Related papers: The Hydra-k partial fields
Pastures are a class of field-like algebraic objects which include both partial fields hyperfields and have nice categorical properties. We prove several lift theorems for representations of matroids over pastures, including a…
Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence…
Vacua of two dimensional incompressible system, such as Fractional Quantum Hall system, are characterized by rational conformal field theory. We develop a method to express the wavefunctions of those systems in terms of chiral vertices. We…
We develop a combinatorial approach to the quantum permutation algebras, as Hopf images of representations of type $\pi:A_s(n)\to B(H)$. We discuss several general problems, including the commutativity and cocommutativity ones, the…
We present a new type of equivalence for representable matroids that uses the automorphisms of the underlying matroid. Two $r\times n$ matrices $A$ and $A'$ representing the same matroid $M$ over a field $F$ are {\it geometrically…
We introduce the n-th Heron variety as the realization space of the (squared) volumes of faces of an n-simplex. Our primary goal is to understand the extent to which Heron's formula, which expresses the area of a triangle as a function of…
Commutative hypercomplex algebras offer significant advantages over traditional quaternions due to their compatibility with linear algebra techniques and efficient computational implementation, which is crucial for broad applicability. This…
Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…
This paper aims to give a short but self-contained introduction into the theory of (wheeled) props, properads, dioperads and operads, and illustrate some of its key ideas in terms of a prop(erad)ic interpretation of simplicial and…
This thesis proposes a combinatorial generalization of a nilpotent operator on a vector space. The resulting object is highly natural, with basic connections to a variety of fields in pure mathematics, engineering, and the sciences. For the…
We present an algebraic framework which simultaneously generalizes the notion of linear subspaces, matroids, valuated matroids, oriented matroids, and regular matroids. To do this, we first introduce algebraic objects called tracts which…
Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.
An interesting example of the deep interrelation between Physics and Mathematics is obtained when trying to impose mathematical boundary conditions on physical quantum fields. This procedure has recently been re-examined with care. Comments…
We prove several Sobolev inequalities, which are then used to establish a fractional Hardy-Sobolev- Maz'ya inequality on the upper halfspace.
Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is…
We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version…
In this paper, we give the matrix version of Horn's hypergeometric function and its confluent cases. We also discuss the regions of convergence, the system of matrix differential equations of bilateral type, differential formulae and…