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Controlled Secure Direct Communication Protocol via the Three-Qubit Partially Entangled Set of States 被引量:7
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作者 Gang Xu Ke Xiao +2 位作者 Zongpeng Li Xin-Xin Niu Michael Ryan 《Computers, Materials & Continua》 SCIE EI 2019年第3期809-827,共19页
In this paper,we first re-examine the previous protocol of controlled quantum secure direct communication of Zhang et al.’s scheme,which was found insecure under two kinds of attacks,fake entangled particles attack a... In this paper,we first re-examine the previous protocol of controlled quantum secure direct communication of Zhang et al.’s scheme,which was found insecure under two kinds of attacks,fake entangled particles attack and disentanglement attack.Then,by changing the party of the preparation of cluster states and using unitary operations,we present an improved protocol which can avoid these two kinds of attacks.Moreover,the protocol is proposed using the three-qubit partially entangled set of states.It is more efficient by only using three particles rather than four or even more to transmit one bit secret information.Given our using state is much easier to prepare for multiqubit states and our protocol needs less measurement resource,it makes this protocol more convenient from an applied point of view. 展开更多
关键词 Controlled secure direct communication cluster state three-qubit partially entangled state entanglement swapping.
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Quantum secure direct communication via partially entangled states 被引量:1
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作者 满忠晓 夏云杰 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第5期1197-1200,共4页
We present in this paper a quantum secure direct communication (QSDC) protocol by using partially entangled states. In the scheme a third party (Trent) is introduced to authenticate the participants. After authent... We present in this paper a quantum secure direct communication (QSDC) protocol by using partially entangled states. In the scheme a third party (Trent) is introduced to authenticate the participants. After authentication, Alice can directly, deterministically and successfully send a secret message to Bob. The security of the scheme is also discussed and confirmed. 展开更多
关键词 quantum secure direct communication partially entangled state
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Quantum communication for satellite-to-ground networks with partially entangled states
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作者 陈娜 权东晓 +1 位作者 裴昌幸 杨宏 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第2期53-61,共9页
To realize practical wide-area quantum communication,a satellite-to-ground network with partially entangled states is developed in this paper.For efficiency and security reasons,the existing method of quantum communic... To realize practical wide-area quantum communication,a satellite-to-ground network with partially entangled states is developed in this paper.For efficiency and security reasons,the existing method of quantum communication in distributed wireless quantum networks with partially entangled states cannot be applied directly to the proposed quantum network.Based on this point,an efficient and secure quantum communication scheme with partially entangled states is presented.In our scheme,the source node performs teleportation only after an end-to-end entangled state has been established by entanglement swapping with partially entangled states.Thus,the security of quantum communication is guaranteed.The destination node recovers the transmitted quantum bit with the help of an auxiliary quantum bit and specially defined unitary matrices.Detailed calculations and simulation analyses show that the probability of successfully transferring a quantum bit in the presented scheme is high.In addition,the auxiliary quantum bit provides a heralded mechanism for successful communication.Based on the critical components that are presented in this article an efficient,secure,and practical wide-area quantum communication can be achieved. 展开更多
关键词 satellite-to-ground quantum communication network partially entangled states entanglementswapping quantum teleportation
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Teleporting a quantum controlled-Not with one target/two targets gate using two partially entangled states
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作者 陈立冰 金锐博 路洪 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第1期30-34,共5页
This paper considers the teleportation of quantum controlled-Not (CNOT) gate by using partially entangled states. Different from the known probability schemes, it presents a method for teleporting a CNOT gate with u... This paper considers the teleportation of quantum controlled-Not (CNOT) gate by using partially entangled states. Different from the known probability schemes, it presents a method for teleporting a CNOT gate with unit fidelity and unit probability by using two partially entangled pairs as quantum channel. The method is applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients μ and ν are (2μ + 2ν - 2μν - 1) ≥ 0. In this scheme, the sender's local generalized measurement described by a positive operator valued measurement (POVM) lies at the heart. It constructs the required POVM. It also puts forward a scheme for teleporting a CNOT with two targets gate with unit fidelity by using same quantum channel. With assistance of local operations and classical communications, three spatially separated users are able to complete the teleportation of a CNOT with two targets gate with probability of (2μ + 2ν - 1). With a proper value of μ and ν, the probability could reach nearly 1. 展开更多
关键词 partially entangled state TELEPORTATION CNOT gate positive operator valued measurement
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Quantum circuits for realizing deterministic and exact teleportation via two partially entangled pairs of particles
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作者 李文东 张建立 顾永建 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第3期482-487,共6页
Deterministic and exact teleportation can be achieved via two partially entangled pairs of particles [Gu Y J 2006 Opt. Comm. 259 385]. The key point of the protocol is a generalized measurement described by a positive... Deterministic and exact teleportation can be achieved via two partially entangled pairs of particles [Gu Y J 2006 Opt. Comm. 259 385]. The key point of the protocol is a generalized measurement described by a positive operator- valued measure, which can be realized by performing a unitary operation in the extended space and a conventional Von Neumann orthogonal measurement. By decomposing the evolution process from the initial state to the final state, we construct the quantum circuits for realizing the unitary operation with quantum Toffoli gates, and thus provide a physical means to realize the teleportation. Our method for constructing quantum circuits differs from the usual methods based on decomposition of unitary matrices, and is convenient for a large class of quantum processes involving generalized measurements. 展开更多
关键词 quantum circuit TELEPORTATION partially entangled state generalized measurement
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Deterministic hierarchical joint remote state preparation with six-particle partially entangled state
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作者 Na Chen Bin Yan +2 位作者 Geng Chen Man-Jun Zhang Chang-Xing Pei 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第9期184-190,共7页
In this paper, we present a novel scheme for hierarchical joint remote state preparation(HJRSP) in a deterministic manner, where two senders can jointly and remotely prepare an arbitrary single-qubit at three receiv... In this paper, we present a novel scheme for hierarchical joint remote state preparation(HJRSP) in a deterministic manner, where two senders can jointly and remotely prepare an arbitrary single-qubit at three receivers' port. A six-particle partially entangled state is pre-shared as the quantum channel. There is a hierarchy among the receivers concerning their powers to reconstruct the target state. Due to various unitary operations and projective measurements, the unit success probability can always be achieved irrespective of the parameters of the pre-shared partially entangled state. 展开更多
关键词 joint remote state preparation hierarchical quantum communication partially entangled state
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Probabilistic Teleportation of a Three-Particle GHZ State via Two Three-Particle Entangled W States
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作者 LIN Xiu LI Hong-Cai 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第6期1018-1022,共5页
A scheme for teleporting an unknown three-particle GHZ state from a sender to either one of two receivers is proposed. In this scheme, the quantum channel is composed of two non-maximally three-particle entangled W st... A scheme for teleporting an unknown three-particle GHZ state from a sender to either one of two receivers is proposed. In this scheme, the quantum channel is composed of two non-maximally three-particle entangled W states. An unknown three-particle GHZ state can be perfectly teleported probabilistically if the sender performs two generalized Bell-state measurements and the Hadamard operation while either one of two receivers introduces an ancillary particle which is one of the final three particle constituting the teleported state, then performs the controlled-not operation with the ancillary particle as the target bit and introduces an appropriate unitary transformation with the help of the other receiver's simple measurements. All kinds of unitary transformations are given in detail. The present scheme may be directly generalized to teleport an unknown multiparticle GHZ state via two three-particle entangled W states used as the quantum channel. 展开更多
关键词 probabilistic teleportation three-particle entangled state partially three-particle entangled W state unitary transformation
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Partially entangled states bridge in quantum teleportation 被引量:5
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作者 Xiao-Fei Cai Xu-Tao Yu +1 位作者 Li-Hui Shi Zai-Chen Zhang 《Frontiers of physics》 SCIE CSCD 2014年第5期646-651,共6页
The traditional method for information transfer in a quantum communication system using partially entangled state resource is quantum distillation or direct teleportation. In order to reduce the waiting time cost in h... The traditional method for information transfer in a quantum communication system using partially entangled state resource is quantum distillation or direct teleportation. In order to reduce the waiting time cost in hop-by-hop transmission and execute independently in each node, we propose a quantum bridging method with partially entangled states to teleport quantum states from source node to destination node. We also prove that the designed specific quantum bridging circuit is feasible for partially entangled states teleportation across multiple intermediate nodes. Compared to two traditional ways, our partially entanglement quantum bridging method uses simpler logic gates, has better security, and can be used in less quantum resource situation. 展开更多
关键词 partially entangled states quantum bridge quantum teleportation quantum logic gate
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Generalized Quantum Two-Qutrit-State Splitting 被引量:2
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作者 YUAN Hao LIU Yi-Min ZHANG Zhan-Jun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第10期873-878,共6页
A three-party scheme for splitting an arbitrary unknown two-qutrit state is proposed,where two non-maximally-entangled three-qutrit states are taken as the quantum channel among three parties.With the sender'shelp... A three-party scheme for splitting an arbitrary unknown two-qutrit state is proposed,where two non-maximally-entangled three-qutrit states are taken as the quantum channel among three parties.With the sender'shelp,if and only if both receivers collaborate together,they can securely share the quantum state in a probabilisticway by introducing an ancilla qutrit and performing appropriate unitary operations.The relation between the successprobability and coefficients characterizing the quantum channel is revealed.The security of the present scheme is analyzedand confirmed.Moreover,the generalization of the three-party scheme to more-party case is also sketched. 展开更多
关键词 generalized quantum state splitting partially entangled state generalized Bell-state measurement single-qutrit projective measurement
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Controlled Remote Preparation of a Two-Qubit State via an Asymmetric Quantum Channel 被引量:2
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作者 王章银 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第2期244-250,共7页
I present a new scheme for probabilistic remote preparation of a general two-qubit state from a sender to either of two receivers.The quantum channel is composed of a partial entangled tripartite Greenberger-Horne-Zei... I present a new scheme for probabilistic remote preparation of a general two-qubit state from a sender to either of two receivers.The quantum channel is composed of a partial entangled tripartite Greenberger-Horne-Zeilinger (GHZ) state and a W-type state.I try to realize the remote two-qubit preparation by using the usual projective measurement and the method of positive operator-valued measure,respectively.The corresponding success probabilities of the scheme with different methods as well as the total classical communication cost required in this scheme are also calculated. 展开更多
关键词 remote state preparation partial entangled Greenberger-Horne-Zeilinger (GHZ) state W-type state projective measurement positive operator-valued measure unitary operation
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Probabilistic quantum teleportation of shared quantum secret
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作者 Hengji Li Jian Li Xiubo Chen 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第9期196-201,共6页
Very recently,Lee et al.proposed a secure quantum teleportation protocol to transfer shared quantum secret between multiple parties in a network[Phys.Rev.Lett.124060501(2020)].This quantum network is encoded with a ma... Very recently,Lee et al.proposed a secure quantum teleportation protocol to transfer shared quantum secret between multiple parties in a network[Phys.Rev.Lett.124060501(2020)].This quantum network is encoded with a maximally entangled GHZ state.In this paper,we consider a partially entangled GHZ state as the entanglement channel,where it can achieve,probabilistically,unity fidelity transfer of the state.Two kinds of strategies are given.One arises when an auxiliary particle is introduced and a general evolution at any receiver's location is then adopted.The other one involves performing a single generalized Bell-state measurement at the location of any sender.This could allow the receivers to recover the transmitted state with a certain probability,in which only the local Pauli operators are performed,instead of introducing an auxiliary particle.In addition,the successful probability is provided,which is determined by the degree of entanglement of the partially multipartite entangled state.Moreover,the proposed protocol is robust against the bit and phase flip noise. 展开更多
关键词 probabilistic quantum teleportation shared quantum secret partially entangled GHZ state
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Accurate Ground State Electronic and Related Properties of Hexagonal Boron Nitride (h-BN)
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作者 Y. Malozovsky C. Bamba +2 位作者 A. Stewart L. Franklin D. Bagayoko 《Journal of Modern Physics》 2020年第6期928-943,共16页
We present an <em>ab-initio</em>, self-consistent density functional theory (DFT) description of ground state electronic and related properties of hexagonal boron nitride (h-BN). We used a local density ap... We present an <em>ab-initio</em>, self-consistent density functional theory (DFT) description of ground state electronic and related properties of hexagonal boron nitride (h-BN). We used a local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO) formalism. We rigorously implemented the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). The method ensures a generalized minimization of the energy that is far beyond what can be obtained with self-consistency iterations using a single basis set. The method leads to the ground state of the material, in a verifiable manner, without employing over-complete basis sets. We report the ground state band structure, band gap, total and partial densities of states, and electron and hole effective masses of hexagonal boron nitride (h-BN). Our calculated, indirect band gap of 4.37 eV, obtained with room temperature experimental lattice constants of <em>a</em> = 2.504 <span style="white-space:nowrap;">&Aring;</span> and <em>c </em>= 6.661 <span style="white-space:nowrap;">&Aring;</span>, is in agreement with the measured value of 4.3 eV. The valence band maximum is slightly to the left of the K point, while the conduction band minimum is at the M point. Our calculated, total width of the valence and total and partial densities of states are in agreement with corresponding, experimental findings. 展开更多
关键词 Density Functional Theory Band Gap Density and partial Density of states Electron and Hole Effective Masses
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Perfect quantum controlled teleportation via a novel threeparticle partially entangled channel 被引量:3
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作者 Chen Na Quan Dongxiao +1 位作者 Yang Hong Pei Changxing 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2015年第6期45-50,共6页
Recently Li et al. proposed special partially entangled states serving as quantum channel in quantum controlled teleportation, while there are some limitations in their scheme. Based on that, we present a possible imp... Recently Li et al. proposed special partially entangled states serving as quantum channel in quantum controlled teleportation, while there are some limitations in their scheme. Based on that, we present a possible improvement in this paper. We construct a novel three-particle partially entangled state which is suitable for perfect controlled teleportation. A simple quantum circuit is designed to obtain this state. We evaluate quantum controlled teleportation from three points of view: teleportation fidelity, success probability and the controller's power. Detailed calculations and simulation analyses show that the constructed state is a suitable channel for controlled teleportation of arbitrary qubits, unit teleportation fidelity and 100% success probability can be achieved. Meanwhile, as long as channel's entanglement degree equals to or greater than 3/4, the controller's power can be guaranteed. 展开更多
关键词 quantum controlled teleportation three-particle partially entangled state quantum circuit
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Routing protocol for wireless quantum multi-hop mesh backbone network based on partially entangled GHZ state 被引量:3
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作者 Pei-Ying Xiong Xu-Tao Yu +2 位作者 Zai-Chen Zhang Hai-Tao Zhan Jing-Yu Hua 《Frontiers of physics》 SCIE CSCD 2017年第4期187-196,共10页
Quantum multi-hop teleportation is important in the field of quantum communication. In this study, we propose a quantum multi-hop communication model and a quantum routing protocol with multi- hop teleportation for wi... Quantum multi-hop teleportation is important in the field of quantum communication. In this study, we propose a quantum multi-hop communication model and a quantum routing protocol with multi- hop teleportation for wireless mesh backbone networks. Based on an analysis of quantum multi-hop protocols, a partially entangled Greenberger-Horne-Zeilinger (GHZ) state is selected as the quantum channel for the proposed protocol. Both quantum and classical wireless channels exist between two neighboring nodes along the route. With the proposed routing protocol, quantum information can be transmitted hop by hop from the source node to the destination node. Based on multi-hop telepor- tation based on the partially entangled GHZ state, a quantum route established with the minimum number of hops. The difference between our routing protocol and the classical one is that in the for- mer, the processes used to find a quantum route and establish quantum channel entanglement occur simultaneously. The Bell state measurement results of each hop are piggybacked to quantum route finding information. This method reduces the total number of packets and the magnitude of air inter- face delay. The deduction of the establishment of a quantum channel between source and destination is also presented here. The final success probability of quantum multi-hop teleportation in wireless mesh backbone networks was simulated and analyzed. Our research shows that quantum multi-hop teleportation in wireless mesh backbone networks through a partially entangled GHZ state is feasible. 展开更多
关键词 wireless mesh backbone network multi-hop teleportation partially entangled GHZ state quantum routing protocol
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Multiple teleportation via partially entangled GHZ state 被引量:2
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作者 Pei-Ying Xiong Xu-Tao Yu +1 位作者 Hai-Tao Zhan Zai-Chen Zhang 《Frontiers of physics》 SCIE CSCD 2016年第4期101-108,共8页
Quantum teleportation is important for quantum comrmmication. We propose a protocol that uses a partially entangled Greenberger-Horne-Zeilinger (GHZ) state for single hop teleportation. Quantum teleportation will su... Quantum teleportation is important for quantum comrmmication. We propose a protocol that uses a partially entangled Greenberger-Horne-Zeilinger (GHZ) state for single hop teleportation. Quantum teleportation will succeed if the sender makes a Bell state measurement, and the receiver performs the Hadamard gate operation, applies appropriate Pauli operators, introduces an auxiliary particle, and applies the corresponding unitary matrix to recover the transmitted state. We also present a protocol to realize multiple teleportation of partially entangled GHZ state without an auxiliary particle. We show that the success probability of the teleportation is Mways [) when the number of teleportat, ions is odd. In order to improve the success probability of a multihop, we introduce the method used in our single hop teleportation, thus proposing a multiple teleportation protocol using anxiliary particles and a unitary matrix. The final success probability is shown to bc improved significantly for the method without auxiliary particles fbr both an odd or even number of teleportations. 展开更多
关键词 auxiliary particle partially entangled GHZ state multiple teleportation protocol
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Characterization of the Partially Folded Monomeric Intermediate of Creatine Kinase
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作者 朴龙斗 周海梦 《Tsinghua Science and Technology》 SCIE EI CAS 2002年第4期347-351,共5页
The importance of understanding the protein folding pathway and intermediates is well recognized on the basis of extensive studies of protein folding in vitro and in vivo. Creatine kinase (CK) is a typical model fo... The importance of understanding the protein folding pathway and intermediates is well recognized on the basis of extensive studies of protein folding in vitro and in vivo. Creatine kinase (CK) is a typical model for studying unfolding and refolding of proteins due to several interesting properties. Recent studies on the folding of CK show that its partially folded monomeric intermediate is present kinetically and is stable at equilibrium. The present paper contains 33 references as a mini review to characterize the properties of CK from studies on the CK folding pathway. Characterization of these intermediates is an essential step toward understanding the mechanism of protein folding. Some well determined schemes are suggested as protein folding models. 展开更多
关键词 creatine kinase INTERMEDIATE partially folded state folding pathway
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Partial approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls
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作者 Chenmu WANG Yanyan WANG 《Frontiers of Mathematics in China》 SCIE CSCD 2020年第4期727-748,共22页
In this paper,we propose the concept of partial approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls,and make a deep discussion on it.We analyze the relationship... In this paper,we propose the concept of partial approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls,and make a deep discussion on it.We analyze the relationship between the partial approximate boundary synchronization and the partial exact boundary synchronization,and obtain sufficient conditions to realize the partial approximate boundary synchronization and necessary conditions of Kalman’s criterion.In addition,with the help of partial synchronization decomposition,a condition that the approximately synchronizable state does not depend on the sequence of boundary controls is also given. 展开更多
关键词 Coupled system of wave equations partial approximate boundary synchronization partially approximately synchronizable state
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Spiking-free HGO-based DSC for flexible joint manipulator
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作者 Dezhi KONG Wendong WANG +3 位作者 Yang WANG Junbo ZHANG Yikai SHI Lingyun KONG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2022年第3期419-431,共13页
The tracking control problem for Flexible Joint Manipulator Control System(FJMCS)with unmeasurable states is addressed in this paper.Firstly,a High-Gain Observer(HGO)is constructed to estimate the unmeasurable states ... The tracking control problem for Flexible Joint Manipulator Control System(FJMCS)with unmeasurable states is addressed in this paper.Firstly,a High-Gain Observer(HGO)is constructed to estimate the unmeasurable states and the uncertainties.Then,a Dynamic Surface Control(DSC)scheme is developed by using the estimation of HGO.The newly proposed controller has two advantages over the existing methods:(A)a novel Spike Suppression Function(SSF)is developed to avoid the estimation spike problem in the existing HGO-based controllers.(B)Unlike the existing observer-based partial feedback control scheme that can only estimate the unmeasurable states,the proposed HGO can estimate both the unmeasurable states and uncertainties.The closed-loop system stability is proved by the Lyapunov theory.Simulation results demonstrate the effectiveness of the proposed controller. 展开更多
关键词 Dynamic surface control Flexible joint manipulator High-gain observer Mismatched uncertainties partial states feedback Spike suppression
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A DFT study on PtMo resistance to SO_2 poisoning 被引量:7
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作者 XIA MeiRong LIU Ying +6 位作者 LI Li XIONG Kun QI XueQiang YANG LinJiang HU BaoShan XUE Yun WEI ZiDong 《Science China Chemistry》 SCIE EI CAS 2013年第7期1004-1008,共5页
Pt is a catalyst in proton exchange membrane fuel cell (PEMFC), and its activity will be degraded in the air due to the exist- ence of SOx impurities. On strategy is introducing of Mo into the Pt catalyst because it... Pt is a catalyst in proton exchange membrane fuel cell (PEMFC), and its activity will be degraded in the air due to the exist- ence of SOx impurities. On strategy is introducing of Mo into the Pt catalyst because it can improve the SOx-tolerance capacity. Based on the aforementioned phenomenon, a density function theory (DFT) study on SOx adsorbed on Pt(111) and PtMo(111) was performed to enhance Pt catalytic activity. The adsorption energy of adsorbed species, the net change, partial density of state (PDOS), and d-band center were calculated and analyzed comparatively. The results show that the presence of Mo-atom weakens the S-Pt bond strength and reduces the adsorption energies for SO2, S and SO3 on PtMo(111). Moreover, the Mo atom weakens the effects of SO2 on the PtMo(lll) electronic structure and makes the catalyst maintains its original electronic structure after SO2 adsorption as compared with Pt(111). 展开更多
关键词 density functional theory SO2 Pt PTMO partial density of states fuel cells ELECTROCATALYSIS
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Lead‑Carbon Batteries toward Future Energy Storage:From Mechanism and Materials to Applications 被引量:5
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作者 Jian Yin Haibo Lin +7 位作者 Jun Shi Zheqi Lin Jinpeng Bao Yue Wang Xuliang Lin Yanlin Qin Xueqing Qiu Wenli Zhang 《Electrochemical Energy Reviews》 SCIE EI 2022年第3期259-290,共32页
The lead acid battery has been a dominant device in large-scale energy storage systems since its invention in 1859.It has been the most successful commercialized aqueous electrochemical energy storage system ever sinc... The lead acid battery has been a dominant device in large-scale energy storage systems since its invention in 1859.It has been the most successful commercialized aqueous electrochemical energy storage system ever since.In addition,this type of battery has witnessed the emergence and development of modern electricity-powered society.Nevertheless,lead acid batteries have technologically evolved since their invention.Over the past two decades,engineers and scientists have been exploring the applications of lead acid batteries in emerging devices such as hybrid electric vehicles and renewable energy storage;these applications necessitate operation under partial state of charge.Considerable endeavors have been devoted to the development of advanced carbon-enhanced lead acid battery(i.e.,lead-carbon battery)technologies.Achievements have been made in developing advanced lead-carbon negative electrodes.Additionally,there has been significant progress in developing commercially available lead-carbon battery products.Therefore,exploring a durable,long-life,corrosion-resistive lead dioxide positive electrode is of significance.In this review,the possible design strategies for advanced maintenance-free lead-carbon batteries and new rechargeable battery configurations based on lead acid battery technology are critically reviewed.Moreover,a synopsis of the lead-carbon battery is provided from the mechanism,additive manufacturing,electrode fabrication,and full cell evaluation to practical applications. 展开更多
关键词 Lead acid battery Lead-carbon battery partial state of charge PbO_(2) Pb
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