIE CSCD 2015年第11期2317-2328,共12页
We study a class of semilinear SchrSdinger equation with electromagnetic fields and the nonlinearity term involving critical growth. We assume that the potential of the equation includes a parameter A and can be negat... We study a class of semilinear SchrSdinger equation with electromagnetic fields and the nonlinearity term involving critical growth. We assume that the potential of the equation includes a parameter A and can be negative in some domain. Moreover, the potential behaves like potential well when the parameter A is large. Using variational methods combining Nehari methods, we prove that the equation has a least energy solution which, as the parameter A becomes large, localized near the bottom of the potential well. Our result is an extension of the corresponding result for the SchrSdinger equation which involves critical growth but does not involve electromagnetic fields. 展开更多
关键词 semilinear Schr6dinger equation least energy solution critical growth electromagnetic fields
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Least energy solutions of nonlinear Schr odinger equations involving the fractional Laplacian and potential wells 被引量:1
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作者 NIU MiaoMiao TANG ZhongWei 《Science China Mathematics》 SCIE CSCD 2017年第2期261-276,共16页
We are concerned with the existence of least energy solutions of nonlinear Schrodinger equations involving the fractional Laplacian(-△)%s u(x)+λV(x)u(x)=u(x)^(p-1),u(x)〉=0,x∈R^N,for sufficiently lar... We are concerned with the existence of least energy solutions of nonlinear Schrodinger equations involving the fractional Laplacian(-△)%s u(x)+λV(x)u(x)=u(x)^(p-1),u(x)〉=0,x∈R^N,for sufficiently large λ,2〈p〈N-2s^-2N for N≥2. V(x) is a real continuous function on RN. Using variational methods we prove the existence of least energy solution uλ(x) which localizes near the potential well int V-1 (0) for A large. Moreover, if the zero sets int V-1 (0) of V(x) include more than one isolated component, then ux(x) will be trapped around all the isolated components. However, in Laplacian case s = 1, when the parameter A is large, the corresponding least energy solution will be trapped around only one isolated component and become arbitrarily small in other components of int V^-1(0). This is the essential difference with the Laplacian problems since the operator (-△)s is nonlocal. 展开更多
关键词 nonlinear SchrSdinger equation least energy solution fractional Laplacian variational methods
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Uniqueness and Radial Symmetry of Least Energy Solution for a Semilinear Neumann Problem
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作者 Zheng-ping Wang Huan-song Zhou 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2008年第3期473-482,共10页
Consider the following Neumann problem d△u- u + k(x)u^p = 0 and u 〉 0 in B1, δu/δv =0 on OB1,where d 〉 0, B1 is the unit ball in R^N, k(x) = k(|x|) ≠ 0 is nonnegative and in C(-↑B1), 1 〈 p 〈 N+2/N... Consider the following Neumann problem d△u- u + k(x)u^p = 0 and u 〉 0 in B1, δu/δv =0 on OB1,where d 〉 0, B1 is the unit ball in R^N, k(x) = k(|x|) ≠ 0 is nonnegative and in C(-↑B1), 1 〈 p 〈 N+2/N-2 with N≥ 3. It was shown in [2] that, for any d 〉 0, problem (*) has no nonconstant radially symmetric least energy solution if k(x) ≡ 1. By an implicit function theorem we prove that there is d0 〉 0 such that (*) has a unique radially symmetric least energy solution if d 〉 d0, this solution is constant if k(x) ≡ 1 and nonconstant if k(x) ≠ 1. In particular, for k(x) ≡ 1, do can be expressed explicitly. 展开更多
关键词 Implicit function theorem least energy solution radial symmetry Neumann problem ELLIPTIC
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Tailoring interatomic active sites for highly selective electrocatalytic biomass conversion reaction
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作者 Xuan Liu Qing Li 《Chinese Chemical Letters》 2025年第4期7-8,共2页
The quest for sustainable energy solutions has intensified the search for alternative feedstocks that can supplement or replace fossil fuels. Obtaining fuels or chemicals through the conversion of renewable biomass is... The quest for sustainable energy solutions has intensified the search for alternative feedstocks that can supplement or replace fossil fuels. Obtaining fuels or chemicals through the conversion of renewable biomass is a promising candidate [1,2]. Some noblemetal-based (e.g., Pt, Pd and Rh) catalysts exhibit significant catalytic activity to the conversion reaction of these biomass. 展开更多
关键词 fossil fuels electrocatalytic biomass conversion obtaining fuels alternative feedstocks interatomic active sites sustainable energy solutions conversion renewable biomass conversion reaction
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Feasibility of Micro-Hydro Power for Rural Electrification in Bangladesh:A Case Study from the Chittagong Hill Tracts
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作者 Ratan Kumar Das Abhijit Date +1 位作者 Harun Chowdhury Hamed Hassan 《Energy Engineering》 2025年第12期4815-4835,共21页
Bangladesh has achieved notable progress in expanding electricity access nationwide.Nonetheless,remote and topographically challenging regions such as the Chittagong Hill Tracts(CHT)continue to face coverage gaps due ... Bangladesh has achieved notable progress in expanding electricity access nationwide.Nonetheless,remote and topographically challenging regions such as the Chittagong Hill Tracts(CHT)continue to face coverage gaps due to grid extension difficulties.This research investigates the technical feasibility of micro-hydro power(MHP)systems as viable off-grid solutions for rural electrification in CHT.Field surveys conducted across various sites assessed available head and flow rates using GPS-based elevation measurements and portable flowmeters.Seasonal fluctuations were factored into the analysis to ensure year-round operational viability.The study involved estimating power output,selecting appropriate turbine types based on head-flow data,and proposing preliminary plant configurations.Results identify multiple locations with adequate head(2.5 to 10.4 m)and flow rates(0.10 to 0.35 m3/s),capable of generating between 1.5 and 16.5 kW,sufficient for essential rural applications.Based on site-specific head and discharge characteristics,Kaplan and Francis turbines were identified as the most suitable configurations,offering high efficiency for the medium-flow,low-to-medium head environments typical of the studied regions.Despite inherent technical potential,challenges such as seasonal variability,infrastructure complexities,and policy deficiencies remain.This investigation addresses a critical knowledge gap in local renewable energy planning.It offers a data-driven foundation for pilot projects and community-scale electrification initiatives in Bangladesh’s remote mountainous areas. 展开更多
关键词 Micro-hydro power(MHP) rural electrification Chittagong Hill Tracts(CHT) renewable energy feasibility head-flow assessment off-grid energy solutions
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电子电路铜箔行业又添一起收购案涉及全球高端IT铜箔
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作者 《印制电路信息》 2025年第7期75-75,共1页
德福科技日前公告了相关收购进展。近日,德福科技与Volta Energy Solutions S.à.r.l(.以下简称“交易对方”“卖方”)签署了《谅解备忘录》,双方就德福科技或其全资控股主体收购Circuit Foil Luxembourg S.a.r.l.(以下简称“卢森... 德福科技日前公告了相关收购进展。近日,德福科技与Volta Energy Solutions S.à.r.l(.以下简称“交易对方”“卖方”)签署了《谅解备忘录》,双方就德福科技或其全资控股主体收购Circuit Foil Luxembourg S.a.r.l.(以下简称“卢森堡铜箔”“标的公司”)100%股权交易达成初步意向,并明确双方后续就本次交易进行排他性谈判、开展尽职调查以及签署《股权购买协议》事宜等事项。 展开更多
关键词 德福科技 Volta energy solutions 收购案
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Shanghai’s Smart and Green Development Story
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作者 WANG RUYING 《China Today》 2025年第11期61-62,共2页
SHANGHAI is blazing a new development track powered by dual engines:one is intelligent manufacturing empowered by cutting-edge technologies,and the other is green development driven by lowcarbon and energy-saving solu... SHANGHAI is blazing a new development track powered by dual engines:one is intelligent manufacturing empowered by cutting-edge technologies,and the other is green development driven by lowcarbon and energy-saving solutions.On September 10,China Today visited two enterprises in Shanghai–Shanghai Schneider Electric Industrial Control Co.,Ltd.and Huaqin Technology Co.,Ltd.–to observe firsthand how global investment and local innovation are jointly shaping Shanghai’s future of high-quality development. 展开更多
关键词 intelligent manufacturing global investment green development smart development energy saving solutions lowcarbon solutions local innovation
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A Least Energy Sign-Changing Solution for Nonlocal Schrödinger Equations with Asymptotically Linear Nonlinearities
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作者 Ni Li 《Journal of Applied Mathematics and Physics》 2025年第6期1997-2011,共15页
In this paper,we are concerned with the following nonlocal Schrödinger equations-L_(K)u+V(x)u=f(x,u),x∈R^(N),Rwhere L_(K)Lis an integro-differential operator of fractional Laplacian type and V is coercive at inf... In this paper,we are concerned with the following nonlocal Schrödinger equations-L_(K)u+V(x)u=f(x,u),x∈R^(N),Rwhere L_(K)Lis an integro-differential operator of fractional Laplacian type and V is coercive at infinity.Combining the Nehari manifold and the quantitative deformation lemma,a least energy sign-changing solution was obtained,and the energy doubling phenomenon was also found. 展开更多
关键词 Nonlocal Schrödinger Equations Least energy Sign-Changing solution Integro-Differential Operator Asymptotically Linear energy Doubling
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EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION TO THE INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ MODEL IN 2-DIMENSION 被引量:6
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作者 王光武 郭柏灵 《Acta Mathematica Scientia》 SCIE CSCD 2017年第5期1361-1372,共12页
In this paper, we prove the existence and uniqueness of the weak solution to the incompressible Navier-Stokes-Landau-Lifshitz equations in two-dimension with finite energy.The main techniques is the Faedo-Galerkin app... In this paper, we prove the existence and uniqueness of the weak solution to the incompressible Navier-Stokes-Landau-Lifshitz equations in two-dimension with finite energy.The main techniques is the Faedo-Galerkin approximation and weak compactness theory. 展开更多
关键词 global finite energy weak solution incompressible Navier-Stokes-Landau-Lifshitz system Faedo-Galerkin method
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Solution for Energies and Mixing of Two 0^+ States in ^(10)He
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作者 H.T.Fortune 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第9期27-28,共2页
Using results from various reactions that populate 10He, I conclude that the ground state has E2n = 1.07(7) MeV and the excited 0+ state is in the region of 2.1-3.1 MeV. The amount of the (sd)2 component in the g... Using results from various reactions that populate 10He, I conclude that the ground state has E2n = 1.07(7) MeV and the excited 0+ state is in the region of 2.1-3.1 MeV. The amount of the (sd)2 component in the ground state is less than about 0.075. 展开更多
关键词 of is on for that solution for Energies and Mixing of Two 0 States in HE
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Everllence Persists in Providing Solutions to Shipping Emissions Compliance
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作者 Wu Xiuxia 《船舶经济贸易》 2025年第6期67-69,共3页
CSSC Power and Shanghai CSSC Mitsui Shipbuilding Diesel Engine jointly held CPGC/CMD-MAN B&W 12G95ME-C10.5-LGIM-EGRTC methanol Engine FAT handover ceremony,the latter is a subsidiary of MAN Energy Solutions(now re... CSSC Power and Shanghai CSSC Mitsui Shipbuilding Diesel Engine jointly held CPGC/CMD-MAN B&W 12G95ME-C10.5-LGIM-EGRTC methanol Engine FAT handover ceremony,the latter is a subsidiary of MAN Energy Solutions(now renamed Everllence)at CSSCPower.Based on MAN-ES latest generation LGIM design platform and control logics,the engine reliability and stability further improve;each engine is furnished with the exhaust recirculation emission system independently developed by Everllence,which is the largest dual-channel exhaust gas recirculation system for the two-stroke engine. 展开更多
关键词 control logicsthe latest generation lgim design platform exhaust recirculation emission system diesel engine methanol engine shipping emissions compliance CSSC Power man energy solutions now
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Towards a (More) Electronic Transmission and Distribution (eT&D)
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作者 Don Tan Damir Novosel 《CES Transactions on Electrical Machines and Systems》 2017年第1期15-25,共11页
The challenges and the path towards a(more)electronic transmission and distribution(eT&D)is presented in this paper.The challenges are first identified together with key stakeholders in the drive for grid moderniz... The challenges and the path towards a(more)electronic transmission and distribution(eT&D)is presented in this paper.The challenges are first identified together with key stakeholders in the drive for grid modernization.A fundamental question is then asked about the investment priority.Six basic characteristics are reviewed,leading to the composition of structured microgrids as the basic functional cell of a modern grid.One example of fractal radial structure and one fractal meshed structure are presented.The likely evolution path is then proposed together with basic technology sets.Specific foundation technologies are discussed in detail,including adiabatic power conversion,3MC technology,medium voltage conversion,distribution-level electronic power transformer and FACTs hardware integration,and back-to-back converters as a universal interconnect element.The rapidly emerging on-wire sensing technology is also discussed.It is pointed out that the distribution-level large electronic power transformer will provide a key component to enable hybrid ac/dc grid flow control and ancillary support for a flexible electronic transmission and distribution(eT&D)systems. 展开更多
关键词 All things grid connected electric power systems electronic transmission&distribution(eT&D) energy solutions flexible electronic transmission systems(FETS) grid modernization large electronic power transformers 3MC converters renewable energy.
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Periodic Solutions of Prescribed Energy for a Class of Symmetric Singular Dynamical Systems
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《Acta Mathematica Sinica,English Series》 SCIE CSCD 1994年第4期410-414,共5页
We consider the following Hamiltonian system: q″(t)+V′(q(t))=0 q ∈C^2(R,R^n\{0}) (HS) where V ∈C^2(R^n\{0},R)is an even function.By looking for closed geodesics,we prove that (HS)has a nonconstant periodic solutio... We consider the following Hamiltonian system: q″(t)+V′(q(t))=0 q ∈C^2(R,R^n\{0}) (HS) where V ∈C^2(R^n\{0},R)is an even function.By looking for closed geodesics,we prove that (HS)has a nonconstant periodic solution of prescribed energy under suitable assumptions.Our main assumption is related with the strong force condition of Gordon. 展开更多
关键词 Periodic solutions of Prescribed energy for a Class of Symmetric Singular Dynamical Systems
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