相关论文: On Necessary and Sufficient Conditions for Differe…

We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…

For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…

If two control systems on manifolds of the same dimension are dynamic equivalent, we prove that either they are static equivalent --i.e. equivalent via a classical diffeomorphism-- or they are both ruled; for systems of different…

Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…

We prove that the category of vector bundles over a fixed smooth manifold and its corresponding category of convenient modules are models for intuitionistic differential linear logic. The exponential modality is modelled by composing the…

We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…

First-order fully implicit as well as implicit--explicit schemes for coupled elliptic-parabolic systems are discussed in [Ern and Meunier, ESAIM: M2AN, 2009] and [Altmann et al., Math.\ Comp., 2021], respectively. The extension of the…

In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…

Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the…

Generalized nonlinear programming is considered without any convexity assumption, capturing a variety of problems that include nonsmooth objectives, combinatorial structures, and set-membership nonlinear constraints. We extend the augmented…

We present interpretation of known results in the theory of discrete asymptotic and discrete conjugate nets from the "discretization by B\"{a}cklund transformations" point of view. We collect both classical formulas of XIXth century…

Let U be a real form of a complex semisimple Lie group, and tau, sigma, a pair of commuting involutions on U. This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and…

We revisit the flatland paradox proposed by \cite{ston1976} which is an example of non-conglomerability. The aim of the paper is to show that the improperness of the prior is not directly involved in the inconsistency. First, we show that…

We discuss some specializations of the frames of flat orthonormal frame bundles over geometries of indefinite signature, and the resulting symmetries of families of embedded Riemannian or pseudo-Riemannian geometries. The specializations…

The aim of the paper is to demonstrate the superiority of Cartan's method over direct methods based on differential elimination for handling otherwise intractable equivalence problems. In this sens, using our implementation of Cartan's…

The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…

Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…

In this article we classify normal forms and unfoldings of linear maps in eigenspaces of (anti)-automorphisms of order two. Our main motivation is provided by applications to linear systems of ordinary differential equations, general and…

Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel…

Discretization methods for ordinary differential equations based on the use of matrix exponentials have been known for decades. This set of ideas has come off age and acquired greater urgency recently, within the context of geometric…