Related papers: Generalized 3x + 1 Mappings : searching for cycles
In this paper, we study the occurrence of patterns in the cycle structures of permutations.
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
A smooth map between smooth manifolds is called a special generic map if it has only definite fold points as its singularities. In this paper, we give conditions for a special generic map into the 3-dimensional Euclidean space to be…
This note presents an approach to studying the iterates of a mapping whose restriction to the complement of a finite set is continuous and open. The main examples to which the approach can be applied are piecewise monotone mappings defined…
In this paper, a polynomial time algorithm for finding the set of all cyclic subsets in a graph is presented. The concept of cyclic subsets has already been introduced in an earlier paper. The algorithm finds cyclic subsets in a graph G by…
We fully classify completely multiplicative sequences which are given by generalised polynomial formulae, and obtain a similar result for (not necessarily completely) multiplicative sequences under the additional restriction that the…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated if the subsets in the cyclic disposal are nonempty, bounded and of nonempty…
A (complete) matching of the cells of a triangulated manifold can be thought as a combinatorial or discrete version of a nonsingular vector field. We give several methods for constructing such matchings.
We study three covering problems in the plane. Our original motivation for these problems come from trajectory analysis. The first is to decide whether a given set of line segments can be covered by up to four unit-sized, axis-parallel…
We present a general bijective approach to planar hypermaps with two main results. First we obtain unified bijections for all classes of maps or hypermaps defined by face-degree constraints and girth constraints. To any such class we…
The majority of graphs whose sandpile groups are known are either regular or simple. We give an explicit formula for a family of non-regular multi-graphs called thick cycles. A thick cycle graph is a cycle where multi-edges are permitted.…
In this paper we describe the dynamics of certain rational maps of the form $k \cdot (x+x^{-1})$ over finite fields of odd characteristic.
We show that for any set of n distinct points in the complex plane, there exists a polynomial p of degree at most n+1 so that the corresponding Newton map, or even the relaxed Newton map, for p has the given points as a super-attracting…
In this expository paper we present some ideas of algebraic topology (more precisely, of homology theory) in a language accessible to non-specialists in the area. A $1$-cycle in a graph is a set $C$ of edges such that every vertex is…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
We consider the Li\'enard equation and we give a sufficient condition to ensure existence and uniqueness of limit cycles. We compare our result with some other existing ones and we give some applications.
In this paper, we introduce and study the iterates of the following family of functions $\varphi_k$ defined on natural numbers which exhibits nice properties. $$\varphi_k(x)=\left\lbrace \begin{array}{ll} x+k, & \mbox{ if $x$ is prime;}\\…
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
We consider (generalized) periods of Maass forms along non-closed geodesics having a closed geodesic as the limit set.