Related papers: Completeness in Partial Differential Fields
In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we develop a framework that deals with perfect nonlinear functions…
In this paper we introduce a working generalization of the theory of Gr\"obner bases for algebras of partial difference polynomials with constant coefficients. One obtains symbolic (formal) computation for systems of linear or non-linear…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
We show that every valued differential field has an immediate strict extension that is spherically complete. We also discuss the issue of uniqueness up to isomorphism of such an extension.
In this short note, we classify the degree-inverting involution on the full square and triangular matrices.
We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial P(T) modulo l. As an application we find the proportion of isogeny classes of abelian varieties with a…
This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…
In this paper we study saturated fractions of factorial designs under the perspective of Algebraic Statistics. We define a criterion to check whether a fraction is saturated or not with respect to a given model. The proposed criterion is…
The article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are…
We present a general form of attribute exploration, a knowledge completion algorithm from Formal Concept Analysis. The aim of our presentation is not only to extend the applicability of attribute exploration by a general description. It may…
We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C^n. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries…
This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving…
We study the theory of a global field k as a k-vector space with a predicate for one of the absolute values on k. For example, we prove that in this language a global field with an ultrametric or real archimedean absolute value has a…
Partial derivatives are used in a variety of different ways within physics. Most notably, thermodynamics uses partial derivatives in ways that students often find confusing. As part of a collaboration with mathematics faculty, we are at the…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
We obtain complete classification of in-equivalent realizations of the Virasoro algebra by Lie vector fields over the three-dimensional field of real numbers. As an application we construct new classes of nonlinear second-order partial…
Standard clustering techniques assume a common configuration for all features in a dataset. However, when dealing with multi-view or longitudinal data, the clusters' number, frequencies, and shapes may need to vary across features to…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
An expansion of a definably complete field either defines a discrete subring, or the image of a definable discrete set under a definable map is nowhere dense. As an application we show a definable version of Lebesgue's differentiation…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…