Related papers: On equivalence of vector-valued maps

We define vector fields, leaves and trajectories for schemes. With these tools, we are able to give a geometrical interpretation and to generalize several results of differential Galois theory and constructions on differential schemes. We…

A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…

Computing the shortest path between two given locations in a road network is an important problem that finds applications in various map services and commercial navigation products. The state-of-the-art solutions for the problem can be…

A labelling of a graph is an assignment of labels to its vertex or edge sets (or both), subject to certain conditions, a well established concept. A labelling of a graph G of order n is termed a numbering when the set of integers {1,...,n}…

We discuss some equivalence relations between the non-relativistic quantum mechanics for particles subjected to potentials and for particles moving freely on background geometries. In particular, we illustrate how selected geometries can be…

We classify all continuous valuations on the space of finite convex functions with values in the same space which are dually epi-translation-invariant and equi- resp. contravariant with respect to volume-preserving linear maps. We thereby…

The graph alignment problem, which considers the optimal node correspondence across networks, has recently gained significant attention due to its wide applications. There are graph alignment methods suited for various network types, but we…

This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…

Vectorized high-definition (HD) map is essential for autonomous driving, providing detailed and precise environmental information for advanced perception and planning. However, current map vectorization methods often exhibit deviations, and…

A vertex ranking of a graph is an assignment of ranks (or colors) to the vertices of the graph, in such a way that any simple path connecting two vertices of equal rank, must contain a vertex of a higher rank. In this paper we study a…

We give a short, mostly elementary and self-contained proof of the classical result that the groups of diffeomorphisms, homeomorphisms, and homotopy equivalences of a surface have the same group of connected components.

Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…

We provide criteria for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. These criteria reduce the projection problem to a certain…

Considered is the problem of local equivalence of generic four-dimensional metrics possessing two commuting and orthogonally transitive Killing vector fields. A sufficient set of eight differential invariants is explicitly constructed,…

We show how to use geometric arguments to prove that the terminal solution to a rough differential equation driven by a geometric rough path can be obtained by driving the same equation by a piecewise linear path. For this purpose, we…

In this paper we introduce a novel polynomial-time algorithm to compute graph invariants based on the modified random walk idea on graphs. However not proved to be a full graph invariant by now, our method gives the right answer for the…

We propose an inverse approach for dealing with interval maps based on the manner whereby their branches are related (folding property), instead of addressing the map equations as a whole. As a main result, we provide a symmetry-breaking…

We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…

Graph embedding is a transformation of vertices of a graph into set of vectors. Good embeddings should capture the graph topology, vertex-to-vertex relationship, and other relevant information about graphs, subgraphs, and vertices. If these…

We introduce several classes of set-valued maps with generalized convexity. We obtain minimax theorems for set-valued maps which satisfy the introduced properties and are not continuous, by using a fixed point theorem for weakly naturally…