Related papers: Hahn Decomposition Theorem of Signed Lattice Measu…

We define the alternating sign matrix polytope as the convex hull of nxn alternating sign matrices and prove its equivalent description in terms of inequalities. This is analogous to the well known result of Birkhoff and von Neumann that…

In this work we establish a connection between copositivity, that is, nonnegativity on the positive orthant, of sparse real Laurent polynomials and discriminants. Specifically, we consider Laurent polynomials in the positive orthant with…

One of the main questions in the theory of normal surface singularities is to understand the relations between their geometry and topology. The lattice cohomology is an important tool in the study of topological properties of a plumbed…

We investigate the decomposition of a set $X$, which positively spans the Euclidean space $\mathbb{R}^{d}$ into a set of minimal positive bases, we call simplices, and into maximal sets positively spanning pointed cones, i.e. cones with…

The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…

The special linear group G=SL_n(Z[x1,...,xk]) (n at least 3 and k finite) is called the universal lattice. Let n be at least 4, p be any real number in (1,\infty). The main result is the following: any finite index subgroup of G has the…

In this paper we study the norm-attainment of positive operators between Banach lattices. By considering an absolute version of James boundaries, we prove that: If $E$ is a reflexive Banach lattice whose order is given by a basis and $F$ is…

There are significant differences between Helmholtz and Hodge's decomposition theorems, but both share a common flavor. This paper is a first step to bring them together. We here produce Helmholtz theorems for differential 1-forms and…

We prove that the signature of an even, symmetric form on a finite rank integral lattice, has signature divisible by 8, provided its associated linking form vanishes in the Witt group of linking forms. Our result generalizes the well know…

A residuated lattice is defined to be integrally closed if it satisfies the equations x\x = e and x/x = e. Every integral, cancellative, or divisible residuated lattice is integrally closed, and, conversely, every bounded integrally closed…

In this review article, first we give the concrete formulas of representations and cohomologies of associative algebras, Lie algebras, pre-Lie algebras, Leibniz algebras and 3-Lie algebras and some of their strong homotopy analogues. Then…

An $n$-dimensional lattice polytope ${\mathcal Q}_\sigma$ can be associated to any composition $\sigma$ of a positive integer $n$, as a special case of constructions due to Pitman--Stanley and Chapoton. The entries of the $h$-vector of…

To study the set of torsion classes of a finite dimensional basic algebra, we use a decomposition, called sign-decomposition, parametrized by elements of $\{\pm1\}^n$ where $n$ is the number of simple modules. If $A$ is an algebra with…

We partly extend the localisation technique from convex geometry to the multiple constraints setting. For a given $1$-Lipschitz map $u\colon\mathbb{R}^n\to\mathbb{R}^m$, $m\leq n$, we define and prove the existence of a partition of…

We generalize the logarithmic decomposition theorem of Deligne-Illusie to a filtered version. There are two applications. The easier one provides a mod $p$ proof for a vanishing theorem in characteristic zero. The deeper one gives rise to a…

A lattice gauge theory with an action polynomial in independent field variables is considered. The link variables are described by unconstrained complex matrices instead of unitary ones. A mechanism which permits to switch off in the…

Magnetic translation symmetry on a finite periodic square lattice is investigated for an arbitrary uniform magnetic field in arbitrary dimensions. It can be used to classify eigenvectors of the Hamiltonian. The system can be converted to…

This paper represents the second in a series of works aimed at reinvigorating the quantum geometrodynamics program. Our approach introduces a lattice regularization of the hypersurface deformation algebra, such that each lattice site…

We will prove the following generalization of the ham sandwich Theorem, conjectured by Imre B\'ar\'any. Given a positive integer $k$ and $d$ nice measures $\mu_1, \mu_2,..., \mu_d$ in $\mathbb{R}^d$ such that $\mu_i (\mathds{R}^d) = k$ for…

It is well-known that the Sobolev spaces $W^{k,p}(\mathbb R^d)$ are vector lattices with respect to the pointwise almost everywhere order if $k \in \{0,1\}$, but not if $k \ge 2$. In this note, we consider negative $k$ and show that the…