In this note, we first classify all topological torus knots lying on the Heegaard torus in Lens spaces, and then we classify Legendrian representatives of torus knots. We show that all Legendrian torus knots in universally ...

The Ram-Yip formula for Macdonald polynomials (at $t=0$) provides a statistic which we call charge. In types $A$ and $C$ it can be defined on tensor products of Kashiwara-Nakashima single column crystals. In this ...

We complement two papers on supertropical valuation theory ([IKR1], [IKR2]) by providing natural examples of m-valuations (= monoid valuations), after that of supervaluations and transmissions between them. The supervaluations ...

The Weyl group of the Cuntz algebra $\mathcal{O}_n$ is investigated. This is (isomorphic to) the group of polynomial automorphisms $\lambda_u$ of $\mathcal{O}_n$, namely those induced by unitaries u that can be written ...

Endomorphisms of graph $C^*$-algebras are investigated. A combinatorial approach to analysis of permutative endomorphisms is developed. Then invertibility criteria for localized endomorphisms are given. Furthermore, ...

Motivated from linear-quadratic optimal control problems for differential-algebraic equations (DAEs), we study the functional analytic properties of the operator associated with the necessary optimality boundary value ...

In this article, we establish some new second main theorems for meromorphic mappings of $\mathbf{C}^m$ into $\mathbf{P}^n(\mathbf{C})$ and moving hypersurfaces with truncated counting functions. As an application, we prove ...

Farkas' lemma is a fundamental result from linear programming providing linear certi cates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly ...

We study natural cluster structures in the rings of regular functions on simple complex Lie groups and Poisson-Lie structutures compatible with these cluster structures. According to our main conjecture, each class in the ...