In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order qua...In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.展开更多
In this paper, the similarity-invariant subspaces of B(H), which is tile Banach algebra of all bounded linear operators on a separable infinite-dimensional Hilbert space H, are completely characterized and the represe...In this paper, the similarity-invariant subspaces of B(H), which is tile Banach algebra of all bounded linear operators on a separable infinite-dimensional Hilbert space H, are completely characterized and the representations of bounded linear maps on B(H) which preserve similarity in both directions are given.展开更多
Let F and G be closed subspaces of the complex Hilbert spaceH, and U and V be closed subspaces of F- and G, respectively. In this paper, using the technique of operator block, we present the necessary and sufficient c...Let F and G be closed subspaces of the complex Hilbert spaceH, and U and V be closed subspaces of F- and G, respectively. In this paper, using the technique of operator block, we present the necessary and sufficient conditions under which （U, V） is a pair of （strictly, non-degenerate） principal invariant subspaces for （F, G）.展开更多
Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the...Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.展开更多
Wave-particle duality is a familiar concept in the theories of the fundamental processes. We have, for example, electromagnetic waves with the photon as the corresponding particle, gravitational waves with the gravito...Wave-particle duality is a familiar concept in the theories of the fundamental processes. We have, for example, electromagnetic waves with the photon as the corresponding particle, gravitational waves with the graviton as the corresponding particle, and Dirac waves with the electron as the corresponding particle. All these theories are stand-alone theories having nothing in common. The outstanding problem is a unified theory of particles and fields. In this paper, we discuss a unified geometrical theory of fields and particles.展开更多
Road visual navigation relies on accurate road models.This study was aimed at proposing an improved scale-invariant feature transform(SIFT)algorithm for recovering depth information from farmland road images,which wou...Road visual navigation relies on accurate road models.This study was aimed at proposing an improved scale-invariant feature transform(SIFT)algorithm for recovering depth information from farmland road images,which would provide a reliable path for visual navigation.The mean image of pixel value in five channels(R,G,B,S and V)were treated as the inspected image and the feature points of the inspected image were extracted by the Canny algorithm,for achieving precise location of the feature points and ensuring the uniformity and density of the feature points.The mean value of the pixels in 5×5 neighborhood around the feature point at an interval of 45ºin eight directions was then treated as the feature vector,and the differences of the feature vectors were calculated for preliminary matching of the left and right image feature points.In order to achieve the depth information of farmland road images,the energy method of feature points was used for eliminating the mismatched points.Experiments with a binocular stereo vision system were conducted and the results showed that the matching accuracy and time consuming for depth recovery when using the improved SIFT algorithm were 96.48%and 5.6 s,respectively,with the accuracy for depth recovery of-7.17%-2.97%in a certain sight distance.The mean uniformity,time consuming and matching accuracy for all the 60 images under various climates and road conditions were 50%-70%,5.0-6.5 s,and higher than 88%,respectively,indicating that performance for achieving the feature points(e.g.,uniformity,matching accuracy,and algorithm real-time)of the improved SIFT algorithm were superior to that of conventional SIFT algorithm.This study provides an important reference for navigation technology of agricultural equipment based on machine vision.展开更多
We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of co...We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.展开更多
In this paper, we find the invariant eigen-operators （IEOs） and the energy-level gap of a system with a two-level atom interacting with single mode cavity field through multi-photon transition in the presence of a K...In this paper, we find the invariant eigen-operators （IEOs） and the energy-level gap of a system with a two-level atom interacting with single mode cavity field through multi-photon transition in the presence of a Kerr-like medium. From this work, one can see that the IEO method in many eases is simpler and easier on obtaining the energy-level gap formula than the usual way.展开更多
Let G be a bounded open subset in the complex plane and let H 2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riem...Let G be a bounded open subset in the complex plane and let H 2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1–1 with respect to the Lebesgue measure on ?D and if the Riemann map belongs to the weak-star closure of the polynomials in H ∞(W). Our main theorem states: in order that for each M ∈ Lat (M z ), there exist u ∈ H ∞(G) such that M = ∨{uνH 2(G)}, it is necessary and sufficient that the following hold:each component of G is a perfectly connected domainthe harmonic measures of the components of G are mutually singularthe set of polynomials is weak-star dense in H ∞(G).Moreover, if G satisfies these conditions, then every M ∈ Lat (M z ) is of the form uH 2(G), where u ∈ H ∞(G) and the restriction of u to each of the components of G is either an inner function or zero.展开更多
This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of ...This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of functions analytic on the open unit disk.展开更多
We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU...We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU（1,1） algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld＇s invariant operator theory of treating timedependent harmonic oscillators.展开更多
The quantum mechanical relationships between time-dependent oscillators, Hamilton-Jacobi theory and an invariant operator are clarified by making reference to a system with a generalized oscillator. We introduce a lin...The quantum mechanical relationships between time-dependent oscillators, Hamilton-Jacobi theory and an invariant operator are clarified by making reference to a system with a generalized oscillator. We introduce a linear transformation in position and momentum, and show that the correspondence between classical and quantum transformations is exactly one-to-one. We found that classical canonical transformations are constructed from quantum unitary transformations as long as we are concerned with linear transformations. We also show the relationship between the invariant operator and a linear transformation.展开更多
In this paper, for an invariant subspace I of the weighted Bergman space, the weighted root operator is defined. We study the weighted root operator and obtain its fundamental properties when the invariant subspace I ...In this paper, for an invariant subspace I of the weighted Bergman space, the weighted root operator is defined. We study the weighted root operator and obtain its fundamental properties when the invariant subspace I has finite index. Furthermore, we give some examples of the root operator and estimate ranks of the operators.展开更多
Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where ...Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.展开更多
Due to limitations to extract invariant features for recognition when the aircraft presents various poses and lacks enough samples for training, a novel algorithm called Weighted Marginal Fisher Analysis with Spatiall...Due to limitations to extract invariant features for recognition when the aircraft presents various poses and lacks enough samples for training, a novel algorithm called Weighted Marginal Fisher Analysis with Spatially Smooth （WMFA-SS） for extracting invariant features in aircraft rec- ognition is proposed. According to the Graph Embedding （GE） framework, Heat Kernel function is firstly introduced to characterize the interclass separability when choosing the weights of penalty graph. Furthermore, Laplacian penalty is applied to constraining the coefficients to be spatially smooth in this algorithm. Laplacian penalty is able to incorporate the prior information that neigh- boring pixels are correlated. Besides, using a Laplacian penalty can also avoid the singularity of Laplacian matrix of intrinsic graph. Once compact representations of the images are obtained, it can be considered as invariant features and then be performed in classification to recognize different patterns of aircraft. Real aircraft recognition experiments show the superiority of our proposed WMFA-SS in comparison to other GE algorithms and the current aircraft recognition algorithm; the accuracy rate of our proposed method is 90.00% for dataset BH-AIR1.0 and 99.25% for dataset BH-AIR2.0.展开更多
In this paper, we prove that every operator in a class of contraction operators on a Banach space whose spectrum contains the unit circle has a nontrivial hyperinvariant subspace.
基金supported by the National Natural Science Foundation of China(Grant No.11371293)the Civil Military Integration Research Foundation of Shaanxi Province,China(Grant No.13JMR13)+2 种基金the Natural Science Foundation of Shaanxi Province,China(Grant No.14JK1246)the Mathematical Discipline Foundation of Shaanxi Province,China(Grant No.14SXZD015)the Basic Research Project Foundation of Weinan City,China(Grant No.2013JCYJ-4)
文摘In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.
基金This research is supported by the Excellent Young Teachers Program of MOE, P. R. C.by National Natural Science Foundation of China (No. 10071047)
文摘In this paper, the similarity-invariant subspaces of B(H), which is tile Banach algebra of all bounded linear operators on a separable infinite-dimensional Hilbert space H, are completely characterized and the representations of bounded linear maps on B(H) which preserve similarity in both directions are given.
基金supported by National Natural Science Foundation of China(Grant No.11326107)supported by National Natural Science Foundation of China(Grant No.11071188)Special Foundation for Excellent Young College and University Teachers(Grant No.405ZK12YQ21-ZZyyy12021)
文摘Let F and G be closed subspaces of the complex Hilbert spaceH, and U and V be closed subspaces of F- and G, respectively. In this paper, using the technique of operator block, we present the necessary and sufficient conditions under which （U, V） is a pair of （strictly, non-degenerate） principal invariant subspaces for （F, G）.
文摘Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.
文摘Wave-particle duality is a familiar concept in the theories of the fundamental processes. We have, for example, electromagnetic waves with the photon as the corresponding particle, gravitational waves with the graviton as the corresponding particle, and Dirac waves with the electron as the corresponding particle. All these theories are stand-alone theories having nothing in common. The outstanding problem is a unified theory of particles and fields. In this paper, we discuss a unified geometrical theory of fields and particles.
基金This work was financially supported by the Zhejiang Science and Technology Department Basic Public Welfare Research Project(LGN18F030001)the Major Project of Zhejiang Science and Technology Department(2016C02G2100540).
文摘Road visual navigation relies on accurate road models.This study was aimed at proposing an improved scale-invariant feature transform(SIFT)algorithm for recovering depth information from farmland road images,which would provide a reliable path for visual navigation.The mean image of pixel value in five channels(R,G,B,S and V)were treated as the inspected image and the feature points of the inspected image were extracted by the Canny algorithm,for achieving precise location of the feature points and ensuring the uniformity and density of the feature points.The mean value of the pixels in 5×5 neighborhood around the feature point at an interval of 45ºin eight directions was then treated as the feature vector,and the differences of the feature vectors were calculated for preliminary matching of the left and right image feature points.In order to achieve the depth information of farmland road images,the energy method of feature points was used for eliminating the mismatched points.Experiments with a binocular stereo vision system were conducted and the results showed that the matching accuracy and time consuming for depth recovery when using the improved SIFT algorithm were 96.48%and 5.6 s,respectively,with the accuracy for depth recovery of-7.17%-2.97%in a certain sight distance.The mean uniformity,time consuming and matching accuracy for all the 60 images under various climates and road conditions were 50%-70%,5.0-6.5 s,and higher than 88%,respectively,indicating that performance for achieving the feature points(e.g.,uniformity,matching accuracy,and algorithm real-time)of the improved SIFT algorithm were superior to that of conventional SIFT algorithm.This study provides an important reference for navigation technology of agricultural equipment based on machine vision.
基金supported by the President Foundation of the Chinese Academy of Sciences and National Natural Science Foundation of China under Grant No.10475657
文摘We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.
文摘In this paper, we find the invariant eigen-operators （IEOs） and the energy-level gap of a system with a two-level atom interacting with single mode cavity field through multi-photon transition in the presence of a Kerr-like medium. From this work, one can see that the IEO method in many eases is simpler and easier on obtaining the energy-level gap formula than the usual way.
基金This work was supported By SWUFE's Key Subjects Construction Items Funds of 211 Project of the 11th Five-Year Plan
文摘Let G be a bounded open subset in the complex plane and let H 2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1–1 with respect to the Lebesgue measure on ?D and if the Riemann map belongs to the weak-star closure of the polynomials in H ∞(W). Our main theorem states: in order that for each M ∈ Lat (M z ), there exist u ∈ H ∞(G) such that M = ∨{uνH 2(G)}, it is necessary and sufficient that the following hold:each component of G is a perfectly connected domainthe harmonic measures of the components of G are mutually singularthe set of polynomials is weak-star dense in H ∞(G).Moreover, if G satisfies these conditions, then every M ∈ Lat (M z ) is of the form uH 2(G), where u ∈ H ∞(G) and the restriction of u to each of the components of G is either an inner function or zero.
文摘This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of functions analytic on the open unit disk.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056.
文摘We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU（1,1） algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld＇s invariant operator theory of treating timedependent harmonic oscillators.
文摘The quantum mechanical relationships between time-dependent oscillators, Hamilton-Jacobi theory and an invariant operator are clarified by making reference to a system with a generalized oscillator. We introduce a linear transformation in position and momentum, and show that the correspondence between classical and quantum transformations is exactly one-to-one. We found that classical canonical transformations are constructed from quantum unitary transformations as long as we are concerned with linear transformations. We also show the relationship between the invariant operator and a linear transformation.
基金Supported by the National Natural Science Foundation of China (Grant Nos.10671028 10971020)
文摘In this paper, for an invariant subspace I of the weighted Bergman space, the weighted root operator is defined. We study the weighted root operator and obtain its fundamental properties when the invariant subspace I has finite index. Furthermore, we give some examples of the root operator and estimate ranks of the operators.
文摘Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.
基金co-supported by the National Key Scientific Instrument and Equipment Development Project (No.2012YQ140032)
文摘Due to limitations to extract invariant features for recognition when the aircraft presents various poses and lacks enough samples for training, a novel algorithm called Weighted Marginal Fisher Analysis with Spatially Smooth （WMFA-SS） for extracting invariant features in aircraft rec- ognition is proposed. According to the Graph Embedding （GE） framework, Heat Kernel function is firstly introduced to characterize the interclass separability when choosing the weights of penalty graph. Furthermore, Laplacian penalty is applied to constraining the coefficients to be spatially smooth in this algorithm. Laplacian penalty is able to incorporate the prior information that neigh- boring pixels are correlated. Besides, using a Laplacian penalty can also avoid the singularity of Laplacian matrix of intrinsic graph. Once compact representations of the images are obtained, it can be considered as invariant features and then be performed in classification to recognize different patterns of aircraft. Real aircraft recognition experiments show the superiority of our proposed WMFA-SS in comparison to other GE algorithms and the current aircraft recognition algorithm; the accuracy rate of our proposed method is 90.00% for dataset BH-AIR1.0 and 99.25% for dataset BH-AIR2.0.
基金the Natural Science Foundation of P.R.China (No.10771039)
文摘In this paper, we prove that every operator in a class of contraction operators on a Banach space whose spectrum contains the unit circle has a nontrivial hyperinvariant subspace.
