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Commutativity and hyponormality of Toeplitz operators on the weighted Bergman space
Yufeng Lu,Chaomei Liu 대한수학회 2009 대한수학회지 Vol.46 No.3
In this paper we give necessary and sufficient conditions that two Toeplitz operators with monomial symbols acting on the weighted Bergman space commute. We also present necessary and sufficient conditions for the hyponormality of Toeplitz operators with some special symbols on the weighted Bergman space. All the results are stated in terms of the Mellin transform of the symbol. In this paper we give necessary and sufficient conditions that two Toeplitz operators with monomial symbols acting on the weighted Bergman space commute. We also present necessary and sufficient conditions for the hyponormality of Toeplitz operators with some special symbols on the weighted Bergman space. All the results are stated in terms of the Mellin transform of the symbol.
The Hyponormal Toeplitz operators on the vector valued Bergman space
Yufeng Lu,Puyu Cui,Yanyue Shi 대한수학회 2014 대한수학회보 Vol.51 No.1
In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators TΦ, where Φ = F +G∗, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space L2 a(D, Cn). We also show some necessary conditions for the hyponormality of TF+G* with F + G∗ 2 h∞ ⓧ Mn×n on L2 a(D, Cn). In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators TΦ, where Φ = F +G∗, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space L2 a(D, Cn). We also show some necessary conditions for the hyponormality of TF+G* with F + G∗ ∈ h∞ ⓧ Mn×n on L2 a(D, Cn).
COMMUTATIVITY AND HYPONORMALITY OF TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACE
Lu, Yufeng,Liu, Chaomei Korean Mathematical Society 2009 대한수학회지 Vol.46 No.3
In this paper we give necessary and sufficient conditions that two Toeplitz operators with monomial symbols acting on the weighted Bergman space commute. We also present necessary and sufficient conditions for the hyponormality of Toeplitz operators with some special symbols on the weighted Bergman space. All the results are stated in terms of the Mellin transform of the symbol.
THE HYPONORMAL TOEPLITZ OPERATORS ON THE VECTOR VALUED BERGMAN SPACE
Lu, Yufeng,Cui, Puyu,Shi, Yanyue Korean Mathematical Society 2014 대한수학회보 Vol.51 No.1
In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where ${\Phi}$ = $F+G^*$, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space $L^2_a(\mathbb{D},\mathbb{C}^n)$. We also show some necessary conditions for the hyponormality of $T_{F+G^*}$ with $F+G^*{\in}h^{\infty}{\otimes}M_{n{\times}n}$ on $L^2_a(\mathbb{D},\mathbb{C}^n)$.
Yang Lu,Yi Lu,Yang Liu,Bo Hu,Yufeng Gong 대한기계학회 2019 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.33 No.6
A dynamics analysis of a novel parallel manipulator with one central rotational actuator and four translational actuators is conducted. A 3D model of the parallel manipulator is constructed and its characteristics and DoF are analyzed. The kinematics formulae are derived for solving the displacement, velocity and acceleration of the moving links. The dynamics formulae are derived for solving the inertial wrench of the moving links, the dynamic active forces along the active limbs, the dynamic active torque applied on a central active leg, and the dynamic constrained force exerted on the central active leg. A theoretical numerical example is given to solve the kinematics and dynamics solutions, and the theoretical solutions are verified by the simulation mechanism in Matlab. Finally, a reachable workspace of the novel parallel manipulator is constructed using CAD variation geometry.
Lu Yi,Wu Jiachuan,Hu Minhui,Zhong Qinghua,Er Limian,Shi Huihui,Cheng Weihui,Chen Ke,Liu Yuan,Qiu Bingfeng,Xu Qiancheng,Lai Guangshun,Wang Yufeng,Luo Yuxuan,Mu Jinbao,Zhang Wenjie,Zhi Min,Sun Jiachen 거트앤리버 소화기연관학회협의회 2023 Gut and Liver Vol.17 No.6
Background/Aims: The accuracy of endosonographers in diagnosing gastric subepithelial lesions (SELs) using endoscopic ultrasonography (EUS) is influenced by experience and subjectivity. Artificial intelligence (AI) has achieved remarkable development in this field. This study aimed to develop an AI-based EUS diagnostic model for the diagnosis of SELs, and evaluated its efficacy with external validation. Methods: We developed the EUS-AI model with ResNeSt50 using EUS images from two hospitals to predict the histopathology of the gastric SELs originating from muscularis propria. The diagnostic performance of the model was also validated using EUS images obtained from four other hospitals. Results: A total of 2,057 images from 367 patients (375 SELs) were chosen to build the models, and 914 images from 106 patients (108 SELs) were chosen for external validation. The sensitivity, specificity, positive predictive value, negative predictive value, and accuracy of the model for differentiating gastrointestinal stromal tumors (GISTs) and non-GISTs in the external validation sets by images were 82.01%, 68.22%, 86.77%, 59.86%, and 78.12%, respectively. The sensitivity, specificity, positive predictive value, negative predictive value, and accuracy in the external validation set by tumors were 83.75%, 71.43%, 89.33%, 60.61%, and 80.56%, respectively. The EUS-AI model showed better performance (especially specificity) than some endosonographers. The model helped improve the sensitivity, specificity, and accuracy of certain endosonographers. Conclusions: We developed an EUS-AI model to classify gastric SELs originating from muscularis propria into GISTs and non-GISTs with good accuracy. The model may help improve the diagnostic performance of endosonographers. Further work is required to develop a multi-modal EUS-AI system.
Coprime Representations and Feedback Stabilization of Discrete Time-varying Linear Systems
Liu Liu,Yufeng Lu 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.2
Within the framework of nest algebra, this paper deals with the stabilization problems of causal, discretetime, time-varying linear systems based on the coprime representations. It is shown that a linear system is stabilizableif and only if it admits a left coprime representation or a right coprime representation. The parametrizationof stabilizing controllers, strong stabilizability and simultaneous stabilizability criteria are characterized in terms ofleft coprime representations alone, or analogously right coprime representations alone.
REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THE BIDISK
ALBASEER, MOHAMMED,LU, YUFENG,SHI, YANYUE Korean Mathematical Society 2015 대한수학회보 Vol.52 No.5
In this paper, we completely characterize the nontrivial reducing subspaces of the Toeplitz operator $T{_{z{^N_1{\bar{z}}^M_2}}$ on the Bergman space $A^2(\mathbb{D}^2)$, where N and M are positive integers.
COMPACT SUMS OF TOEPLITZ PRODUCTS ON WEIGHTED DIRICHLET SPACE OF THE UNIT BALL
Hu, Yinyin,Lu, Yufeng Korean Mathematical Society 2019 대한수학회보 Vol.56 No.2
On the weighted Dirichlet space, by the Sobolev's embedding theorem, we characterize the compactness for operators which are finite sums of products of several Toeplitz operators. Moreover, the essential spectrum of Toeplitz operator is characterized.