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Characterizations of Lie higher and Lie triple derivations on triangular algebras
Jiankui Li,Qihua Shen 대한수학회 2012 대한수학회지 Vol.49 No.2
In this paper, we show that under certain conditions every Lie higher derivation and Lie triple derivation on a triangular algebra are proper, respectively. The main results are then applied to (block) upper triangular matrix algebras and nest algebras.
Characterizations of (Jordan) derivations on Banach algebras with local actions
Jiankui Li,Shan Li,Kaijia Luo 대한수학회 2023 대한수학회논문집 Vol.38 No.2
Let $\mathcal{A}$ be a unital Banach $*$-algebra and $\mathcal{M}$ be a unital $*$-$\mathcal{A}$-bimodule. If $W$ is a left separating point of $\mathcal{M}$, we show that every $*$-derivable mapping at $W$ is a Jordan derivation, and every $*$-left derivable mapping at $W$ is a Jordan left derivation under the condition $W \mathcal{A}=\mathcal{A}W$. Moreover we give a complete description of linear mappings $\delta$ and $\tau$ from $\mathcal{A}$ into $\mathcal{M}$ satisfying $\delta(A)B^*+A\tau(B)^*=0$ for any $A, B\in \mathcal{A}$ with $AB^*=0$ or $\delta(A)\circ B^*+A\circ\tau(B)^*=0$ for any $A, B\in \mathcal{A}$ with $A\circ B^*=0$, where $A\circ B=AB+BA$ is the Jordan product.
Characterizations of Jordan derivable mappings at the unit element
Jiankui Li,Shan Li,Kaijia Luo 대한수학회 2022 대한수학회보 Vol.59 No.2
Let $\mathcal{A}$ be a unital Banach algebra, $\mathcal{M}$ a unital $\mathcal{A}$-bimodule, and $\delta$ a linear mapping from $\mathcal{A}$ into $\mathcal{M}$. We prove that if $\delta$ satisfies $\delta(A)A^{-1}+A^{-1}\delta(A)+A\delta(A^{-1})+\delta(A^{-1})A=0$ for every invertible element $A$ in $\mathcal{A}$, then $\delta$ is a Jordan derivation. Moreover, we show that $\delta$ is a Jordan derivable mapping at the unit element if and only if $\delta$ is a Jordan derivation. As an application, we answer the question posed in \cite[Problem 2.6]{E}.
CHARACTERIZATIONS OF LIE HIGHER AND LIE TRIPLE DERIVATIONS ON TRIANGULAR ALGEBRAS
Li, Jiankui,Shen, Qihua Korean Mathematical Society 2012 대한수학회지 Vol.49 No.2
In this paper, we show that under certain conditions every Lie higher derivation and Lie triple derivation on a triangular algebra are proper, respectively. The main results are then applied to (block) upper triangular matrix algebras and nest algebras.
Web Tension Estimation by Local Contact Force Measurement in Roll-to-Roll Manufacturing
Yiwei Jin,Jiankui Chen,Zhouping Yin 한국정밀공학회 2020 International Journal of Precision Engineering and Vol.21 No.11
Web tension and its distribution are key factors in the operation of web systems, the roll to roll (R2R) manufacturing of flexible electronics brings even higher requirements for it. To effectively get the web tension at any position on the R2R process line, a new web tension estimation method by measuring the local contact force is investigated in this paper, which can not only estimate the web tension, but also the web tension distribution. This study attempts to derive the approximate fitting formula between the local contact force and the web tension. Firstly, the schematic of web tension estimation method by local contact force measurement is presented; Then the mass spring model is used to derive the governing equations, which is discretized and solved by Improved Euler method. And approximate fitting formula of the local contact force with tension is derived based on the numerical results. Finally, to validate the fitting formula, the experiments are carried out to detect the local contact force and estimate both the web tension and its distribution.
CHARACTERIZATIONS OF CENTRALIZERS AND DERIVATIONS ON SOME ALGEBRAS
Jun He,Jiankui Li,Wenhua Qian 대한수학회 2017 대한수학회지 Vol.54 No.2
A linear mapping $\phi$ on an algebra $\mathcal{A}$ is called a centralizable mapping at $G\in\mathcal{A}$ if $\phi(AB)=\phi(A)B=A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$, and $\phi$ is called a derivable mapping at $G\in\mathcal{A}$ if $\phi(AB)=\phi(A)B+A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$. A point $G$ in $\mathcal{A}$ is called a full-centralizable point (resp. full-derivable point) if every centralizable (resp. derivable) mapping at $G$ is a centralizer (resp. derivation). We prove that every point in a von Neumann algebra or a triangular algebra is a full-centralizable point. We also prove that a point in a von Neumann algebra is a full-derivable point if and only if its central carrier is the unit.
Xiao Yue,Jiankui Chen,Yiqun Li,Rong Zou,Zhihao Sun,Xiaochuan Cao,Song Zhang 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.4
Skid-steered mobile robots are often used in outdoor exploration due to their robust mechanical structure and high maneuverability. When they track reference path on a slope with boundaries, ensuring the tracking accuracy and stability of the skid-steered mobile robot is the major target. However, the gravity makes the relationship between wheels and ground more complex on the slope, and variational slope angle also makes it difficult for tracking control. The common control methods focus on plane motion, where only the plane forces are taken into account and the gravity is normally ignored. It may lead to some performance limitations such as the accuracy of motion on a slope. To address these problems, a model predictive control strategy combined with a fuzzy system is proposed in this paper, which has considered the dynamics of the body and wheels on the slope. We improved the two dimensional kinematics and dynamics model of the robot, which makes the three dimensional motion control more accurate. And the control method allows the robot to adapt to slopes with different angles and to make the path tracking stable to curvature mutation. Both experiment and simulation results demonstrate the effectiveness and superiority of the proposed model and method.
Kexin Peng,Jiankui Guo,Haifeng Chen,Mali Xie,Xi Zhang,Xudong Huang,Guiying Xing,Linjun Shao,Chenze Qi 한국섬유공학회 2023 Fibers and polymers Vol.24 No.11
In this paper, copper phthalocyanine and polystyrene composite superfine fibers were readily prepared by electrospinning technology. After treating these composite fibers with paraformaldehyde in concentrated H2SO4 solution, the copper phthalocyanine molecules were covalently bonded to the polystyrene molecules. Meanwhile, the polystyrene molecules in the fibers were cross-linked to endow these fibers with excellent solvent resistance. The photocatalytic performance of this novel fibrous catalyst was evaluated by photodegradation of methyl orange in the presence of H2O2. The effects of light source, H2O2 dosage, catalyst loading, and temperature on the fiber catalyzed photodegradation of methyl orange were carefully studied. The photodegradation percentage of methyl orange in aqueous solution was up to ~ 97% under optimized reaction conditions. At last, this fibrous catalyst was readily recovered by simple filtration and reused for three times with satisfied photodegradation activities. In all, we have developed a facile way to prepare copper phthalocyanine functionalized polystyrene superfine fibers with excellent photocatalytic performance.
Non-fragile Robust Finite-time H∞ Control for Nonlinear Stochastic Itô Systems Using Neural Network
Zhiguo Yan,Guoshan Zhang,Jiankui Wang 제어·로봇·시스템학회 2012 International Journal of Control, Automation, and Vol.10 No.5
This paper deals with the problem of non-fragile robust finite-time H∞ control for a class of uncertain nonlinear stochastic Itô systems via neural network. First, applying multi-layer feedback neural networks, the nonlinearity is approximated by linear differential inclusion (LDI) under state-space representation. Then, a sufficient condition is proposed for the existence of non-fragile state feedback finite-time H∞ controller in terms of matrix inequalities. Furthermore, the problem of non-fragile robust finite-time H∞ control is reduced to the optimization problem involving linear matrix inequalities (LMIs), and the detailed solving algorithm is given for the restricted LMIs. Finally, an example is given to illustrate the effectiveness of the proposed method.
CHARACTERIZATIONS OF CENTRALIZERS AND DERIVATIONS ON SOME ALGEBRAS
He, Jun,Li, Jiankui,Qian, Wenhua Korean Mathematical Society 2017 대한수학회지 Vol.54 No.2
A linear mapping ${\phi}$ on an algebra $\mathcal{A}$ is called a centralizable mapping at $G{\in}{\mathcal{A}}$ if ${\phi}(AB)={\phi}(A)B= A{\phi}(B)$ for each A and B in $\mathcal{A}$ with AB = G, and ${\phi}$ is called a derivable mapping at $G{\in}{\mathcal{A}}$ if ${\phi}(AB)={\phi}(A)B+A{\phi}(B)$ for each A and B in $\mathcal{A}$ with AB = G. A point G in A is called a full-centralizable point (resp. full-derivable point) if every centralizable (resp. derivable) mapping at G is a centralizer (resp. derivation). We prove that every point in a von Neumann algebra or a triangular algebra is a full-centralizable point. We also prove that a point in a von Neumann algebra is a full-derivable point if and only if its central carrier is the unit.