For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f...For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.展开更多
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
Estimated ocean subsurface fields derived from satellite observations provide potential data sources for operational marine environmental monitoring and prediction systems.This study employs a statistic regression rec...Estimated ocean subsurface fields derived from satellite observations provide potential data sources for operational marine environmental monitoring and prediction systems.This study employs a statistic regression reconstruction method,in combination with domestic autonomous sea surface height and sea surface temperature observations from the Haiyang-2(HY-2)satellite fusion data,to establish an operational quasi-realtime three-dimensional(3D)temperature and salinity products over the Maritime Silk Road.These products feature a daily temporal resolution and a spatial resolution of 0.25°×0.25°and exhibit stability and continuity.We have demonstrated the accuracy of the reconstructed thermohaline fields in capturing the 3D thermohaline variations through comprehensive statistical evaluations,after comparing them against Argo observations and ocean analysis data from 2022.The results illustrate that the reconstructed fields effectively represent seasonal variations in oceanic subsurface structures,along with structural changes resulting from mesoscale processes,and the upper ocean’s responses to tropical cyclones.Furthermore,the incorporation of HY-2 satellite observations notably enhances the accuracy of temperature and salinity reconstructions in the Northwest Pacific Ocean and marginally improves salinity reconstruction accuracy in the North Indian Ocean when compared to the World Ocean Atlas 2018 monthly climatology thermohaline fields.As a result,the reconstructed product holds promise for providing quasi-real-time 3D temperature and salinity field information to facilitate fast decisionmaking during emergencies,and also offers foundational thermohaline fields for operational ocean reanalysis and forecasting systems.These contributions enhance the safety and stability of ocean subsurface activities and navigation.展开更多
Energy consumption and environmental impact considerations of machining processes are viewed as important issues for the global trends towards sustainable manufacturing. The existing research of reducing energy consum...Energy consumption and environmental impact considerations of machining processes are viewed as important issues for the global trends towards sustainable manufacturing. The existing research of reducing energy consumption and environmental impacts of machining processes greatly focuses on design and planning activities, but is reasonably sparse for production operation activities. This paper explores a systematic methodology that incorporates energy consumption and environmental impact considerations into the production operation of machining processes. Firstly, the framework of the methodology is proposed to establish the generic procedures for integrating the above considerations in production operation activities. As the two key issues of the framework, the profile index value matrix is determined by valuing the individual quantity of energy consumption and environmental impacts of machining each job on each machine, and the multi-criteria models are constructed by the operational methods. Furthermore, with the guideline of the framework, the specific formulations are modeled by two sub-models for the parallel machine scheduling problem, in which makespan and energy consumption are the optimizing objectives as well as the constraints of environmental impact considerations. The specific formulations provide a practical method to integrate energy consumption and environmental impact considerations into the scheduling activity, and also can serve as a reference to other activities in the production operation. The case study for a batch of jobs, including seven kinds of gears in the machining shop floor, is presented to demonstrate the application of the specific formulations of the methodology. The proposed methodology provides potential opportunities for reducing energy consumption and environmental impacts in machining processes, and helps production managers in decision-making on the issues of energy consumption and environmental impacts in the production operation.展开更多
To explore the problems of dynamic change in production demand and operating contradiction in production process, a new extension theory-based production operation method is proposed. The core is the demand requisitio...To explore the problems of dynamic change in production demand and operating contradiction in production process, a new extension theory-based production operation method is proposed. The core is the demand requisition, contradiction resolution and operation classification. For the demand requisition, the deep and comprehensive demand elements are collected by the conjugating analysis. For the contradiction resolution, the conflict between the demand and operating elements are solved by the extension reasoning, extension transformation and consistency judgment. For the operating classification, the operating importance among the operating elements is calculated by the extension clustering so as to guide the production operation and ensure the production safety. Through the actual application in the cascade reaction process of high-density polyethylene (HDPE) of a chemical plant, cases study and comparison show that the proposed extension theory-based production operation method is significantly better than the traditional experience-based operation method in actual production process, which exploits a new way to the research on the production operating methods for industrial process.展开更多
In order to guarantee the overall production performance of the multiple departments in an air-condition production industry, multidisciplinary design optimization model for production system is established based on t...In order to guarantee the overall production performance of the multiple departments in an air-condition production industry, multidisciplinary design optimization model for production system is established based on the multi-agent technology. Local operation models for departments of plan, marketing, sales, purchasing, as well as production and warehouse are formulated into individual agents, and their respective local objectives are collectively formulated into a multi-objective optimization problem. Considering the coupling effects among the correlated agents, the optimization process is carried out based on self-adaptive chaos immune optimization algorithm with mutative scale. The numerical results indicate that the proposed multi-agent optimization model truly reflects the actual situations of the air-condition production system. The proposed multi-agent based multidisciplinary design optimization method can help companies enhance their income ratio and profit by about 33% and 36%, respectively, and reduce the total cost by about 1.8%.展开更多
In order to improve production and operation ability of medium and small-sized enterprises, an assessment-index system of production and operation ability was proposed, and a corresponding assessment model was establi...In order to improve production and operation ability of medium and small-sized enterprises, an assessment-index system of production and operation ability was proposed, and a corresponding assessment model was established based on BP neural network. The conjunction weights of the neural network were continuously modified from output layer to input layer in the process of neural network training to reduce the errors between the anticipated and actual outputs. The results from an example show that this method is reliable and feasible. The production and operation abilitv of an enterorise with assessed result of 0.833 is fairly oowerful, and that with assessed result of 0.644 is average.展开更多
Developing production and operation in scales in the major grain producing areas is the direction of the paper. Seizing the opportunity of modem agriculture comprehensive reform in two plains （Songnen Plain and Sanji...Developing production and operation in scales in the major grain producing areas is the direction of the paper. Seizing the opportunity of modem agriculture comprehensive reform in two plains （Songnen Plain and Sanjiang Plain） of Heilongjiang Province and supporting to build a new type of production and management based on the big grain production householding, which plays demonstration and leading roles, have an important strategic position in improving agricultural comprehensive production capacity and ensuring national food security. In this paper, based on the survey data about the big grain production households production operations and analyses of the obstacles in expansion of production in Heilongjiang Province, specific suggestions in supporting the development of the big grain production household were put forward, such as, increasing agricultural production socialized level; perfecting the service system of land transferring; improving financial policies and farmer-friendly policy measures and perfecting the agriculture socialized service system.展开更多
The main body of household operation in the rural household contract responsibility system of our country has developed to the present stage,and has formed the situation that three kinds of rural households coexist,na...The main body of household operation in the rural household contract responsibility system of our country has developed to the present stage,and has formed the situation that three kinds of rural households coexist,namely,ordinary rural households,major professional households and family farms. The agricultural production and operation of three kinds of household plays an important role in supporting the rapid development of modern agriculture in China. Under the new situation of deepening the rural reform and realizing the goal of well-off society in an all-round way,it is of great practical significance to make a thorough investigation and study on the present situation and approaches relating to the construction of the agricultural production and operation capacity for the three kinds of rural households.展开更多
Optimizing operational parameters for syngas production of Texaco coal-water slurry gasifier studied in this paper is a complicated nonlinear constrained problem concerning 3 BP(Error Back Propagation) neural networks...Optimizing operational parameters for syngas production of Texaco coal-water slurry gasifier studied in this paper is a complicated nonlinear constrained problem concerning 3 BP(Error Back Propagation) neural networks. To solve this model, a new 3-layer cultural evolving algorithm framework which has a population space, a medium space and a belief space is firstly conceived. Standard differential evolution algorithm(DE), genetic algorithm(GA), and particle swarm optimization algorithm(PSO) are embedded in this framework to build 3-layer mixed cultural DE/GA/PSO(3LM-CDE, 3LM-CGA, and 3LM-CPSO) algorithms. The accuracy and efficiency of the proposed hybrid algorithms are firstly tested in 20 benchmark nonlinear constrained functions. Then, the operational optimization model for syngas production in a Texaco coal-water slurry gasifier of a real-world chemical plant is solved effectively. The simulation results are encouraging that the 3-layer cultural algorithm evolving framework suggests ways in which the performance of DE, GA, PSO and other population-based evolutionary algorithms(EAs) can be improved,and the optimal operational parameters based on 3LM-CDE algorithm of the syngas production in the Texaco coalwater slurry gasifier shows outstanding computing results than actual industry use and other algorithms.展开更多
In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechani...In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.展开更多
The development of quantum optics theory based on the method of integration within an ordered product of operators(IWOP)has greatly stimulated the study of quantum states in the light field,especially non-Gaussian sta...The development of quantum optics theory based on the method of integration within an ordered product of operators(IWOP)has greatly stimulated the study of quantum states in the light field,especially non-Gaussian states with various non-classical properties.In this paper,the two-mode squeezing operator is derived with integral theory within the Weyl ordering product of operators using a combinatorial field in which one mode is a chaotic field and the other mode is a vacuum field.The density operator of the new light field,its entanglement property and photon number distribution are analyzed.We also note that tracing a three-mode pure state can yield this new light field.These methods represent a theoretical approach to investigating new density operators of light fields.展开更多
The meteorological operation system production database used in the stations at the extension of Lanzhou Regional Meteorological Center (LRMC), is an important part of the second period project setting up items. The s...The meteorological operation system production database used in the stations at the extension of Lanzhou Regional Meteorological Center (LRMC), is an important part of the second period project setting up items. The system includes the database, function module and self-safeguard system. The products of the system can be easily explanted from VMS to UNIX, and their functions can not be affected.展开更多
By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antino...By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.展开更多
In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product space...In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product spaces. In addition, we give new proofs for some known results.展开更多
For the first time,we derive the compact forms of normalization factors for photon-added（-subtracted） two-mode squeezed thermal states by using the P-representation and the integration within an ordered product of o...For the first time,we derive the compact forms of normalization factors for photon-added（-subtracted） two-mode squeezed thermal states by using the P-representation and the integration within an ordered product of operators（IWOP） technique.It is found that these two factors are related to the Jacobi polynomials.In addition,some new relationships for Jacobi polynomials are presented.展开更多
By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials wh...By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.展开更多
文摘For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.
基金Project supported by the Foundation for Young Talents in College of Anhui Province, China (Grant Nos. gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions, China (Grant Nos. 2022AH051580 and 2022AH051586)。
文摘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.
基金The China-ASEAN Marine Cooperation Foundationthe Fundamental Research Funds for the Central Universities under contract No.B210203041+1 种基金the Postgraduate Research&Practice Innovation Program of Jiangsu Province under contract No.KYCX23_0657the opening project of the Key Laboratory of Marine Environmental Information Technology of Ministry of Natural Resources under contract No.521037412.
文摘Estimated ocean subsurface fields derived from satellite observations provide potential data sources for operational marine environmental monitoring and prediction systems.This study employs a statistic regression reconstruction method,in combination with domestic autonomous sea surface height and sea surface temperature observations from the Haiyang-2(HY-2)satellite fusion data,to establish an operational quasi-realtime three-dimensional(3D)temperature and salinity products over the Maritime Silk Road.These products feature a daily temporal resolution and a spatial resolution of 0.25°×0.25°and exhibit stability and continuity.We have demonstrated the accuracy of the reconstructed thermohaline fields in capturing the 3D thermohaline variations through comprehensive statistical evaluations,after comparing them against Argo observations and ocean analysis data from 2022.The results illustrate that the reconstructed fields effectively represent seasonal variations in oceanic subsurface structures,along with structural changes resulting from mesoscale processes,and the upper ocean’s responses to tropical cyclones.Furthermore,the incorporation of HY-2 satellite observations notably enhances the accuracy of temperature and salinity reconstructions in the Northwest Pacific Ocean and marginally improves salinity reconstruction accuracy in the North Indian Ocean when compared to the World Ocean Atlas 2018 monthly climatology thermohaline fields.As a result,the reconstructed product holds promise for providing quasi-real-time 3D temperature and salinity field information to facilitate fast decisionmaking during emergencies,and also offers foundational thermohaline fields for operational ocean reanalysis and forecasting systems.These contributions enhance the safety and stability of ocean subsurface activities and navigation.
基金supported by National Natural Science Foundation of China (Grant No. 50775228)Program for New Century Excellent Talents in University of Ministry of Education, China (Grant No. NCET-07-0907)Chongqing Provincal Natural Science Foundation of China (Grant No. 2010BB0055)
文摘Energy consumption and environmental impact considerations of machining processes are viewed as important issues for the global trends towards sustainable manufacturing. The existing research of reducing energy consumption and environmental impacts of machining processes greatly focuses on design and planning activities, but is reasonably sparse for production operation activities. This paper explores a systematic methodology that incorporates energy consumption and environmental impact considerations into the production operation of machining processes. Firstly, the framework of the methodology is proposed to establish the generic procedures for integrating the above considerations in production operation activities. As the two key issues of the framework, the profile index value matrix is determined by valuing the individual quantity of energy consumption and environmental impacts of machining each job on each machine, and the multi-criteria models are constructed by the operational methods. Furthermore, with the guideline of the framework, the specific formulations are modeled by two sub-models for the parallel machine scheduling problem, in which makespan and energy consumption are the optimizing objectives as well as the constraints of environmental impact considerations. The specific formulations provide a practical method to integrate energy consumption and environmental impact considerations into the scheduling activity, and also can serve as a reference to other activities in the production operation. The case study for a batch of jobs, including seven kinds of gears in the machining shop floor, is presented to demonstrate the application of the specific formulations of the methodology. The proposed methodology provides potential opportunities for reducing energy consumption and environmental impacts in machining processes, and helps production managers in decision-making on the issues of energy consumption and environmental impacts in the production operation.
基金Supported by the National Natural Science Foundation of China(61104131)the Fundamental Research Funds for Central Universities(ZY1111)
文摘To explore the problems of dynamic change in production demand and operating contradiction in production process, a new extension theory-based production operation method is proposed. The core is the demand requisition, contradiction resolution and operation classification. For the demand requisition, the deep and comprehensive demand elements are collected by the conjugating analysis. For the contradiction resolution, the conflict between the demand and operating elements are solved by the extension reasoning, extension transformation and consistency judgment. For the operating classification, the operating importance among the operating elements is calculated by the extension clustering so as to guide the production operation and ensure the production safety. Through the actual application in the cascade reaction process of high-density polyethylene (HDPE) of a chemical plant, cases study and comparison show that the proposed extension theory-based production operation method is significantly better than the traditional experience-based operation method in actual production process, which exploits a new way to the research on the production operating methods for industrial process.
基金Project(60973132)supported by the National Natural Science Foundation of ChinaProject(2010B050400005)supported by the Science and Research Program of Guangdong Province,China
文摘In order to guarantee the overall production performance of the multiple departments in an air-condition production industry, multidisciplinary design optimization model for production system is established based on the multi-agent technology. Local operation models for departments of plan, marketing, sales, purchasing, as well as production and warehouse are formulated into individual agents, and their respective local objectives are collectively formulated into a multi-objective optimization problem. Considering the coupling effects among the correlated agents, the optimization process is carried out based on self-adaptive chaos immune optimization algorithm with mutative scale. The numerical results indicate that the proposed multi-agent optimization model truly reflects the actual situations of the air-condition production system. The proposed multi-agent based multidisciplinary design optimization method can help companies enhance their income ratio and profit by about 33% and 36%, respectively, and reduce the total cost by about 1.8%.
基金Project 2001FJJ036 supported by Society Science Foundation of Henan Province
文摘In order to improve production and operation ability of medium and small-sized enterprises, an assessment-index system of production and operation ability was proposed, and a corresponding assessment model was established based on BP neural network. The conjunction weights of the neural network were continuously modified from output layer to input layer in the process of neural network training to reduce the errors between the anticipated and actual outputs. The results from an example show that this method is reliable and feasible. The production and operation abilitv of an enterorise with assessed result of 0.833 is fairly oowerful, and that with assessed result of 0.644 is average.
基金Supported by the Stage Achievement of Social Science Fund Project of Heilongjiang Province and the Application of Technology Research(12C053)the Development Project in Heilongjiang Province(2013R0242)
文摘Developing production and operation in scales in the major grain producing areas is the direction of the paper. Seizing the opportunity of modem agriculture comprehensive reform in two plains （Songnen Plain and Sanjiang Plain） of Heilongjiang Province and supporting to build a new type of production and management based on the big grain production householding, which plays demonstration and leading roles, have an important strategic position in improving agricultural comprehensive production capacity and ensuring national food security. In this paper, based on the survey data about the big grain production households production operations and analyses of the obstacles in expansion of production in Heilongjiang Province, specific suggestions in supporting the development of the big grain production household were put forward, such as, increasing agricultural production socialized level; perfecting the service system of land transferring; improving financial policies and farmer-friendly policy measures and perfecting the agriculture socialized service system.
基金Supported by Social Science Fund Project of Hubei Province in 2016(2016106)
文摘The main body of household operation in the rural household contract responsibility system of our country has developed to the present stage,and has formed the situation that three kinds of rural households coexist,namely,ordinary rural households,major professional households and family farms. The agricultural production and operation of three kinds of household plays an important role in supporting the rapid development of modern agriculture in China. Under the new situation of deepening the rural reform and realizing the goal of well-off society in an all-round way,it is of great practical significance to make a thorough investigation and study on the present situation and approaches relating to the construction of the agricultural production and operation capacity for the three kinds of rural households.
基金Supported by the National Natural Science Foundation of China(61174040,U1162110,21206174)Shanghai Commission of Nature Science(12ZR1408100)
文摘Optimizing operational parameters for syngas production of Texaco coal-water slurry gasifier studied in this paper is a complicated nonlinear constrained problem concerning 3 BP(Error Back Propagation) neural networks. To solve this model, a new 3-layer cultural evolving algorithm framework which has a population space, a medium space and a belief space is firstly conceived. Standard differential evolution algorithm(DE), genetic algorithm(GA), and particle swarm optimization algorithm(PSO) are embedded in this framework to build 3-layer mixed cultural DE/GA/PSO(3LM-CDE, 3LM-CGA, and 3LM-CPSO) algorithms. The accuracy and efficiency of the proposed hybrid algorithms are firstly tested in 20 benchmark nonlinear constrained functions. Then, the operational optimization model for syngas production in a Texaco coal-water slurry gasifier of a real-world chemical plant is solved effectively. The simulation results are encouraging that the 3-layer cultural algorithm evolving framework suggests ways in which the performance of DE, GA, PSO and other population-based evolutionary algorithms(EAs) can be improved,and the optimal operational parameters based on 3LM-CDE algorithm of the syngas production in the Texaco coalwater slurry gasifier shows outstanding computing results than actual industry use and other algorithms.
基金Project supported by the National Natural Science Foundation of China(Grant No.11775208)the Foundation for Young Talents at the College of Anhui Province,China(Grant Nos.gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions of China(Grant Nos.KJ2020A0638 and 2022AH051586)。
文摘In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.
基金Project supported by the National Natural Science Foundation of China(Grant No.11775208)the Foundation for Young Talents in College of Anhui Province,China(Grant Nos.gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions of China(Grant Nos.KJ2020A0638 and 2022AH051586)。
文摘The development of quantum optics theory based on the method of integration within an ordered product of operators(IWOP)has greatly stimulated the study of quantum states in the light field,especially non-Gaussian states with various non-classical properties.In this paper,the two-mode squeezing operator is derived with integral theory within the Weyl ordering product of operators using a combinatorial field in which one mode is a chaotic field and the other mode is a vacuum field.The density operator of the new light field,its entanglement property and photon number distribution are analyzed.We also note that tracing a three-mode pure state can yield this new light field.These methods represent a theoretical approach to investigating new density operators of light fields.
文摘The meteorological operation system production database used in the stations at the extension of Lanzhou Regional Meteorological Center (LRMC), is an important part of the second period project setting up items. The system includes the database, function module and self-safeguard system. The products of the system can be easily explanted from VMS to UNIX, and their functions can not be affected.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)
文摘By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.
基金the Project of Development Plan of the State Key Fundamental Research Major Project of NNSFC,and NSFZJ.
文摘In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product spaces. In addition, we give new proofs for some known results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11264018 and 60978009)the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91121023)+1 种基金the National Basic Research Project of China (Grant No. 2011CBA00200)the Young Talents Foundation of Jiangxi Normal University,China
文摘For the first time,we derive the compact forms of normalization factors for photon-added（-subtracted） two-mode squeezed thermal states by using the P-representation and the integration within an ordered product of operators（IWOP） technique.It is found that these two factors are related to the Jacobi polynomials.In addition,some new relationships for Jacobi polynomials are presented.
基金supported by the National Natural Science Foundation of China(Grant No.11175113)the Fundamental Research Funds for the Central Universities of China(Grant No.WK2060140013)
文摘By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.
