For an element $\Psi$ in the graded vector space $\Omega^*(M, TM)$ of tangent bundle valued forms on a smooth manifold $M$, $\Psi$-submanifold is defined as submanifold $N$ $M$ such that $\Psi_{|N} \in \Omega^*(N, TN)$. The class $\Psi$-submanifolds encompasses calibrated submanifolds, complex submanifolds and all Lie subgroups compact groups. carries natural algebra structure, given by Frolich...

With the $\Omega$-operators for Virasoro algebra \cite{BF} and super in \cite{CL, CLL}, we get Ovsienko-Roger superalgebras this paper then use it to classify all simple cuspidal modules $\bZ$-graded $\frac12\bZ$-graded superalgebras. By result, can easily Harish-Chandra over some related Lie superalgebras, including $N=1$ BMS$_3$ algebra, $W(2,2)$, etc.

In this article we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for computing , if it exists, a rational, Darbouxian, Liouvillian or Riccati first integral with bounded degree of a polynomial planar vector field. We give probabilistic and deterministic algorithms. The arithmetic comp...

$A^2\_{\alpha}$ will denote the weighted $L^2$ Bergman space. Given a subset $S$ of open unit disc we define $\Omega(S)$ to be infimum ${s \mid \exists f \in A^2\_{s-2}, ; f\neq 0,$ having as its zero set$}$. By classical results on Hardy space there are sets for which $\Omega(S)=1$. Using von Neumann dimension techniques and cusp forms give examples where $1<\Omega(S)<\infty$. using left order...

Let $D\geq 1$ and $q\geq 3$ be two integers. $H(D)=H(D,q)$ denote the $D$-dimensional Hamming graph over a $q$-element set. ${\mathcal T}(D)$ Terwilliger algebra of $H(D)$. $V(D)$ standard T}(D)$-module. $\omega$ complex scalar. We consider unital associative $\mathfrak K_\omega$ defined by generators relations. The are $A$ $B$. relations $A^2 B-2 ABA +B A^2 =B+\omega A$, $B^2A-2 BAB+AB^2=A+\om...

Fragments of first-order logic over words can often be characterized in terms of finite monoids or finite semigroups. Usually these algebraic descriptions yield decidability of the question whether a given regular language is definable in a particular fragment. An effective algebraic characterization can be obtained from identities of so-called omega-terms. In order to show that a given fragmen...

For a group $G$ and $\omega\in Z^{3}(G, \text{U}(1))$, an $\omega$-anomalous action on C*-algebra $B$ is $\text{U}(1)$-linear monoidal functor between 2-groups $\text{2-Gr}(G, \text{U}(1), \omega)\rightarrow \underline{\text{Aut}}(B)$, where the latter denotes 2-group of $*$-automorphisms $B$. The class $[\omega]\in H^{3}(G, \text{U}(1))$ called anomaly action. We show for every $n\ge 2$ finite...