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 ...

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 ...

We extend the notion of matroid representations by matrices over fields by considering new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This ...

For regular strangeness-free linear differential-algebraic equations (DAEs) the definition of an adjoint DAE is straightforward. This definition can be formally extended to general linear DAEs. In this paper, we analyze ...