Related papers: Intrinsic and Apparent Singularities in Flat Diffe…
We prove that every flat nonlinear discrete-time system can be decomposed by coordinate transformations into a smaller-dimensional subsystem and an endogenous dynamic feedback. For flat continuous-time systems, no comparable result is…
We give a topological and geometrical description of focus-focus singularities of integrable Hamiltonian systems. In particular, we explain why the monodromy around these singularities is non-trivial, a result obtained before by J.J.…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
A basic problem in machine learning is to find a mapping $f$ from a low dimensional latent space $\mathcal{Y}$ to a high dimensional observation space $\mathcal{X}$. Modern tools such as deep neural networks are capable to represent general…
In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.
In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…
In this paper we study holomorphic properties of infinite dimensional spin factors. Among the infinite dimensional Banach spaces with homogeneous open unit balls, we show that the spin factors are natural outlier spaces in which to ask the…
Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diverse structure that includes singularities similar to harmonic…
The objective of this paper is to discuss invariants of singularities of algebraic schemes over fields of positive characteristic, and to show how they yield the simplification of singularities. We focus here on invariants which arise in an…
The structural invariant subspaces of the discrete-time singular Hamiltonian system are used in 1] to give an analytic nonrecursive expression of all the admissible trajectories. A deeper insight into the features of these subspaces,…
The present work establishes necessary and sufficient conditions for a nonlinear system with two inputs to be described by a specific triangular form. Except for some regularity conditions, such triangular form is flat. This may lead to the…
In the following, we offer a novel approach to modeling the observed effects currently attributed to the theoretical concepts of `dark energy', `dark matter', and `dark flow'. Instead of assuming the existence of these theoretical concepts,…
It is widely recognized that no tractable necessary and sufficient conditions exist for determining whether a system is, in general, differentially flat. However, specific cases do provide such conditions. For instance, driftless systems…
The deautonomisation of birational maps that have the singularity confinement property, i.e. the construction of nonautonomous versions of such maps that preserve the singularity properties of the original, has proven crucial in our…
This paper is concerned with investigating the asymptotic behavior of the gradients of solutions to a class of elliptic systems with general boundary data, especially covering the Lam\'{e} systems, in a narrow region. The novelty of this…
Optical singularities, which are positions within an electromagnetic field where certain field parameters become undefined, hold significant potential for applications in areas such as super-resolution microscopy, sensing, and…
Parallel robots admit generally several solutions to the direct kinematics problem. The aspects are associated with the maximal singularity free domains without any singular configurations. Inside these regions, some trajectories are…
We define discrete flat surfaces in hyperbolic 3-space from the perspective of discrete integrable systems and prove properties that justify the definition. We show how these surfaces correspond to previously defined discrete constant mean…
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…
We study spaces with a cuspidal (or horn-like) singularity embedded in a smooth Riemannian manifold and analyze the geodesics in these spaces which start at the singularity. This provides a basis for understanding the intrinsic geometry of…