Related papers: Dependence of vector fields and singular controls
Let $\Omega$ be a non-singular syplectic form on some vector space $V$. Denote by $S^{n}_{k}(\Omega)$ the set of all $k$-dimensional planes $s$ in $V$ such that the restriction of $\Omega$ onto $s$ is singular. For the cases when $k=2,n-2$…
Using a tight binding model we calculate the conductance of monovalent atomic chains for different contact geometries. The leads connected to the chains are modelled as semi-infinite fcc lattices with different orientations and couplings.…
While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of…
We consider the monotonic tracking control problem for continuous-time single-input single-output linear systems using output-feedback linear controllers in this paper. We provide the necessary and sufficient conditions for this problem to…
Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly…
Numerical and experimental realizations of quantum control are closely connected to the properties of the mapping from the control to the unitary propagator. For bilinear quantum control problems, no general results are available to fully…
In this paper we extend the work in the conference paper 'On the Controllability and Observability of Heterogeneous Networked Systems with distinct node dimensions and inner-coupling matrices' wherein the controllability and observability…
A large class of real $3$-dimensional nilpotent polynomial vector fields of arbitrary degree is considered. The aim of this work is to present general properties of the discrete and continuous dynamical systems induced by these vector…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
We study how the problem of observables is fully resolved for background independent theories defined on finite graphs. We argue the correct analogue of coordinate independence is the invariance under changes of graph labels, a kind of…
The existence of a nowhere zero real vector field implies a well-known restriction on a compact manifold. But all manifolds admit nowhere zero complex vector fields. The relation between these observations is clarified.
Singular complex analytic vector fields on the Riemann surfaces enjoy several geometric properties (singular means that poles and essential singularities are admissible). We describe relations between singular complex analytic vector fields…
Notions of freedom and independence for hypergraphs of models of a theory are defined. Properties of these notions and their applications to some natural classes of theories are studied.
Control code is a concept that is closely related to a frequently occurring practitioner's view on what is a program: code that is capable of controlling the behaviour of some machine. We present a logical approach to explain issues…
On a manifold equipped with a bivector field, we introduce for every Hamiltonian a Lagrangian on paths valued in the cotangent space whose stationary points projects onto Hamiltonian vector fields. We show that the remaining components of…
Non-smooth vector fields does not have necessarily the property of uniqueness of solution passing through a point and this is responsible to enrich the behavior of the system. Even on the plane non-smooth vector fields can be chaotic, a…
Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
Motivated by research on contraction analysis and incremental stability/stabilizability the study of 'differential properties' has attracted increasing attention lately. Previously lifts of functions and vector fields to the tangent bundle…
In this article we further develop the theory of valuation independence and study its relation with classical notions in valuation theory such as immediate and defectless extensions. We use this general theory to settle two open questions…