Related papers: Orthogonally connected sets
A successive continuation method for locating connecting orbits in parametrized systems of autonomous ODEs is considered. A local convergence analysis is presented and several illustrative numerical examples are given.
In this paper, we study maximal antipodal sets in simply connected exceptional compact symmetric spaces. Combining our results with the existing literature, we obtain a complete classification of maximal antipodal sets in all such spaces.…
A recent proposal of new sets of squeezed states is seen as a particular case of a general context admitting realistic physical Hamiltonians. Such improvements reveal themselves helpful in the study of associated squeezing effects.…
Given an orthogonal representation of a compact group, we show that any element of the connected component of the isometry group of the orbit space lifts to an equivariant isometry of the original Euclidean space. Corollaries include a…
Positive spanning sets span a given vector space by nonnegative linear combinations of their elements. These have attracted significant attention in recent years, owing to their extensive use in derivative-free optimization. In this…
A brief introduction to the theory of ordered sets and lattice theory is given. To illustrate proof techniques in the theory of ordered sets, a generalization of a conjecture of Daykin and Daykin, concerning the structure of posets that can…
Heteroclinic connections are trajectories that link invariant sets for an autonomous dynamical flow: these connections can robustly form networks between equilibria, for systems with flow-invariant spaces. In this paper we examine the…
We prove the existence of minimal heteroclinic orbits for a class of fourth order O.D.E. systems with variational structure. In our general set-up, the set of equilibria of these systems is a union of manifolds, and the heteroclinic orbits…
A method to construct trihamiltonian extensions of a separable system is presented. The procedure is tested for systems, with a natural Hamiltonian, separable in classical sense in one of the four orthogonal separable coordinate systems of…
Necessary and sufficient conditions for a finite connected graph with a strict partial order on vertices to be a combinatorial invariant of pseudoharmonic function are obtained.
In this paper, we study some relationships existing between some particular mathematical structures: discrete surfaces coming from discrete topology and mathematical morphology, poset-based connected manifolds coming from discrete topology,…
We survey the state of the union-closed sets conjecture.
In this paper, we analyze the chain control sets of linear control systems on connected Lie groups. Our main result shows that the compactness of the central subgroup associated with the drift is a necessary and sufficient condition to…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem. The obtained conditions are more complicated than those for the classical commutant lifting…
We examine synchronization between identical chaotic systems. A rigorous criteria is presented which, if satisfied, guarantees that the coupling produces linearly stable synchronous motion. The criteria can also be used to design couplings…
The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to…
In this paper, we introduce the notion of $\mathcal{M}$-convergence and $\mathcal{MN}$-convergence structures in posets, which, in some sense, generalise the well-known Scott-convergence and order-convergence structures. As results, we give…
This paper states a definition of homotopic rotation set for higher genus surface homeomorphisms, as well as a collection of results that justify this definition. We first prove elementary results: we prove that this rotation set is…