After the birth of quantum mechanics, the notion in physics that the frequency of light is the only factor that determines the energy of a single photon has played a fundamental role. However, under the assumption tha...After the birth of quantum mechanics, the notion in physics that the frequency of light is the only factor that determines the energy of a single photon has played a fundamental role. However, under the assumption that the theory of Lewis-Riesenfeld invariants is applicable in quantum optics, it is shown in the present work that this widely accepted notion is valid only for light described by a time-independent Hamiltonian, i.e., for light in media satisfying the conditions, ε(t) = ε(0), u(t) = u(0), and σ(t) = 0 simultaneously. The use of the Lewis Riesenfeld invariant operator method in quantum optics leads to a marvelous result: the energy of a single photon propagating through time-varying linear media exhibits nontrivial time dependence without a change of frequency.展开更多
In this paper,a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity.With considering th...In this paper,a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity.With considering the effect of unknown input nonlinearity from the piezoelectric actuator,operator based controllers are designed to guarantee the robust stability of the nonlinear free vibration control system.Simultaneously,for ensuring the desired tracking performance and reducing the effect of unknown input nonlinearity,operator based tracking compensator and estimation structure are given,respectively.Finally,both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.展开更多
We investigate the general condition for an operator to be unitary.This condition is introduced according to the definition of the position operator in curved space.In a particular case,we discuss the concept of trans...We investigate the general condition for an operator to be unitary.This condition is introduced according to the definition of the position operator in curved space.In a particular case,we discuss the concept of translation operator in curved space followed by its relation with an anti-Hermitian generator.Also we introduce a universal formula for adjoint of an arbitrary linear operator.Our procedure in this paper is totally different from others,as we explore a general approach based only on the algebra of the operators.Our approach is only discussed for the translation operators in one-dimensional space and not for general operators.展开更多
With deployment of measurement units,fitting static equivalent models of distribution networks(DNs)by linear regression has been recognized as an effective method in power flow analysis of a transmission network.Incre...With deployment of measurement units,fitting static equivalent models of distribution networks(DNs)by linear regression has been recognized as an effective method in power flow analysis of a transmission network.Increasing volatility of measurements caused by variable distributed renewable energy sources makes it more difficult to accurately fit such equivalent models.To tackle this challenge,this letter proposes a novel data-driven method to improve equivalency accuracy of DNs with distributed energy resources.This letter provides a new perspective that an equivalent model can be regarded as a mapping from internal conditions and border voltages to border power injections.Such mapping can be established through 1)Koopman operator theory,and 2)physical features of power flow equations at the root node of a DN.Performance of the proposed method is demonstrated on the IEEE 33-bus and IEEE 136-bus test systems connected to a 661-bus utility system.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
Following up Neuts' idea, the SPH-distribution class associated with bounded Q matrices for infinite Markov chains is denned. The main result in this paper is to characterize the SPH class through the derivatives ...Following up Neuts' idea, the SPH-distribution class associated with bounded Q matrices for infinite Markov chains is denned. The main result in this paper is to characterize the SPH class through the derivatives of the distribution functions. Based on the characterization theorem, closure properties, the expansion, uniform approximation, and the matrix representations of the SPH class are also discussed by the derivatives of the distribution functions at origin.展开更多
This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be a...This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.展开更多
We prove that every homomorphism of the algebra P<sub><em>n</em></sub> into the algebra of operators on a Hilbert space is completely bounded. We show that the contractive homomorphism introduc...We prove that every homomorphism of the algebra P<sub><em>n</em></sub> into the algebra of operators on a Hilbert space is completely bounded. We show that the contractive homomorphism introduced by Parrott, which is not completely contractive, is completely bounded (similar to a completely contractive homomorphism). We also show that homomorphisms of the algebra <span style="white-space:normal;">P</span><sub style="white-space:normal;"><em>n</em></sub> generate completely positive maps over the algebras <em>C</em>(T<sup><em>n</em></sup>)and <em>M</em><sub>2</sub>(<em>C</em>(T<sup><em>n</em></sup>)).展开更多
By applying the Fourier analysis, we study the spectral properties of R- filters. Further, we prove that R-filters are a generalization of least squares polynomial adjustment, and we give the geometric interpretation ...By applying the Fourier analysis, we study the spectral properties of R- filters. Further, we prove that R-filters are a generalization of least squares polynomial adjustment, and we give the geometric interpretation of R-filters.展开更多
We prove that every matrix </span><i><span style="font-family:"">F</span></i><span style="font-size:6.5pt;line-height:102%;font-family:宋体;">∈</span>...We prove that every matrix </span><i><span style="font-family:"">F</span></i><span style="font-size:6.5pt;line-height:102%;font-family:宋体;">∈</span><i><span style="font-family:"">M</span></i><sub><span style="font-family:"">k </span></sub><span style="font-family:"">(P<sub>n</sub>)</span><span style="font-family:""> is associated </span><span style="font-family:"">with</span><span style="font-family:""> </span><span style="font-family:"">the</span><span style="font-family:""> smallest positive integer </span><i><span style="font-family:"">d</span></i><span style="font-family:""> (<i>F</i>)</span><span style="font-size:8.0pt;line-height:102%;font-family:宋体;">≠</span><span style="font-family:"">1</span><span style="font-family:""> such that </span><i><span style="font-family:"">d </span></i><span style="font-family:"">(<i>F</i>)</span><span style="font-family:宋体;">‖</span><i><span style="font-family:"">F</span></i><span style="font-family:宋体;">‖</span><sub><span style="font-size:9px;line-height:102%;font-family:宋体;">∞</span></sub><span style="font-family:""> </span><span style="font-family:"">is always bigger than the sum of the operator norms of the Fourier coefficients of <i>F</i>. We establish some inequalities for matrices of complex polynomials. In application, we show that von Neumann’s inequality hold</span><span style="font-family:"">s</span><span style="font-family:""> up to the constant </span><span style="font-family:"">2<sup>n </sup></span><span style="font-family:"">for matrices of the algebra</span><span style="font-family:""> <i>M</i><sub>k </sub>(P<sub>n</sub>).</span><span style="font-family:""></span> </p> <br /> <span style="font-family:;" "=""></span>展开更多
A two-dimensional periodic array of quantum dots with two laterally coupled leads in a magnetic field is considered. The model of electron transport through the system based on the theory of self-adjoint extensions of...A two-dimensional periodic array of quantum dots with two laterally coupled leads in a magnetic field is considered. The model of electron transport through the system based on the theory of self-adjoint extensions of symmetric operators is suggested. We obtain the formula for the transmission coefficient and investigate its dependence on the magnetic field.展开更多
The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such op...The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.展开更多
In the past,arms used in the fields of industry and robotics have been designed not to vibrate by increasing their mass and stiffness.The weight of arms has tended to be reduced to improve speed of operation,and decre...In the past,arms used in the fields of industry and robotics have been designed not to vibrate by increasing their mass and stiffness.The weight of arms has tended to be reduced to improve speed of operation,and decrease the cost of their production.Since the weight saving makes the arms lose their stiffness and therefore vibrate more easily,the vibration suppression control is needed for realizing the above purpose.Incidentally,the use of various smart materials in actuators has grown.In particular,a shape memory alloy(SMA)is applied widely and has several advantages:light weight,large displacement by temperature change,and large force to mass ratio.However,the SMA actuators possess hysteresis nonlinearity between their own temperature and displacement obtained by the temperature.The hysteretic behavior of the SMA actuators affects their control performance.In previous research,an operator-based control system including a hysteresis compensator has been proposed.The vibration of a flexible arm is dealt with as the controlled object;one end of the arm is clamped and the other end is free.The effectiveness of the hysteresis compensator has been confirmed by simulations and experiments.Nevertheless,the feedback signal of the previous designed system has increased exponentially.It is difficult to use the system in the long-term because of the phenomenon.Additionally,the SMA actuator generates and radiates heat because electric current passing through the SMA actuator provides heat,and strain on the SMA actuator is generated.With long-time use of the SMA actuator,the environmental temperature around the SMA actuator varies through radiation of the heat.There exists a risk that the ambient temperature change dealt with as disturbance affects the temperature and strain of the SMA actuator.In this research,a design method of the operator-based control system is proposed considering the long-term use of the system.In the method,the hysteresis characteristics of the SMA actuator and the temperature change around the actuator are considered.The effectiveness of the proposed method is verified by simulations and experiments.展开更多
A significant number of studies have been carried out on the generalized Lebesgue spaces L^p(x), Sobolev spaces W^1,p(x) and Herz spaces. In this paper, we demonstrated a characterization of boundedness of the fractio...A significant number of studies have been carried out on the generalized Lebesgue spaces L^p(x), Sobolev spaces W^1,p(x) and Herz spaces. In this paper, we demonstrated a characterization of boundedness of the fractional maximal operator with variable kernel on Herz-Morrey spaces.展开更多
This paper deals with a class of nonlinear boundary value problems which appears in the study of models of flows through porous media. Existence results of asymptotic bifurcation and continua are reported both for ope...This paper deals with a class of nonlinear boundary value problems which appears in the study of models of flows through porous media. Existence results of asymptotic bifurcation and continua are reported both for operator equations and for boundary value problems.展开更多
Resources shared in e-Science have critical requirements on security.Thus subjective trust management is essential to guarantee users' collaborations and communications on such a promising infrastructure.As an import...Resources shared in e-Science have critical requirements on security.Thus subjective trust management is essential to guarantee users' collaborations and communications on such a promising infrastructure.As an important nature of subjective trust,uncertainty should be preserved and exhibited in trust definition,representation and evolution.Consider the drawbacks of existing mechanisms based on random mathematics and fuzzy theory,this paper designs an uncertainty enhanced trust evolution strategy based on cloud model theory.We define subjective trust as trust cloud.Then we propose new algorithms to propagate,aggregate and update trust.Furthermore,based on the concept of similar cloud,a method to assess trust level is put forward.The simulation results show the effiectiveness,rationality and efficiency of our proposed strategy.展开更多
基金supported by National Research Foundation of Korea Grant funded by the Korean Government (No. 2009-0077951)
文摘After the birth of quantum mechanics, the notion in physics that the frequency of light is the only factor that determines the energy of a single photon has played a fundamental role. However, under the assumption that the theory of Lewis-Riesenfeld invariants is applicable in quantum optics, it is shown in the present work that this widely accepted notion is valid only for light described by a time-independent Hamiltonian, i.e., for light in media satisfying the conditions, ε(t) = ε(0), u(t) = u(0), and σ(t) = 0 simultaneously. The use of the Lewis Riesenfeld invariant operator method in quantum optics leads to a marvelous result: the energy of a single photon propagating through time-varying linear media exhibits nontrivial time dependence without a change of frequency.
文摘In this paper,a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity.With considering the effect of unknown input nonlinearity from the piezoelectric actuator,operator based controllers are designed to guarantee the robust stability of the nonlinear free vibration control system.Simultaneously,for ensuring the desired tracking performance and reducing the effect of unknown input nonlinearity,operator based tracking compensator and estimation structure are given,respectively.Finally,both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.
文摘We investigate the general condition for an operator to be unitary.This condition is introduced according to the definition of the position operator in curved space.In a particular case,we discuss the concept of translation operator in curved space followed by its relation with an anti-Hermitian generator.Also we introduce a universal formula for adjoint of an arbitrary linear operator.Our procedure in this paper is totally different from others,as we explore a general approach based only on the algebra of the operators.Our approach is only discussed for the translation operators in one-dimensional space and not for general operators.
基金supported by the Research Grants Council of Hong Kong,China,through ECS Award No.24210220。
文摘With deployment of measurement units,fitting static equivalent models of distribution networks(DNs)by linear regression has been recognized as an effective method in power flow analysis of a transmission network.Increasing volatility of measurements caused by variable distributed renewable energy sources makes it more difficult to accurately fit such equivalent models.To tackle this challenge,this letter proposes a novel data-driven method to improve equivalency accuracy of DNs with distributed energy resources.This letter provides a new perspective that an equivalent model can be regarded as a mapping from internal conditions and border voltages to border power injections.Such mapping can be established through 1)Koopman operator theory,and 2)physical features of power flow equations at the root node of a DN.Performance of the proposed method is demonstrated on the IEEE 33-bus and IEEE 136-bus test systems connected to a 661-bus utility system.
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Supported by the National Natural Science Foundation of China (70171059)
文摘Following up Neuts' idea, the SPH-distribution class associated with bounded Q matrices for infinite Markov chains is denned. The main result in this paper is to characterize the SPH class through the derivatives of the distribution functions. Based on the characterization theorem, closure properties, the expansion, uniform approximation, and the matrix representations of the SPH class are also discussed by the derivatives of the distribution functions at origin.
基金supported by the Explore Foundation of Weapon Development (Grant No 7130620)
文摘This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.
文摘We prove that every homomorphism of the algebra P<sub><em>n</em></sub> into the algebra of operators on a Hilbert space is completely bounded. We show that the contractive homomorphism introduced by Parrott, which is not completely contractive, is completely bounded (similar to a completely contractive homomorphism). We also show that homomorphisms of the algebra <span style="white-space:normal;">P</span><sub style="white-space:normal;"><em>n</em></sub> generate completely positive maps over the algebras <em>C</em>(T<sup><em>n</em></sup>)and <em>M</em><sub>2</sub>(<em>C</em>(T<sup><em>n</em></sup>)).
基金Project supported by the National Basic Research Program of China (973 Program) (No. NKBRPC-2004CB318003)the Knowledge Innovation Program of the Chinese Academy of Sciences(No. KJCX2-YW-S02)the National Natural Science Foundation of China (No. 10771205)
文摘By applying the Fourier analysis, we study the spectral properties of R- filters. Further, we prove that R-filters are a generalization of least squares polynomial adjustment, and we give the geometric interpretation of R-filters.
文摘We prove that every matrix </span><i><span style="font-family:"">F</span></i><span style="font-size:6.5pt;line-height:102%;font-family:宋体;">∈</span><i><span style="font-family:"">M</span></i><sub><span style="font-family:"">k </span></sub><span style="font-family:"">(P<sub>n</sub>)</span><span style="font-family:""> is associated </span><span style="font-family:"">with</span><span style="font-family:""> </span><span style="font-family:"">the</span><span style="font-family:""> smallest positive integer </span><i><span style="font-family:"">d</span></i><span style="font-family:""> (<i>F</i>)</span><span style="font-size:8.0pt;line-height:102%;font-family:宋体;">≠</span><span style="font-family:"">1</span><span style="font-family:""> such that </span><i><span style="font-family:"">d </span></i><span style="font-family:"">(<i>F</i>)</span><span style="font-family:宋体;">‖</span><i><span style="font-family:"">F</span></i><span style="font-family:宋体;">‖</span><sub><span style="font-size:9px;line-height:102%;font-family:宋体;">∞</span></sub><span style="font-family:""> </span><span style="font-family:"">is always bigger than the sum of the operator norms of the Fourier coefficients of <i>F</i>. We establish some inequalities for matrices of complex polynomials. In application, we show that von Neumann’s inequality hold</span><span style="font-family:"">s</span><span style="font-family:""> up to the constant </span><span style="font-family:"">2<sup>n </sup></span><span style="font-family:"">for matrices of the algebra</span><span style="font-family:""> <i>M</i><sub>k </sub>(P<sub>n</sub>).</span><span style="font-family:""></span> </p> <br /> <span style="font-family:;" "=""></span>
基金Project supported by the Federal Targeted Program"Scientific and Educational Human Resources for Innovation-Driven Russia"(Grant Nos. P689 NK-526P,14.740.11.0879,16.740.11.0030,and 2012-1.2.2-12-000-1001-047)the Russian Foundation for Basic Researches (Grant No. 11-08-00267)the Federal Targeted Program "Researches and Development in the Priority Directions Developments of a Scientific and Technological Complex of Russia 2007-2013" (Grant No. 07.514.11.4146)
文摘A two-dimensional periodic array of quantum dots with two laterally coupled leads in a magnetic field is considered. The model of electron transport through the system based on the theory of self-adjoint extensions of symmetric operators is suggested. We obtain the formula for the transmission coefficient and investigate its dependence on the magnetic field.
文摘The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.
文摘In the past,arms used in the fields of industry and robotics have been designed not to vibrate by increasing their mass and stiffness.The weight of arms has tended to be reduced to improve speed of operation,and decrease the cost of their production.Since the weight saving makes the arms lose their stiffness and therefore vibrate more easily,the vibration suppression control is needed for realizing the above purpose.Incidentally,the use of various smart materials in actuators has grown.In particular,a shape memory alloy(SMA)is applied widely and has several advantages:light weight,large displacement by temperature change,and large force to mass ratio.However,the SMA actuators possess hysteresis nonlinearity between their own temperature and displacement obtained by the temperature.The hysteretic behavior of the SMA actuators affects their control performance.In previous research,an operator-based control system including a hysteresis compensator has been proposed.The vibration of a flexible arm is dealt with as the controlled object;one end of the arm is clamped and the other end is free.The effectiveness of the hysteresis compensator has been confirmed by simulations and experiments.Nevertheless,the feedback signal of the previous designed system has increased exponentially.It is difficult to use the system in the long-term because of the phenomenon.Additionally,the SMA actuator generates and radiates heat because electric current passing through the SMA actuator provides heat,and strain on the SMA actuator is generated.With long-time use of the SMA actuator,the environmental temperature around the SMA actuator varies through radiation of the heat.There exists a risk that the ambient temperature change dealt with as disturbance affects the temperature and strain of the SMA actuator.In this research,a design method of the operator-based control system is proposed considering the long-term use of the system.In the method,the hysteresis characteristics of the SMA actuator and the temperature change around the actuator are considered.The effectiveness of the proposed method is verified by simulations and experiments.
文摘A significant number of studies have been carried out on the generalized Lebesgue spaces L^p(x), Sobolev spaces W^1,p(x) and Herz spaces. In this paper, we demonstrated a characterization of boundedness of the fractional maximal operator with variable kernel on Herz-Morrey spaces.
文摘This paper deals with a class of nonlinear boundary value problems which appears in the study of models of flows through porous media. Existence results of asymptotic bifurcation and continua are reported both for operator equations and for boundary value problems.
基金Supported by the National Natural Science Foundation of China under Grant No.60703048the Open Foundation of State Key Lab of Software Engineering of Wuhan University under Grant No.SKLSE20080720the Open Foundation of State Key Laboratory for Novel Software Technology of Nanjing University under Grant No.KFKT2009B22
文摘Resources shared in e-Science have critical requirements on security.Thus subjective trust management is essential to guarantee users' collaborations and communications on such a promising infrastructure.As an important nature of subjective trust,uncertainty should be preserved and exhibited in trust definition,representation and evolution.Consider the drawbacks of existing mechanisms based on random mathematics and fuzzy theory,this paper designs an uncertainty enhanced trust evolution strategy based on cloud model theory.We define subjective trust as trust cloud.Then we propose new algorithms to propagate,aggregate and update trust.Furthermore,based on the concept of similar cloud,a method to assess trust level is put forward.The simulation results show the effiectiveness,rationality and efficiency of our proposed strategy.