相关论文: Answer to question Nr. 55

We enhance the pointed quandle counting invariant of linkoids through the use of quivers analogously to quandle coloring quivers. This allows us to generalize the in-degree polynomial invariant of links to linkoids. Additionally, we…

We introduce the notion of a diagram category and discuss its application to the invariant theory of classical groups and super groups, with some indications concerning extensions to quantum groups and quantum super groups. Tensor functors…

We use Artin-Schreier base change to construct counterexamples to a Kummer-Vandiver type question for function fields.

In [14], the second named author constructed the bracket invariant [.] of virtual knots valued in pictures (linear combinations of virtual knot diagrams with some crossing information omitted), such that for many diagrams K, the following…

In this paper, we revise the concept of noncommutative vector fields introduced previously in Ref. [1,2], extending the framework, adding new results and clarifying the old ones. Using appropriate algebraic tools certain shortcomings in the…

We extend a result due to Kawai on block varieties for blocks with abelian defect groups to blocks with arbitrary defect groups. This partially answers a question by J. Rickard.

We greatly expand upon the results of Kochengin, Oliker and Tempeski [S. Kochengin, V. Oliker, O. von Tempeski, On the design of reflectors with prescribed distribution of virtual sources and intensities, Inverse Problems 14 (1998)…

We introduce Courant 1-derivations, which describe a compatibility between Courant algebroids and linear (1,1)-tensor fields and lead to the notion of Courant-Nijenhuis algebroids. We provide examples of Courant 1-derivations on exact…

We prove equality of the vector field (iterated commutator) type and the regular contact type, which together with the Bloom theorem on equality of the Levi-form type and the regular contact type provides a complete solution of a long…

Covering numbers of convex bodies based on homothetical copies and related illumination numbers are well-known in combinatorial geometry and, for example, related to Hadwiger's famous covering problem. Similar numbers can be defined by…

We give an effective characterisation of the walls in the variation of geometric invariant theory problem associated to a quiver and a dimension vector.

Comment on P. Walker, Nature 453 (2008) 864, http://www.nature.com/nature/journal/v453/n7197/full/453864a.html

These notes form the next episode in a series of articles dedicated to a detailed proof of a cohomological index formula for transversally elliptic pseudo-differential operators and applications. The first two chapters are already available…

In this paper we study polynomial maps of vector spaces and their eigenvectors and eigenvalues. The new quantity called complanart is defined. Complanarts determine complanarity of solution vectors of systems of polynomial equations.…

Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…

This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…

We incorporate quandle cocycle information into the quandle coloring quivers we defined in arXiv:1807.10465 to define weighted directed graph-valued invariants of oriented links we call \textit{quandle cocycle quivers}. This construction…

This paper serves as the first extension of the topic of dominator colorings of graphs to the setting of digraphs. We establish the dominator chromatic number over all possible orientations of paths and cycles. In this endeavor we discover…

We show that the basic results on the paper referred in the title [J. Phys. A: Math. Gen. v. 35 (2002) 5333-5345], concerning the derivation of the Ermakov invariant from Noether symmetry methods, are not new.

It is well known that the square is not a Strebel's point (i.e., its extremal Beltrami coefficient is not Teichmuller). Many years ago, Reiner Kuhnau posed the question: does there exist in the case of a "long" rectangle the corresponding…