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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 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.
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 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 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.
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.
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.
2-LOCAL DERIVATIONS ON C<sup>*</sup>-ALGEBRAS
Wenbo Huang,Jiankui Li Korean Mathematical Society 2024 대한수학회보 Vol.61 No.3
In this paper, we prove that every 2-local derivation on several classes of C<sup>*</sup>-algebras, such as unital properly infinite, type I or residually finite-dimensional C<sup>*</sup>-algebras, is a derivation. We show that the following statements are equivalent: (1) every 2-local derivation on a C<sup>*</sup>-algebra is a derivation, (2) every 2-local derivation on a unital primitive antiliminal and no properly infinite C<sup>*</sup>-algebra is a derivation. We also show that every 2-local derivation on a group C<sup>*</sup>-algebra C<sup>*</sup>(𝔽) or a unital simple infinite-dimensional quasidiagonal C<sup>*</sup>-algebra, which is stable finite antiliminal C<sup>*</sup>-algebra, is a derivation.
Preparation and effect evaluation of rigid polyurethane flame retardant modified by graphene
Jianlian Liu,Binghuan Wang,Kui Zi,Jiankui Yu,Peisuo Li 한국탄소학회 2023 Carbon Letters Vol.33 No.7
In this study, we investigate the impact of Isophorone diisocyanate functionalized graphene oxide (IPDI-GO) on the flame retardancy of rigid polyurethane foam (RPUF). IPDI-GO was synthesized and introduced into the RPUF matrix. The flame retardancy of RPUF was significantly enhanced by the incorporation of IPDI-GO, as evidenced by a reduction in peak heat release rate (PHRR) by 25% and total smoke production (TSP) by 15% in comparison to pure RPUF when IPDI-GO was incorporated at 3 wt%. Scanning electron microscopy (SEM) revealed that IPDI-GO contributed to the formation of a compact, continuous char layer on the RPUF surface. This study underscores the potential of IPDI-GO as a promising flame retardant additive for RPUF.