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
In this article,we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrodinger type operator(—Δ)^2+V%2 in R%n(n≥5)with V being a nonnegat...In this article,we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrodinger type operator(—Δ)^2+V%2 in R%n(n≥5)with V being a nonnegative potential satisfying the reverse Holder inequality.Furt her more,we prove the boundedness of the variation operators on associated Morrey spaces.In the proof of the main results,we always make use of the variation inequalities associated with the hea t semigroup genera ted by the biharmonic operator(-Δ)2.展开更多
Solar arrays are important and indispensable parts of spacecraft and provide energy support for spacecraft to operate in orbit and complete on-orbit missions.When a spacecraft is in orbit,because the solar array is ex...Solar arrays are important and indispensable parts of spacecraft and provide energy support for spacecraft to operate in orbit and complete on-orbit missions.When a spacecraft is in orbit,because the solar array is exposed to the harsh space environment,with increasing working time,the performance of its internal electronic components gradually degrade until abnormal damage occurs.This damage makes solar array power generation unable to fully meet the energy demand of a spacecraft.Therefore,timely and accurate detection of solar array anomalies is of great significance for the on-orbit operation and maintenance management of spacecraft.In this paper,we propose an anomaly detection method for spacecraft solar arrays based on the integrated least squares support vector machine(ILS-SVM)model:it selects correlated telemetry data from spacecraft solar arrays to form a training set and extracts n groups of training subsets from this set,then gets n corresponding least squares support vector machine(LS-SVM)submodels by training on these training subsets,respectively;after that,the ILS-SVM model is obtained by integrating these submodels through a weighting operation to increase the prediction accuracy and so on;finally,based on the obtained ILS-SVM model,a parameterfree and unsupervised anomaly determination method is proposed to detect the health status of solar arrays.We use the telemetry data set from a satellite in orbit to carry out experimental verification and find that the proposed method can diagnose solar array anomalies in time and can capture the signs before a solar array anomaly occurs,which reflects the applicability of the method.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
In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and fo...In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in Hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found.展开更多
In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By u...In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.展开更多
As a generalization of grand Furuta inequality,recently Furuta obtain:If A≥ B≥0 with A>0,then for t∈[0,1]and p1,p2,p3,p4≥1, A t 2[A- t 2{A t 2(A/ t 2 Bp 1A /t2 )p 2A t 2}p 3A /t2 ]p 4A t 2 1 [{(p1/t)p2+t}p3-t]p...As a generalization of grand Furuta inequality,recently Furuta obtain:If A≥ B≥0 with A>0,then for t∈[0,1]and p1,p2,p3,p4≥1, A t 2[A- t 2{A t 2(A/ t 2 Bp 1A /t2 )p 2A t 2}p 3A /t2 ]p 4A t 2 1 [{(p1/t)p2+t}p3-t]p4+t]≤A. In this paper,we generalize this result for three operators as follow:If A≥B≥C≥0 with B>0,t∈[0,1]and p1,p2,···,p2n/1,p2n≥1 for a natural number n.Then the following inequalities hold for r≥t, A1/t+r≥ [A r 2[B /t 2{B t 2······[B /t 2{B t 2(B /t 2 ←B /t 2 n times Bt 2 n/1 times by turns Cp 1B /t 2)p 2B t 2}p 3B /t 2]p 4···B t 2}p 2n/1B /t 2 B /t 2 n times Bt 2 n/1 times by turns→ ]p 2nA r 2] 1/t+r q[2n]+r/t, where q[2n]≡{···[{[(p1/t)p2+t]p3/t}p4+t]p5/···/t}p2n+t /t and t alternately n times appear .展开更多
The paper proposes a scalable fuzzy approach for mapping the status of the environment integrating several distinct models exploiting geo big data. The process is structured into two phases: the first one can exploit ...The paper proposes a scalable fuzzy approach for mapping the status of the environment integrating several distinct models exploiting geo big data. The process is structured into two phases: the first one can exploit products yielded by distinct models of remote sensing image interpretation defined in the scientific literature, and knowledge of domain experts, possibly ill-defined, for computing partial evidence of a phenomenon. The second phase integrates the partial evidence maps through a learning mechanism exploiting ground truth to compute a synthetic Environmental Status Indicator (ESI) map. The proposal resembles an ensemble approach with the difference that the aggregation is not necessarily consensual but can model a distinct decision attitude in between pessimistic and optimistic. It is scalable and can be implemented in a distributed processing framework, so as to make feasible ESI mapping in near real time to support land monitoring. It is exemplified to map the presence of standing water areas, indicator of water resources, agro-practices or natural hazard from remote sensing by considering different models.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
Using an operator ordering method for some commutative superposition operators,we introduce two new multi-variable special polynomials and their generating functions,and present some new operator identities and integr...Using an operator ordering method for some commutative superposition operators,we introduce two new multi-variable special polynomials and their generating functions,and present some new operator identities and integral formulas involving the two special polynomials.Instead of calculating compli-cated partial differential,we use the special polynomials and their generating functions to concsely address the normalzation,photoount distributions and Wigner distributions of several quantum states that can be realized physically,the rsults of which provide real convenience for further investigating the properties and applications of these states.展开更多
This paper discusses some problems on the cardinal spline interpolation correspond-ing to infinite order differential operators.The remainder formulas and a dual theorem are es-tablished for some convolution classes,w...This paper discusses some problems on the cardinal spline interpolation correspond-ing to infinite order differential operators.The remainder formulas and a dual theorem are es-tablished for some convolution classes,where the kernels are PF densities.Moreover,the exacterror of approximation of a convolution class with interpolation cardinal splines is determined.The exact values of average n-Kolmogorov widths are obtained for the convolution class.展开更多
§1.IntroductionThis paper deals with linear partial differential operators with real principalsymbol.Let P(x,D)be such an operator of mth order with C~∞ coefficients definedin an open subset Ω of R^n and p_m(x,...§1.IntroductionThis paper deals with linear partial differential operators with real principalsymbol.Let P(x,D)be such an operator of mth order with C~∞ coefficients definedin an open subset Ω of R^n and p_m(x,ξ)be its principal symbol.According to thedefinition given by Duistermaat and Hmander(see[1]),P(x,D)is called ofprincipal type at x^0 ∈Ω if for any ξ∈R^n\0 satisfying p_m(x^0,ξ)=0,x=x^0 is not theprojection in Ω of the bicharacteristic strip of P(x,D)through(x^0,ξ).Under thiscondition,they proved that there exists a neighborhood U of x^0,U,such that forany real number s,展开更多
As parameter independent yet simple techniques,the energy operator(EO)and its variants have received considerable attention in the field of bearing fault feature detection.However,the performances of these improved EO...As parameter independent yet simple techniques,the energy operator(EO)and its variants have received considerable attention in the field of bearing fault feature detection.However,the performances of these improved EO techniques are subjected to the limited number of EOs,and they cannot reflect the non-linearity of the machinery dynamic systems and affect the noise reduction.As a result,the fault-related transients strengthened by these improved EO techniques are still subject to contamination of strong noises.To address these issues,this paper presents a novel EO fusion strategy for enhancing the bearing fault feature nonlinearly and effectively.Specifically,the proposed strategy is conducted through the following three steps.First,a multi-dimensional information matrix(MDIM)is constructed by performing the higher order energy operator(HOEO)on the analysis signal iteratively.MDIM is regarded as the fusion source of the proposed strategy with the properties of improving the signal-to-interference ratio and suppressing the noise in the low-frequency region.Second,an enhanced manifold learning algorithm is performed on the normalized MDIM to extract the intrinsic manifolds correlated with the fault-related impulses.Third,the intrinsic manifolds are weighted to recover the fault-related transients.Simulation studies and experimental verifications confirm that the proposed strategy is more effective for enhancing the bearing fault feature than the existing methods,including HOEOs,the weighting HOEO fusion,the fast Kurtogram,and the empirical mode decomposition.展开更多
The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuiti...The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuitionistic uncertain linguistic variables and the concept of the expected value and accuracy function,some new dependent aggregation operators with intuitionistic uncertain linguistic information including the dependent intuitionistic uncertain linguistic ordered weighted average(DIULOWA)operator,the dependent intuitionistic uncertain linguistic ordered weighted geometric(DIULOWG)operator,the generalized dependent intuitionistic uncertain linguistic ordered weighted aggregation(GDIULOWA)operator and so on are developed,in which the associated weights only depend on the aggregated arguments.Also,we study some desirable properties of the aggregation operators.Moreover,the approach of multiple attribute group decision making with intuitionistic uncertain linguistic information based on the developed operators is proposed.Finally,an illustrative numerical example is given to show the practicality and effectiveness of the proposed approaches.展开更多
In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study ...In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study of a class of fourth order operators and their third order boundary operators. These third order operators are generalizations of the Dirichlet-to-Neumann operator.展开更多
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.
基金supported by the National Natural Science Foundation of China(11701453)Fundamental Research Funds for the Central Universities(31020180QD05)+2 种基金The second author was supported by the National Natural Science Foundation of China(11971431,11401525)the Natural Science Foundation of Zhejiang Province(LY18A010006)and the first Class Discipline of Zhejiang-A(Zhejiang Gongshang University-Statistics).
文摘In this article,we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrodinger type operator(—Δ)^2+V%2 in R%n(n≥5)with V being a nonnegative potential satisfying the reverse Holder inequality.Furt her more,we prove the boundedness of the variation operators on associated Morrey spaces.In the proof of the main results,we always make use of the variation inequalities associated with the hea t semigroup genera ted by the biharmonic operator(-Δ)2.
基金supported by the National Natural Science Foundation of China(7190121061973310).
文摘Solar arrays are important and indispensable parts of spacecraft and provide energy support for spacecraft to operate in orbit and complete on-orbit missions.When a spacecraft is in orbit,because the solar array is exposed to the harsh space environment,with increasing working time,the performance of its internal electronic components gradually degrade until abnormal damage occurs.This damage makes solar array power generation unable to fully meet the energy demand of a spacecraft.Therefore,timely and accurate detection of solar array anomalies is of great significance for the on-orbit operation and maintenance management of spacecraft.In this paper,we propose an anomaly detection method for spacecraft solar arrays based on the integrated least squares support vector machine(ILS-SVM)model:it selects correlated telemetry data from spacecraft solar arrays to form a training set and extracts n groups of training subsets from this set,then gets n corresponding least squares support vector machine(LS-SVM)submodels by training on these training subsets,respectively;after that,the ILS-SVM model is obtained by integrating these submodels through a weighting operation to increase the prediction accuracy and so on;finally,based on the obtained ILS-SVM model,a parameterfree and unsupervised anomaly determination method is proposed to detect the health status of solar arrays.We use the telemetry data set from a satellite in orbit to carry out experimental verification and find that the proposed method can diagnose solar array anomalies in time and can capture the signs before a solar array anomaly occurs,which reflects the applicability of the method.
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.
文摘In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in Hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found.
基金supported by Natural Science Foundation of China(No.11171220) Support Projects of University of Shanghai for Science and Technology(No.14XPM01)
文摘In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.
基金Supported by the Science Foundation of Ministry of Education of China(208081) Supported by the Natural Science Foundation of Henan Province(102300410012 2007110016 2008B110006)
文摘As a generalization of grand Furuta inequality,recently Furuta obtain:If A≥ B≥0 with A>0,then for t∈[0,1]and p1,p2,p3,p4≥1, A t 2[A- t 2{A t 2(A/ t 2 Bp 1A /t2 )p 2A t 2}p 3A /t2 ]p 4A t 2 1 [{(p1/t)p2+t}p3-t]p4+t]≤A. In this paper,we generalize this result for three operators as follow:If A≥B≥C≥0 with B>0,t∈[0,1]and p1,p2,···,p2n/1,p2n≥1 for a natural number n.Then the following inequalities hold for r≥t, A1/t+r≥ [A r 2[B /t 2{B t 2······[B /t 2{B t 2(B /t 2 ←B /t 2 n times Bt 2 n/1 times by turns Cp 1B /t 2)p 2B t 2}p 3B /t 2]p 4···B t 2}p 2n/1B /t 2 B /t 2 n times Bt 2 n/1 times by turns→ ]p 2nA r 2] 1/t+r q[2n]+r/t, where q[2n]≡{···[{[(p1/t)p2+t]p3/t}p4+t]p5/···/t}p2n+t /t and t alternately n times appear .
文摘The paper proposes a scalable fuzzy approach for mapping the status of the environment integrating several distinct models exploiting geo big data. The process is structured into two phases: the first one can exploit products yielded by distinct models of remote sensing image interpretation defined in the scientific literature, and knowledge of domain experts, possibly ill-defined, for computing partial evidence of a phenomenon. The second phase integrates the partial evidence maps through a learning mechanism exploiting ground truth to compute a synthetic Environmental Status Indicator (ESI) map. The proposal resembles an ensemble approach with the difference that the aggregation is not necessarily consensual but can model a distinct decision attitude in between pessimistic and optimistic. It is scalable and can be implemented in a distributed processing framework, so as to make feasible ESI mapping in near real time to support land monitoring. It is exemplified to map the presence of standing water areas, indicator of water resources, agro-practices or natural hazard from remote sensing by considering different models.
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 National Natural Science Foundation of China(Grant No.11347026)the Natural Science Foundation of Shandong Province(Grant Nos.ZR2016AM03 and ZR2017M A011).
文摘Using an operator ordering method for some commutative superposition operators,we introduce two new multi-variable special polynomials and their generating functions,and present some new operator identities and integral formulas involving the two special polynomials.Instead of calculating compli-cated partial differential,we use the special polynomials and their generating functions to concsely address the normalzation,photoount distributions and Wigner distributions of several quantum states that can be realized physically,the rsults of which provide real convenience for further investigating the properties and applications of these states.
文摘This paper discusses some problems on the cardinal spline interpolation correspond-ing to infinite order differential operators.The remainder formulas and a dual theorem are es-tablished for some convolution classes,where the kernels are PF densities.Moreover,the exacterror of approximation of a convolution class with interpolation cardinal splines is determined.The exact values of average n-Kolmogorov widths are obtained for the convolution class.
文摘§1.IntroductionThis paper deals with linear partial differential operators with real principalsymbol.Let P(x,D)be such an operator of mth order with C~∞ coefficients definedin an open subset Ω of R^n and p_m(x,ξ)be its principal symbol.According to thedefinition given by Duistermaat and Hmander(see[1]),P(x,D)is called ofprincipal type at x^0 ∈Ω if for any ξ∈R^n\0 satisfying p_m(x^0,ξ)=0,x=x^0 is not theprojection in Ω of the bicharacteristic strip of P(x,D)through(x^0,ξ).Under thiscondition,they proved that there exists a neighborhood U of x^0,U,such that forany real number s,
基金supported by the National Natural Science Foundation of China (Grant Nos.52172406 and 51875376)the China Postdoctoral Science Foundation (Grant Nos.2022T150552 and 2021M702752)the Suzhou Prospective Research Program,China (Grant No.SYG202111)。
文摘As parameter independent yet simple techniques,the energy operator(EO)and its variants have received considerable attention in the field of bearing fault feature detection.However,the performances of these improved EO techniques are subjected to the limited number of EOs,and they cannot reflect the non-linearity of the machinery dynamic systems and affect the noise reduction.As a result,the fault-related transients strengthened by these improved EO techniques are still subject to contamination of strong noises.To address these issues,this paper presents a novel EO fusion strategy for enhancing the bearing fault feature nonlinearly and effectively.Specifically,the proposed strategy is conducted through the following three steps.First,a multi-dimensional information matrix(MDIM)is constructed by performing the higher order energy operator(HOEO)on the analysis signal iteratively.MDIM is regarded as the fusion source of the proposed strategy with the properties of improving the signal-to-interference ratio and suppressing the noise in the low-frequency region.Second,an enhanced manifold learning algorithm is performed on the normalized MDIM to extract the intrinsic manifolds correlated with the fault-related impulses.Third,the intrinsic manifolds are weighted to recover the fault-related transients.Simulation studies and experimental verifications confirm that the proposed strategy is more effective for enhancing the bearing fault feature than the existing methods,including HOEOs,the weighting HOEO fusion,the fast Kurtogram,and the empirical mode decomposition.
基金Supported by the National Natural Science Foundation of China(71761027)Ningbo Natural Science Foundation(2015A610161)。
文摘The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuitionistic uncertain linguistic variables and the concept of the expected value and accuracy function,some new dependent aggregation operators with intuitionistic uncertain linguistic information including the dependent intuitionistic uncertain linguistic ordered weighted average(DIULOWA)operator,the dependent intuitionistic uncertain linguistic ordered weighted geometric(DIULOWG)operator,the generalized dependent intuitionistic uncertain linguistic ordered weighted aggregation(GDIULOWA)operator and so on are developed,in which the associated weights only depend on the aggregated arguments.Also,we study some desirable properties of the aggregation operators.Moreover,the approach of multiple attribute group decision making with intuitionistic uncertain linguistic information based on the developed operators is proposed.Finally,an illustrative numerical example is given to show the practicality and effectiveness of the proposed approaches.
基金supported by NSF grant DMS-1509505a postdoctoral fellowship of the National Science Foundation(No.DMS-1103786)
文摘In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study of a class of fourth order operators and their third order boundary operators. These third order operators are generalizations of the Dirichlet-to-Neumann operator.