Related papers: Generic uniqueness of a structured matrix factoriz…
A conjugation-free geometric presentation of a fundamental group is a presentation with the natural topological generators $x_1, ..., x_n$ and the cyclic relations: $x_{i_k}x_{i_{k-1}} ... x_{i_1} = x_{i_{k-1}} ... x_{i_1} x_{i_k} = ... =…
We prove a general theorem showing that iterated skew polynomial extensions of the type which fit the conditions needed by Cauchon's deleting derivations theory and by the Goodearl-Letzter stratification theory are unique factorisation…
Braid matrices $\hat{R}(\theta)$, corresponding to vector representations, are spectrally decomposed obtaining a ratio $f_{i}(\theta)/f_{i}(-\theta)$ for the coefficient of each projector $P_{i}$ appearing in the decomposition. This…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first…
This paper introduces a geometric mechanics framework for constrained systems on principal bundles through \emph{compatible pairs} $(\mathcal{D}, \lambda)$, addressing fundamental challenges in gauge-constrained physical systems. We…
Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their…
Digital Geometry software should reflect the generality of the underlying mathe- matics: mapping the latter to the former requires genericity. By designing generic solutions, one can effectively reuse digital geometry data structures and…
We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the…
A generalised notion of connection on a fibre bundle E over a manifold M is presented. These connections are characterised by a smooth distribution on E which projects onto a (not necessarily integrable) distribution on M and which, in…
The article gives a ring theoretic perspective on cluster algebras. Gei{\ss}-Leclerc-Schr\"oer prove that all cluster variables in a cluster algebra are irreducible elements. Furthermore, they provide two necessary conditions for a cluster…
We find conditions that guarantee that a decomposition of a generic third-order tensor in a minimal number of rank-$1$ tensors (canonical polyadic decomposition (CPD)) is unique up to permutation of rank-$1$ tensors. Then we consider the…
A classical tool in the study of real closed fields are the fields $K((G))$ of generalised power series (i.e., formal sums with well-ordered support) with coefficients in a field $K$ of characteristic 0 and exponents in an ordered abelian…
For the implicit systems of first order ordinary differential equations on the plane there is presented the complete local classification of generic singularities of family of its phase curves up to smooth orbital equivalence. Besides the…
Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in R^d. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry…
This paper deals with strong structural controllability of linear systems. In contrast to existing work, the structured systems studied in this paper have a so-called zero/nonzero/arbitrary structure, which means that some of the entries…
We introduce a class of doubly infinite complex Jacobi matrices determined by a simple convergence condition imposed on the diagonal and off-diagonal sequences. For each Jacobi matrix belonging to this class, an analytic function, called a…
The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially-filled tensors subject to rank…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
Partial duality generalizes the fundamental concept of the geometric dual of an embedded graph. A partial dual is obtained by forming the geometric dual with respect to only a subset of edges. While geometric duality preserves the genus of…