Unsupervised methods based on density representation have shown their abilities in anomaly detection,but detection performance still needs to be improved.Specifically,approaches using normalizing flows can accurately ...Unsupervised methods based on density representation have shown their abilities in anomaly detection,but detection performance still needs to be improved.Specifically,approaches using normalizing flows can accurately evaluate sample distributions,mapping normal features to the normal distribution and anomalous features outside it.Consequently,this paper proposes a Normalizing Flow-based Bidirectional Mapping Residual Network(NF-BMR).It utilizes pre-trained Convolutional Neural Networks(CNN)and normalizing flows to construct discriminative source and target domain feature spaces.Additionally,to better learn feature information in both domain spaces,we propose the Bidirectional Mapping Residual Network(BMR),which maps sample features to these two spaces for anomaly detection.The two detection spaces effectively complement each other’s deficiencies and provide a comprehensive feature evaluation from two perspectives,which leads to the improvement of detection performance.Comparative experimental results on the MVTec AD and DAGM datasets against the Bidirectional Pre-trained Feature Mapping Network(B-PFM)and other state-of-the-art methods demonstrate that the proposed approach achieves superior performance.On the MVTec AD dataset,NF-BMR achieves an average AUROC of 98.7%for all 15 categories.Especially,it achieves 100%optimal detection performance in five categories.On the DAGM dataset,the average AUROC across ten categories is 98.7%,which is very close to supervised methods.展开更多
Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that...Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that the irregularity of the electron phase-space orbits could be caused in several ways, such as varying the wiggler amplitude and inducing sidebands. Based on a Hamiltonian model with a set of self-consistent differential equations, it is shown in this paper that the electron- beam normalized plasma frequency functions not only couple the electron motion with the FEL wave, which results in the evolution of the FEL wave field and a possible power saturation at a large beam current, but also cause the irregularity of the electron phase-space orbits when the normalized plasma frequency has a sufficiently large value, even if the initial energy of the electron is equal to the synchronous energy or the FEL wave does not reach power saturation.展开更多
Let X be a Banach space, S(X) be the unit sphere of X, φ be a function: S(X)→ S(X *) such that φ(x)∈ x, and v φ(ε) =inf 1-12x+y: x,y∈S(X), and 〈φ(x), x-y 〉≥ε, 0≤ε≤2, whe...Let X be a Banach space, S(X) be the unit sphere of X, φ be a function: S(X)→ S(X *) such that φ(x)∈ x, and v φ(ε) =inf 1-12x+y: x,y∈S(X), and 〈φ(x), x-y 〉≥ε, 0≤ε≤2, where x is the set of norm 1 supporting functionals of S(X) at x. A geometric concept, modulus of V convexity V(ε)= sup {V φ(ε), for all φ: S(X)→S(X *)}, is introduced; the properties of V(ε) and the relationship between V(ε) and other geometric concepts are discussed. The main result is that V12>0 implies normal structure.展开更多
The study of fuzzy sets is specifically designed to mathematically represent uncertainty and vagueness by assigning values of membership to objects that belong to a particular set. This notion has been broadly extende...The study of fuzzy sets is specifically designed to mathematically represent uncertainty and vagueness by assigning values of membership to objects that belong to a particular set. This notion has been broadly extended to other areas of topology where various topological concepts have been shown to hold on fuzzy topology. Some notions naturally extend to closure spaces without requiring a lot of modification of the underlying topological ideas. This work investigates the variants of normality on fuzzy isotone spaces.展开更多
Landscape in colleges and universities is mainly composed of plant landscape.Plant space landscape has a profound impact on the campus landscape construction.This paper investigates and analyzes four plant landscape s...Landscape in colleges and universities is mainly composed of plant landscape.Plant space landscape has a profound impact on the campus landscape construction.This paper investigates and analyzes four plant landscape space plots in the Yaohu Campus of Jiangxi Normal University to understand their characteristics,in order to provide reference for the construction of plant landscape space in southern colleges and universities.展开更多
In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dyna...In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.展开更多
Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the co...Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.展开更多
In order to develop and improve the fixed point theorems in cone metric spaces, some new fixed point theorems are presented for two mappings in cone metric spaces which satisfy contractive conditions, where the cone i...In order to develop and improve the fixed point theorems in cone metric spaces, some new fixed point theorems are presented for two mappings in cone metric spaces which satisfy contractive conditions, where the cone is not necessarily normal. Our results generalize fixed point theorems of Abbas, Jungck and Stojan Radenovi in cone metric spaces.展开更多
In this paper, some new existence and uniqueness of common fixed points for four mappings are obtained, which do not satisfy continuity and commutation on non-normal cone metric spaces. These results improve and gener...In this paper, some new existence and uniqueness of common fixed points for four mappings are obtained, which do not satisfy continuity and commutation on non-normal cone metric spaces. These results improve and generalize several well-known comparable results in the literature.展开更多
基金This work was supported in part by the National Key R&D Program of China 2021YFE0110500in part by the National Natural Science Foundation of China under Grant 62062021in part by the Guiyang Scientific Plan Project[2023]48-11.
文摘Unsupervised methods based on density representation have shown their abilities in anomaly detection,but detection performance still needs to be improved.Specifically,approaches using normalizing flows can accurately evaluate sample distributions,mapping normal features to the normal distribution and anomalous features outside it.Consequently,this paper proposes a Normalizing Flow-based Bidirectional Mapping Residual Network(NF-BMR).It utilizes pre-trained Convolutional Neural Networks(CNN)and normalizing flows to construct discriminative source and target domain feature spaces.Additionally,to better learn feature information in both domain spaces,we propose the Bidirectional Mapping Residual Network(BMR),which maps sample features to these two spaces for anomaly detection.The two detection spaces effectively complement each other’s deficiencies and provide a comprehensive feature evaluation from two perspectives,which leads to the improvement of detection performance.Comparative experimental results on the MVTec AD and DAGM datasets against the Bidirectional Pre-trained Feature Mapping Network(B-PFM)and other state-of-the-art methods demonstrate that the proposed approach achieves superior performance.On the MVTec AD dataset,NF-BMR achieves an average AUROC of 98.7%for all 15 categories.Especially,it achieves 100%optimal detection performance in five categories.On the DAGM dataset,the average AUROC across ten categories is 98.7%,which is very close to supervised methods.
基金Project supported by the Science Foundation of Department of Education of Sichuan Province,China (Grant No.12233454)the Youth Foundation of Department of Education of Sichuan Province,China (Grant No.10ZB080)the Xihua University Foundation,China (Grant No.Z0913306)
文摘Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that the irregularity of the electron phase-space orbits could be caused in several ways, such as varying the wiggler amplitude and inducing sidebands. Based on a Hamiltonian model with a set of self-consistent differential equations, it is shown in this paper that the electron- beam normalized plasma frequency functions not only couple the electron motion with the FEL wave, which results in the evolution of the FEL wave field and a possible power saturation at a large beam current, but also cause the irregularity of the electron phase-space orbits when the normalized plasma frequency has a sufficiently large value, even if the initial energy of the electron is equal to the synchronous energy or the FEL wave does not reach power saturation.
文摘Let X be a Banach space, S(X) be the unit sphere of X, φ be a function: S(X)→ S(X *) such that φ(x)∈ x, and v φ(ε) =inf 1-12x+y: x,y∈S(X), and 〈φ(x), x-y 〉≥ε, 0≤ε≤2, where x is the set of norm 1 supporting functionals of S(X) at x. A geometric concept, modulus of V convexity V(ε)= sup {V φ(ε), for all φ: S(X)→S(X *)}, is introduced; the properties of V(ε) and the relationship between V(ε) and other geometric concepts are discussed. The main result is that V12>0 implies normal structure.
文摘The study of fuzzy sets is specifically designed to mathematically represent uncertainty and vagueness by assigning values of membership to objects that belong to a particular set. This notion has been broadly extended to other areas of topology where various topological concepts have been shown to hold on fuzzy topology. Some notions naturally extend to closure spaces without requiring a lot of modification of the underlying topological ideas. This work investigates the variants of normality on fuzzy isotone spaces.
文摘Landscape in colleges and universities is mainly composed of plant landscape.Plant space landscape has a profound impact on the campus landscape construction.This paper investigates and analyzes four plant landscape space plots in the Yaohu Campus of Jiangxi Normal University to understand their characteristics,in order to provide reference for the construction of plant landscape space in southern colleges and universities.
文摘In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.
基金Project supported by the Natural Science Foundation of Sichuan Province of China(No.2005A132)
文摘Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.
基金Foundation item： Supported by the NNSF of China（10771212） Supported by the Natural Science Foundation of Xuzhou Normal University（09KLB03）
文摘In order to develop and improve the fixed point theorems in cone metric spaces, some new fixed point theorems are presented for two mappings in cone metric spaces which satisfy contractive conditions, where the cone is not necessarily normal. Our results generalize fixed point theorems of Abbas, Jungck and Stojan Radenovi in cone metric spaces.
文摘In this paper, some new existence and uniqueness of common fixed points for four mappings are obtained, which do not satisfy continuity and commutation on non-normal cone metric spaces. These results improve and generalize several well-known comparable results in the literature.
