Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

biharmonic surfaces in euclidean space $mathbb{e}^3$ are firstly studied from a differential geometric point of view by bang-yen chen, who showed that the only biharmonic surfaces are minimal ones. a surface $x : m^2rightarrowmathbb{e}^{3}$ is called biharmonic if $delta^2x=0$, where $delta$ is the laplace operator of $m^2$. we study the $l_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

There is an embedding of affine vertex algebras $V^k(\mathfrak{gl}_n) \hookrightarrow V^k(\mathfrak{sl}_{n+1})$, and the coset $\mathcal{C}^k(n) = \text{Com}(V^k(\mathfrak{gl}_n), V^k(\mathfrak{sl}_{n+1}))$ a natural generalization parafermion algebra $\mathfrak{sl}_2$. It was called generalized parafermions by third author shown to arise as one-parameter quotient universal two-parameter $\math...

We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k

If I is a (two-sided) ideal of ring R, we let $${\text {ann}}_l(I)=\{r\in R\mid rI=0\},$$ {ann}}_r(I)=\{r\in Ir=0\},$$ and {ann}}(I)={\text {ann}}_l(I)\cap {\text {ann}}_r(I)$$ be the left, right double annihilators. An said to an annihilator if $$I={\text {ann}}(J)$$ for some J (equivalently, {ann}}({\text {ann}}(I))=I$$ ). We study ideals Leavitt path algebras graph $$C^*$$ -algebras. Let $$L...