Related papers: Answer to question Nr. 55

We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.

We generalise a classical example given by Krein in 1953. We compute the difference of the resolvents and the difference of the spectral projections explicitly. We further give a full description of the unitary invariants, i.e., of the…

There exist two versions of the covariant Schwinger term in the literature. They only differ by a sign. However, we shall show that this is an essential difference. We shall carefully (taking all signs into account) review the existing…

The "odd transgression" introduced by the authors in an earlier article is applied to construct and study the inverse image functor in the theory of Courant algebroids.

We give a natural sufficient condition for an intersection graph of compact convex sets in R^d to have a balanced separator of sublinear size. This condition generalizes several previous results on sublinear separators in intersection…

We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible…

Differential $p$-forms and $q$-vector fields with constant coefficients are studied. Differential $p$-forms of degrees $p=1,2,n-1,n$ with constant coefficients on a smooth $n$-dimensional manifold $M$ are characterized. In the contravariant…

Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…

Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.

We define an algebra of contravariant symbols on $S^2$ and give an algebraic proof of the Correspondence Principle for that algebra.

In the broad range of studies related to quantum graphs, quantum graph spectra appear as a topic of special interest. They are important in the context of diffusion type problems posed on metric graphs. Theoretical findings suggest that…

For any primitive matrix $M\in\mathbb{R}^{n\times n}$ with positive diagonal entries, we prove the existence and uniqueness of a positive vector $\mathbf{x}=(x_1,\dots,x_n)^t$ such that $M\mathbf{x}=(\frac{1}{x_1},\dots,\frac{1}{x_n})^t$.…

We study quivers with relations given by non-commutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of quiver mutations at arbitrary vertices. This…

We introduce a generalization of representations of quivers that contains also representations of posets, vectorspace problems and other matrix problems. Many examples, some of which are given in the paper, show that the language of marked…

We give a counterexample to the proof in the literature [K-Theory 25 (2002), 215-231] of the existence of linear representatives of higher Chow groups of number fields.

This is a remark on a recent post by P. Denton, S. Parke, T. Tao, X. Zhang, Eigenvectors from eigenvalues, arXiv:1908.03795v1

A comment to the paper by S. Chen, H. B\"uttner, and J. Voit, [Phys. Rev. Lett. {\bf 87}, 087205 (2001)].

Let M be a smooth manifold, A a local algebra in sense of Andr\'e Weil, M^{A} the manifold of near points on M of kind A and X(M^{A}) the module of vector fields on M^{A}. We give a new definition of vector fields on M^{A} and we show that…

Iosevich and Senger (2008) showed that if a subset of the d-dimensional vector space over a finite field is large enough, then it contains many k-tuples of mutually orthogonal vectors. In this note, we provide a graph theoretic proof of…

I. M. Gelfand and D. B. Fuks have studied the cohomology of the Lie algebra of vector fields on a manifold. In this article, we generalize their main tools to compute the Leibniz cohomology, by extending the two spectral sequences…