Related papers: On Necessary and Sufficient Conditions for Differe…

We study a Lie algebra $\mathcal A_{a_1,\ldots,a_{n-1}}$ of deformed skew-symmetric $n \times n$ matrices endowed with a Lie bracket given by a choice of deformed symmetric matrix. The deformations are parametrized by a sequence of real…

An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary…

We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix…

We present a broadly applicable structurally flat triangular form for x-flat control-affine systems with three inputs. Building on recent results for the derivative structure of flat outputs, we define the triangular form together with…

Starting from nonlocal symmetries related to B\"acklund transformation (BT), many interesting results can be obtained. Taking the well known potential KdV (pKdV) equation as an example, a new type of nonlocal symmetry in elegant and compact…

Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…

Backlund transformations (BTs) are a useful tool for integrating nonlinear partial differential equations (PDEs). However, the significance of BTs in linear problems should not be ignored. In fact, an important linear system of PDEs in…

Let $A$ be a unital locally matrix algebra. Among the examples of such algebras are: (1) an infinite tensor product $\otimes M_{n_i}(\mathbb{F})$ of matrix algebras over a field $\mathbb{F}$, and (2) the Clifford algebra of a nondegenerate…

For smooth manifolds equipped with various geometric structures, we construct complexes that replace the de Rham complex in providing an alternative fine resolution of the sheaf of locally constant functions. In case that the geometric…

Fix a noetherian scheme S. For any flat map f: X->Y of separated essentially-finite-type perfect S-schemes we define a canonical derived-category map c(f):\H(X)->f^!\H(Y), the fundamental class of f, where \H(Z) is the (pre-)Hochschild…

In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…

This paper presents a novel implicit representation of solid models. With this representation, every solid model can be effectively presented by three layered depth-normal images (LDNIs) that are perpendicular to three orthogonal axes…

If ${A}$ has no eigenvalues on the closed negative real axis, and $B$ is arbitrary square complex, the matrix-matrix exponentiation is defined as $A^B:=e^{\log({A}){B}}$. This function arises, for instance, in Von Newmann's…

We consider the following quasi-linear parabolic system of backward partial differential equations: $(\partial_t+L)u+f(\cdot,\cdot,u, \nabla u\sigma)=0$ on $[0,T]\times \mathbb{R}^d\qquad u_T=\phi$, where $L$ is a possibly degenerate second…

The aim of this paper is to give a new method to construct explicit formulas for algebraic differential operators of any order on a finitely generated projective module $E$ on a commutative unital ring $A$. We moreover give explicit…

We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…

In this contribution, we present a constructive method to derive flat sampled-data models for continuous-time flat systems through an implicit Euler-discretization. We show how the sampled-data model can be used subsequently for a…

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…

In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…

We study a class of conditional independence models for discrete data with the property that one or more log-linear interactions are defined within two different marginal distributions and then constrained to 0; all the conditional…