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Wigner function of optical cumulant operator and its dissipation in thermo-entangled state representation
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作者 张科 李兰兰 范洪义 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第6期205-210,共6页
To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive t... To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion. 展开更多
关键词 Wigner function optical cumulant operator dissipation evolution thermo-entangled state representation integration within ordered product of operators
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Optimizing near-carbon-free nuclear energy systems:advances in reactor operation digital twin through hybrid machine learning algorithms for parameter identification and state estimation
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作者 Li‑Zhan Hong He‑Lin Gong +3 位作者 Hong‑Jun Ji Jia‑Liang Lu Han Li Qing Li 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2024年第8期177-203,共27页
Accurate and efficient online parameter identification and state estimation are crucial for leveraging digital twin simulations to optimize the operation of near-carbon-free nuclear energy systems.In previous studies,... Accurate and efficient online parameter identification and state estimation are crucial for leveraging digital twin simulations to optimize the operation of near-carbon-free nuclear energy systems.In previous studies,we developed a reactor operation digital twin(RODT).However,non-differentiabilities and discontinuities arise when employing machine learning-based surrogate forward models,challenging traditional gradient-based inverse methods and their variants.This study investigated deterministic and metaheuristic algorithms and developed hybrid algorithms to address these issues.An efficient modular RODT software framework that incorporates these methods into its post-evaluation module is presented for comprehensive comparison.The methods were rigorously assessed based on convergence profiles,stability with respect to noise,and computational performance.The numerical results show that the hybrid KNNLHS algorithm excels in real-time online applications,balancing accuracy and efficiency with a prediction error rate of only 1%and processing times of less than 0.1 s.Contrastingly,algorithms such as FSA,DE,and ADE,although slightly slower(approximately 1 s),demonstrated higher accuracy with a 0.3%relative L_2 error,which advances RODT methodologies to harness machine learning and system modeling for improved reactor monitoring,systematic diagnosis of off-normal events,and lifetime management strategies.The developed modular software and novel optimization methods presented offer pathways to realize the full potential of RODT for transforming energy engineering practices. 展开更多
关键词 Parameter identification state estimation Reactor operation digital twin Reduced order model Inverse problem
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Key Issues for Modelling, Operation, Management and Diagnosis of Lithium Batteries: Current States and Prospects
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作者 Bo Yang Yucun Qian +2 位作者 Jianzhong Xu Yaxing Ren Yixuan Chen 《Energy Engineering》 EI 2024年第8期2085-2091,共7页
1 Introduction.With the continuous growth of the global population,the energy demand continues to increase.However,due to the dominance of fossil fuels in global energy and fossil fuels are non-renewable,it has led to... 1 Introduction.With the continuous growth of the global population,the energy demand continues to increase.However,due to the dominance of fossil fuels in global energy and fossil fuels are non-renewable,it has led to the global energy crisis[1].Besides,the use of fossil fuels will generate a mass of air pollutants(e.g.,carbon dioxide,sulfur dioxide,etc.),which will cause serious environmental pollution,climate change[2],etc.To resolve the aforementioned issues,countries around the world have implemented a variety of measures hoping to fundamentally adjust the global energy structure and achieve sustainable development.Thereinto,“Paris Agreement”reached in 2015 under the framework of“United Nations Framework Convention on Climate Change”aims to control the increase in the average temperature of the globe to within 2°C below preindustrial levels,and thereafter to peak global greenhouse gas emissions as soon as possible,continuously decreasing thereafter[3].United Kingdom plans to reduce the average exhaust emissions of“new cars”to approximately 50–70 g/km by 20230,which is roughly half of what it is now[4].In addition,China proposed a plan at“United Nations General Assembly”in 2020 to peak carbon dioxide emissions by 2030 and strive to achieve carbon neutrality by 2060.It is a fact that the whole world is committed to changing the current energy structure,protecting the Earth’s ecology,and achieving global sustainable development[5]. 展开更多
关键词 Lithium batteries optimization operation MODELLING state estimation life prediction fault diagnosis
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Transformer real-time reliability model based on operating conditions 被引量:9
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作者 HE Jian CHENG Lin SUN Yuan-zhang 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2007年第3期378-383,共6页
Operational reliability evaluation theory reflects real-time reliability level of power system. The component failure rate varies with operating conditions. The impact of real-time operating conditions such as ambient... Operational reliability evaluation theory reflects real-time reliability level of power system. The component failure rate varies with operating conditions. The impact of real-time operating conditions such as ambient temperature and transformer MVA (megavolt-ampere) loading on transformer insulation life is studied in this paper. The formula of transformer failure rate based on the winding hottest-spot temperature (HST) is given. Thus the real-time reliability model of transformer based on oper- ating conditions is presented. The work is illustrated using the 1979 IEEE Reliability Test System. The changes of operating conditions are simulated by using hourly load curve and temperature curve, so the curves of real-time reliability indices are ob- tained by using operational reliability evaluation. 展开更多
关键词 operational reliability real-time reliability model TRANSFORMER Winding hottest-pot temperature (HST)
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The Design of I/O Subsystem in Satellite Real-Time Microkernel Operating System 被引量:1
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作者 Liu Xiaodong & Li Lianzhi (Dept. of Computer Science & Engineering, Harbin Institute of Technology, 150001, P. R. China) Qian Chunlai(Beijiing Institute of Radio Measurement, 100854, P. R. China) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1998年第3期77-81,共5页
One of the most important features of modern minor satellites is to realize autonomous moving. The performance of the satellite autonomous computer operating system acting as the control center is utmost important. Th... One of the most important features of modern minor satellites is to realize autonomous moving. The performance of the satellite autonomous computer operating system acting as the control center is utmost important. The recent trend in operating system development is adopting microkernel architecture which holds such advantages as microminiaturization, modularity, portability and extendibility. The performance of I/O subsystem is currently receiving considerable research attention. Object-orientation offers an approach to application development in which software system can be constructed by composing and refining the pre-designed plug-compatible software components.It also starts with some basic notions fairly well accepted in computer science, namely encapsulation and reuse. In this paper, a new object-oriented real-time I/O subsystem model has been designed.In this model, the traditional I/O subsystem framework is discarded and a stream mechanism based on the object-oriented concept is introduced. In addition, the I/O requests are classified according to their time emergency to obtain real-time performance. So, this model meets such satelliteperformance requirements as reliability, flexibility, portability and real-time performance. 展开更多
关键词 Satellite operating system I/O subsystem OBJECT-ORIENTED real-time
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Digital arc welding power supply based on real-time operating system
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作者 张红兵 黄石生 周漪清 《China Welding》 EI CAS 2007年第3期1-5,共5页
A digital arc welding power supply was designed with the advanced reduced instruction set computer machine (ARM) and embedded real-time multi-task operating system micro C/OS- Ⅱ. The ARM, with its powerful calculat... A digital arc welding power supply was designed with the advanced reduced instruction set computer machine (ARM) and embedded real-time multi-task operating system micro C/OS- Ⅱ. The ARM, with its powerful calculating speed and complete peripheral equipments, is very suitable to work as the controller of the digital power supply. The micro C/OS- Ⅱ transplanted in ARM, helps to improve the respondent speed against various welding signals, as well as the reliability of the controlling software. The welding process consists of nine tasks. The tasks of great significance on reliability of the welder, for example, the A/D conversion of current and voltage, enjoy top priority. To avoid simultaneous-sharing on A/D converter and LCD module, two semaphores are introduced in to ensure the smooth performance of the welding power supply. Proven by experiments ,the ARM and the micro C/OS- Ⅱ can greatly improve both the respondent speed and the reliability of the digital welder. 展开更多
关键词 micro C/OS-Ⅱ real-time operating system DIGITIZATION arc welding power supply
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A Smart Phone-oriented Embedded Real-time Operating System
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作者 Wang Jigang1, Gu Guochang2, Xu Lifeng1 ( 1 . Chengdu Institute, Central Academy of ZTE Corporation, Chengdu 610041, China 2. Computer Science and Technology Institute of Harbin Engineering University, Harbin 150001, China) 《ZTE Communications》 2005年第4期6-10,共5页
This article presents an embedded Smart Phone Operating System (SPOS) independently designed by ZTE Corporation. The SPOS is based on single kernel architecture with its multi-task real-time kernel supporting hardware... This article presents an embedded Smart Phone Operating System (SPOS) independently designed by ZTE Corporation. The SPOS is based on single kernel architecture with its multi-task real-time kernel supporting hardware platforms and resources of mainstream mobile phones. It has remarkable advantages such as highly efficient and dynamic power management, priority - based preemptive scheduling, fast startup, a variety of drivers, and excellent system stability and operability. For the development of upper layer communication protocols and application software, the SPOS provides wireless communication interfaces and the application program framework. 展开更多
关键词 PHONE SPOS TIME A Smart Phone-oriented Embedded real-time operating System
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Real-time embedded software testing method based on extended finite state machine 被引量:6
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作者 Yongfeng Yin Bin Liu Hongying Ni 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第2期276-285,共10页
The reliability of real-time embedded software directly determines the reliability of the whole real-time embedded sys- tem, and the effective software testing is an important way to ensure software quality and reliab... The reliability of real-time embedded software directly determines the reliability of the whole real-time embedded sys- tem, and the effective software testing is an important way to ensure software quality and reliability. Based on the analysis of the characteristics of real-time embedded software, the formal method is introduced into the real-time embedded software testing field and the real-time extended finite state machine (RT-EFSM) model is studied firstly. Then, the time zone division method of real-time embedded system is presented and the definition and description methods of time-constrained transition equivalence class (timeCTEC) are presented. Furthermore, the approaches of the testing sequence and test case generation are put forward. Finally, the proposed method is applied to a typical avionics real- time embedded software testing practice and the examples of the timeCTEC, testing sequences and test cases are given. With the analysis of the testing result, the application verification shows that the proposed method can effectively describe the real-time embedded software state transition characteristics and real-time requirements and play the advantages of the formal methods in accuracy, effectiveness and the automation supporting. Combined with the testing platform, the real-time, closed loop and automated simulation testing for real-time embedded software can be realized effectively. 展开更多
关键词 real-time system real-time embedded software for- mal method extended finite state machine (EFSM) testing se- quence test case.
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Research on Optimal Configuration of Energy Storage in Wind-Solar Microgrid Considering Real-Time Electricity Price
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作者 Zhenzhen Zhang Qingquan Lv +4 位作者 Long Zhao Qiang Zhou Pengfei Gao Yanqi Zhang Yimin Li 《Energy Engineering》 EI 2023年第7期1637-1654,共18页
Capacity allocation and energy management strategies for energy storage are critical to the safety and economical operation of microgrids.In this paper,an improved energymanagement strategy based on real-time electric... Capacity allocation and energy management strategies for energy storage are critical to the safety and economical operation of microgrids.In this paper,an improved energymanagement strategy based on real-time electricity price combined with state of charge is proposed to optimize the economic operation of wind and solar microgrids,and the optimal allocation of energy storage capacity is carried out by using this strategy.Firstly,the structure and model of microgrid are analyzed,and the outputmodel of wind power,photovoltaic and energy storage is established.Then,considering the interactive power cost between the microgrid and the main grid and the charge-discharge penalty cost of energy storage,an optimization objective function is established,and an improved energy management strategy is proposed on this basis.Finally,a physicalmodel is built inMATLAB/Simulink for simulation verification,and the energy management strategy is compared and analyzed on sunny and rainy days.The initial configuration cost function of energy storage is added to optimize the allocation of energy storage capacity.The simulation results show that the improved energy management strategy can make the battery charge-discharge response to real-time electricity price and state of charge better than the traditional strategy on sunny or rainy days,reduce the interactive power cost between the microgrid system and the power grid.After analyzing the change of energy storage power with cost,we obtain the best energy storage capacity and energy storage power. 展开更多
关键词 Energy storage optimization real-time electricity price state of charge energy management strategy interactive power
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Verifiable quantum secret sharing scheme based on orthogonal product states
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作者 白晨明 刘璐 张素娟 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第7期178-187,共10页
In the domain of quantum cryptography,the implementation of quantum secret sharing stands as a pivotal element.In this paper,we propose a novel verifiable quantum secret sharing protocol using the d-dimensional produc... In the domain of quantum cryptography,the implementation of quantum secret sharing stands as a pivotal element.In this paper,we propose a novel verifiable quantum secret sharing protocol using the d-dimensional product state and Lagrange interpolation techniques.This protocol is initiated by the dealer Alice,who initially prepares a quantum product state,selected from a predefined set of orthogonal product states within the C~d■C~d framework.Subsequently,the participants execute unitary operations on this product state to recover the underlying secret.Furthermore,we subject the protocol to a rigorous security analysis,considering both eavesdropping attacks and potential dishonesty from the participants.Finally,we conduct a comparative analysis of our protocol against existing schemes.Our scheme exhibits economies of scale by exclusively employing quantum product states,thereby realizing significant cost-efficiency advantages.In terms of access structure,we adopt a(t, n)-threshold architecture,a strategic choice that augments the protocol's practicality and suitability for diverse applications.Furthermore,our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol. 展开更多
关键词 quantum secret sharing quantum product state threshold scheme unitary operations
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A Real-time Updated Model Predictive Control Strategy for Batch Processes Based on State Estimation
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作者 杨国军 李秀喜 钱宇 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2014年第3期318-329,共12页
Nonlinear model predictive control(NMPC) is an appealing control technique for improving the performance of batch processes, but its implementation in industry is not always possible due to its heavy on-line computati... Nonlinear model predictive control(NMPC) is an appealing control technique for improving the performance of batch processes, but its implementation in industry is not always possible due to its heavy on-line computation. To facilitate the implementation of NMPC in batch processes, we propose a real-time updated model predictive control method based on state estimation. The method includes two strategies: a multiple model building strategy and a real-time model updated strategy. The multiple model building strategy is to produce a series of sim-plified models to reduce the on-line computational complexity of NMPC. The real-time model updated strategy is to update the simplified models to keep the accuracy of the models describing dynamic process behavior. The me-thod is validated with a typical batch reactor. Simulation studies show that the new method is efficient and robust with respect to model mismatch and changes in process parameters. 展开更多
关键词 batch process exothermic batch reactor nonlinear model predictive control state estimation real-time model update
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Low-Power Operational Amplifier for Real-Time Signal Processing System of Micro Air Vehicle
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作者 王竹萍 仲顺安 聂丹丹 《Journal of Beijing Institute of Technology》 EI CAS 2010年第3期353-356,共4页
A low-power complementary metal oxide semiconductor(CMOS) operational amplifier (op-amp) for real-time signal processing of micro air vehicle (MAV) is designed in this paper.Traditional folded cascode architectu... A low-power complementary metal oxide semiconductor(CMOS) operational amplifier (op-amp) for real-time signal processing of micro air vehicle (MAV) is designed in this paper.Traditional folded cascode architecture with positive channel metal oxide semiconductor(PMOS) differential input transistors and sub-threshold technology are applied under the low supply voltage.Simulation results show that this amplifier has significantly low power,while maintaining almost the same gain,bandwidth and other key performances.The power required is only 0.12 mW,which is applicable to low-power and low-voltage real-time signal acquisition and processing system. 展开更多
关键词 microelectromechanical system(MEMS) operational amplifier(op-amp) LOW-POWER real-time signal processing system micro air vehicle(MAV)
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Real-Time Operation of Microgrids
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作者 Salem Al-Agtash Asma Alkhraibat +1 位作者 Mohamad Al Hashem Nisrein Al-Mutlaq 《Energy and Power Engineering》 2021年第1期51-66,共16页
Microgrid (MG) systems effectively integrate a generation mix of solar, wind, and other renewable energy resources. The intermittent nature of renewable resources and the unpredictable weather conditions contribute la... Microgrid (MG) systems effectively integrate a generation mix of solar, wind, and other renewable energy resources. The intermittent nature of renewable resources and the unpredictable weather conditions contribute largely to the unreliability of microgrid real-time operation. This paper investigates the behavior of microgrid for different intermittent scenarios of photovoltaic generation in real-time. Reactive power coordination control and load shedding mechanisms are used for reliable operation and are implemented using OPAL-RT simulator integrated with Matlab. In an islanded MG, load shedding can be an effective mechanism to maintain generation-load balance. The microgrid of the German Jordanian University (GJU) is used for illustration. The results show that reactive power coordination control not only stabilizes the MG operation in real-time but also reduces power losses on transmission lines. The results also show that the power losses at some substations are reduced by a range of 6% - 9.8%. 展开更多
关键词 Microgrid real-time operation Reactive Power Control Load Shedding OPAL-RT MATLAB
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A simulation-based software to support the real-time operational parameters selection of tunnel boring machines
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作者 Yaman Zendaki Ba Trung Cao +2 位作者 Abdullah Alsahly Steffen Freitag Gunther Meschke 《Underground Space》 SCIE EI CSCD 2024年第1期176-196,共21页
With the fact that the main operational parameters of the construction process in mechanized tunneling are currently selected based on monitoring data and engineering experience without exploiting the advantages of co... With the fact that the main operational parameters of the construction process in mechanized tunneling are currently selected based on monitoring data and engineering experience without exploiting the advantages of computer methods,the focus of this work is to develop a simulation-based real-time assistant system to support the selection of operational parameters.The choice of an appropriate set of these parameters(i.e.,the face support pressure,the grouting pressure,and the advance speed)during the operation of tunnel boring machines(TBM)is determined by evaluating different tunneling-induced soil-structure interactions such as the surface settlement,the associated risks on existing structures and the tunnel lining behavior.To evaluate soil-structure behavior,an advanced process-oriented numerical simulation model based on the finite cell method is utilized.To enable the real-time prediction capability of the simulation model for a practical application during the advancement of TBMs,surrogate models based on the Proper Orthogonal Decomposition and Radial Basis Functions(POD-RBF)are adopted.The proposed approach is demonstrated through several synthetic numerical examples inspired by the data of real tunnel projects.The developed methods are integrated into a user-friendly application called SMART to serve as a support platform for tunnel engineers at construction sites.Corresponding to each user adjustment of the input parameters,i.e.,each TBM driving scenario,approximately two million outputs of soil-structure interactions are quickly predicted and visualized in seconds,which can provide the site engineers with a rough estimation of the impacts of the chosen scenario on structural responses of the tunnel and above ground structures. 展开更多
关键词 Numerical simulation Surrogate model real-time prediction Proper orthogonal decomposition Radial basis functions TBM operation Smart construction
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Specifying Requirements of Real-Time System with Rules and Templates 被引量:8
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作者 Wu Guo-qing Xiao Hai-feng +1 位作者 Zheng Pen Ying Shi 《Wuhan University Journal of Natural Sciences》 EI CAS 2000年第3期278-284,共7页
This paper presents a model specifying requirements of real-time systems. Different from existing researches, this model mainly uses rules and templates to represent hierarchical FSMs (Finite State Machine). In this m... This paper presents a model specifying requirements of real-time systems. Different from existing researches, this model mainly uses rules and templates to represent hierarchical FSMs (Finite State Machine). In this model, one rule corresponds to one state transition of FSM and one template corresponds to one FSM. Rules and information with respect to a FSM can be written in a template. So templates include not only state diagrams, but also information that can not be described by FSM, such as performance requirements. The specification using this model consists of a collection of templates and it is easy for users to understand and to review. After introduced the related researches and principles of the model, this paper specifies requirements of a real-time system with this model, and discusses characters of this model in the end. 展开更多
关键词 requirements specification model requirements specification real-time system finite state machine
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A Concept of Dynamically Reconfigurable Real-time Vision System for Autonomous Mobile Robotics 被引量:3
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作者 Aymeric De Cabrol Thibault Garcia +1 位作者 Patrick Bonnin Maryline Chetto 《International Journal of Automation and computing》 EI 2008年第2期174-184,共11页
This paper describes specific constraints of vision systems that are dedicated to be embedded in mobile robots. If PC-based hardware architecture is convenient in this field because of its versatility, flexibility, pe... This paper describes specific constraints of vision systems that are dedicated to be embedded in mobile robots. If PC-based hardware architecture is convenient in this field because of its versatility, flexibility, performance, and cost, current real-time operating systems are not completely adapted to long processing with varying duration, and it is often necessary to oversize the system to guarantee fail-safe functioning. Also, interactions with other robotic tasks having more priority are difficult to handle. To answer this problem, we have developed a dynamically reconfigurable vision processing system, based on the innovative features of Cleopatre real-time applicative layer concerning scheduling and fault tolerance. This framework allows to define emergency and optional tasks to ensure a minimal quality of service for the other subsystems of the robot, while allowing to adapt dynamically vision processing chain to an exceptional overlasting vision process or processor overload. Thus, it allows a better cohabitation of several subsystems in a single hardware, and to develop less expensive but safe systems, as they will be designed for the regular case and not rare exceptional ones. Finally, it brings a new way to think and develop vision systems, with pairs of complementary operators. 展开更多
关键词 real-time vision dynamic reconfiguration embedded systems ROBUSTNESS real-time operating system
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New Bosonic Operator Ordering Identities Gained by the Entangled State Representation and Two-Variable Hermite Polynomials 被引量:3
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作者 FANHong-Yi FANYue 《Communications in Theoretical Physics》 SCIE CAS CSCD 2002年第3期297-300,共4页
Based on the technique of integration within an ordered product of operators, we derive new bosonic operators, ordering identities by using entangled state representation and the properties of two-variable Hermite pol... Based on the technique of integration within an ordered product of operators, we derive new bosonic operators, ordering identities by using entangled state representation and the properties of two-variable Hermite polynomials , and vice versa. In doing so, some concise normally (antinormally) ordering operator identities, such as : are obtained. 展开更多
关键词 operator ordering entangled state two-variable Hermite polynomials
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Photon-added and photon-subtracted displaced Fock states and their non-classical properties 被引量:1
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作者 司坤 张淼 贾焕玉 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第11期4887-4892,共6页
A new kind of quantum optical state, photon-added and -subtracted displaced Fock states, is introduced by applying the inverse of bosonic creation and annihilation operators to displaced Fock states. The quantum stati... A new kind of quantum optical state, photon-added and -subtracted displaced Fock states, is introduced by applying the inverse of bosonic creation and annihilation operators to displaced Fock states. The quantum statistical properties of these states are investigated by numerical methods. Numerical results indicate that these states reveal some interesting non-classical properties, such as anti-bunching effects, sub-Poisson distributions and negativities of their Wigner functions. 展开更多
关键词 Boson inverse operators photon-added and -subtracted states non-classical property
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Thermal Wigner Operator in Coherent Thermal State Representation and Its Application 被引量:2
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作者 FANHong-Yi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2002年第3期289-292,共4页
In the coherent thermal state representation we introduce thermal Wigner operator and find that it is'squeezed' under the thermal transformation. The thermal Wigner operator provides us with a new direct and n... In the coherent thermal state representation we introduce thermal Wigner operator and find that it is'squeezed' under the thermal transformation. The thermal Wigner operator provides us with a new direct and neatapproach for deriving Wigner functions of thermal states. 展开更多
关键词 coherent thermal state thermal Wigner operator
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Wigner Function:from Ensemble Average of Density Operator to Its Matrix Element in Entangled Pure States 被引量:2
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作者 FANHong-Yi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2002年第5期533-536,共4页
We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quant... We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom. 展开更多
关键词 Wigner function ensemble average of density operator matrix element in entangled pure states
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