Related papers: Function space bases in the dune-functions module

In this paper we present a novel representation for deformation fields of 3D shapes, by considering the induced changes in the underlying metric. In particular, our approach allows to represent a deformation field in a coordinate-free way…

In this paper we study Rota-Baxter modules with emphasis on the role played by the Rota-Baxter operators and resulting difference between Rota-Baxter modules and the usual modules over an algebra. We introduce the concepts of free,…

We present an efficient implementation of a surface Green's-function method for atomistic modeling of surfaces within the framework of density functional theory using a pseudopotential localized basis set approach. In this method, the…

Modern software typically performs more than one functionality. These functionalities or features are not always organized in a way for modules representing these features to be used individually. Many software engineering approaches like…

We present an approach to develop folds for nested data types using dependent types. We call such folds $\textit{dependently typed folds}$, they have the following properties. (1) Dependently typed folds are defined by well-founded…

Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…

The key innovation in this paper is an open-source, high-performance iterative solver for high contrast, strongly anisotropic elliptic partial differential equations implemented within dune-pdelab. The iterative solver exploits a robust,…

Sensor-based Human Activity Recognition (HAR) underpins many ubiquitous and wearable computing applications, yet current models remain limited by scarce labels, sensor heterogeneity, and weak generalization across users, devices, and…

In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan et al, Nucl.Phys.B862:553-575,2012]. Here we develop a general formalism of rectangle boundary states using…

This chapter describes modal decompositions in the framework of matrix factorizations. We highlight the differences between classic space-time decompositions and 2D discrete transforms and discuss the general architecture underpinning…

We first review the properties of the conventional $\tau$-functions of the KP and Toda-lattice hierarchies. A straightforward generalization is then discussed. It corresponds to passing from differential to finite-difference equations; it…

Using linear functional-based duality of modules, we generalize the syndrome decoding algorithm of linear codes over finite fields to those over finite commutative rings. Moreover, If the ring is local the algorithm is simplified by…

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions.…

Recently, a lot of papers proposed to use neural networks to approximately solve partial differential equations (PDEs). Yet, there has been a lack of flexible framework for convenient experimentation. In an attempt to fill the gap, we…

The goal of this paper is to prove that the classifying spaces of categories of algebras governed by a prop can be determined by using function spaces on the category of props. We first consider a function space of props to define the…

Deep neural networks (DNNs) have achieved remarkable empirical success, yet the absence of a principled theoretical foundation continues to hinder their systematic development. In this survey, we present differential equations as a…

Modern modeling languages for general physical systems, such as Modelica, Amesim, or Simscape, rely on Differential Algebraic Equations (DAE), i.e., constraints of the form f(dot{x},x,u)=0. This drastically facilitates modeling from first…

In this paper we give description of free and cofree objects in the category of operator sequence spaces. First we show that this category possess the same duality theory as category of normed spaces, then with the aid of these results we…

Membrane particles such as proteins and lipids organize into zones that perform unique functions. Here, I introduce a topological and category-theoretic framework to represent particle and zone intra-scale interactions and inter-scale…

In this article, we study the properties of a class of functional spaces which arise from the investigation of nonlinear differential equations. We establish some integral inequalities then by applying these inequalities, we prove some…