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We present a simple construction of hat tilings. The construction can be carried out by superimposing a triangular grid on a specially colored image and reading off the orientation of the tiles. We show that our construction produces valid…
Approximation by polynomials on a triangle is studied in the Sobolev space $W_2^r$ that consists of functions whose derivatives of up to $r$-th order have bounded $L^2$ norm. The first part aims at understanding the orthogonal structure in…
For explicit interface tracking in three dimensions, we propose a linear MARS method that (a) represents the interface by a partially ordered set of glued surfaces and approximates each glued surface with a triangular mesh, (b) maintains an…
The aim of this paper is to start the study of images of graded polynomials on full matrix algebras. We work with the matrix algebra $M_n(K)$ over a field $K$ endowed with its canonical $\mathbb{Z}_n$-grading (Vasilovsky's grading). We…
This work introduces author's theory of Bruhat-Tits buildings over higher dimensional local fields. The theory is illustrated with the buildings for PGL(2) and PGL(3) for one- and two-dimensional local fields.
A polygonal complex in euclidean 3-space is a discrete polyhedron-like structure with finite or infinite polygons as faces and finite graphs as vertex-figures, such that a fixed number r of faces surround each edge. It is said to be regular…
Recently Belopolskaya and Suhov studied Markov process's in a random environment, where the environment changes in likeness to a Markov process. Constructions were made to allow the process to "interact with the environment", this was done…
Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…
The concept of a Dirac algebroid, which is a linear almost Dirac structure on a vector bundle, was designed to generate phase equations for mechanical systems with linear nonholonomic constraints. We apply it to systems with magnetic-like…
A matroid is a machine capturing linearity of mathematical objects and producing combinatorial structures. Matroid structure arises everywhere since linearity is a ubiquitous concept. One natural way to obtain matroids is by considering…
Synthetic algebraic geometry is a new approach to algebraic geometry. It consists in using homotopy type theory extended with three axioms, together with the interpretation of these in a higher version of the Zariski topos, in order to do…
Iterated planar contact manifolds are a generalization of three dimensional planar contact manifolds to higher dimensions. We study some basic topological properties of iterated planar contact manifolds and discuss several examples and…
Let $F$ be a local non-archimedian field of positive characteristic, $D$ be a skew-field with center $F$ and $ G=D^{\star}$ be the multiplicative group of $D$. The goal of this paper is to provide a canonical decomposition of any complex…
A simple construction is presented, which generalises piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature,…
In this paper we will give an explicit construction of the geometric model for a prescribed extension of a function field in several variables over a number field. As a by-product, we will also prove the existence of quasi-galois closed…
This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space,…
In engineering practice one often encounters planar problems, where the corresponding vector space of forces, velocities or (infinitesimal) displacements is three dimensional. This paper shows how these spaces can be factorized, such that…
We investigate the problem of probing the local spatial structure of the magnetic field of the interstellar medium using multi-frequency polarized maps of the synchrotron emission at radio wavelengths. We focus in this paper on the…
We present a general and model-independent method to obtain an effective Markovian quantum kinetic equation for the expectation value of a slowly evolving scalar field in an adiabatically evolving background from first principles of…
This paper introduces a framework designed to accurately predict piecewise linear mappings of arbitrary meshes via a neural network, enabling training and evaluating over heterogeneous collections of meshes that do not share a…