Related papers: Cell decomposition and definable functions for wea…

This is the first of a series of articles providing a foundation for the theory of Drinfeld modular forms of arbitrary rank r. In the present part, we develop the analytic theory. Most of the work goes into defining and studying the…

We propose a novel approach for studying rooted trees by using functions that we will call descent functions. We provide a construction method for rooted trees that allows to study their properties through the use of descent functions.…

We analyze the partition function of two dimensional Yang-Mills theory on a family of surfaces of infinite genus. These surfaces have a recursive structure, which was used by one of us to compute the partition function that results in a…

Using complex methods combined with Baire's Theorem we show that one-sided extendability, extendability and real analyticity are rare phenomena on various spaces of functions in the topological sense. These considerations led us to…

The applications of the partial fraction decomposition in control and systems engineering are several. In this letter, we propose a new interpretation of residues in the partial fraction decomposition, which is employed for the following…

We investigate the structure of the $p$-divisor for the Jouanolou foliation where we show, under some conditions, that it can be irreducible or has a $p$-factor. We study the reduction modulo $p$ of foliations on the projective plane and…

We construct a small regular cellular decomposition of the Fulton MacPherson operad $FM_2$ that is compatible with the operad composition. The cells are indexed by trees with edges of two colors and vertices labelled by cells of the cacti…

The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…

Decomposable ordered structures were introduced in \cite{OnSt} to develop a general framework to study `finite-dimensional' totally ordered structures. This paper continues this work to include decomposable structures on which a ordered…

The moduli space of Riemann surfaces with at least two punctures can be decomposed into a cell complex by using a particular family of ribbon graphs called Nakamura graphs. We distinguish the moduli space with all punctures labelled from…

The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…

Let $T$ be a complete, model-complete, geometric dp-minimal $\mathcal{L}$-theory of topological fields of characteristic $0$ and let $T(\partial)$ be the theory of expansions of models of $T$ by a derivation $\partial$. We assume that…

Building on prior work, we analyze the decomposition of the restriction of an irreducible representation of SL_2(k), for k a p-adic field of odd residual characteristic, to a maximal compact subgroup K. The pattern of the decomposition…

Let R be an associative ring with possible extra structure. R is said to be weakly small if there are countably many 1-types over any finite subset of R. It is locally P if the algebraic closure of any finite subset of R has property P. It…

In this paper we study the $p$-adic analytic geometry of the basic unitary group Rapoport-Zink spaces $\M_K$ with signature $(1,n-1)$. Using the theory of Harder-Narasimhan filtration of finite flat groups developed by Fargues in…

We describe an algorithm to decompose rational functions from which we determine the poset of groups fixing these functions.

We develop a theory of descent and forms of tensor categories over arbitrary fields. We describe the general scheme of classification of such forms using algebraic and homotopical language, and give examples of explicit classification of…

The theory of fractional calculus in the complex plane was not built with a specific application in mind. The main obstacle to application was the difficulty with obtaining analytic continuations of fractional derivatives and integrals. It…

Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…

We introduce a general constructive method to find a p-basis (and the Ulm invariants) of a finite Abelian p-group M. This algorithm is based on Groebner bases theory. We apply this method to determine the additive structure of…