Finding the conductors in circular networks from boundary measurements
We investigate the properties of the least-squares solution of the system of equations with a matrix being the incidence matrix of a given undirected connected graph and we propose an algorithm that uses this solution for finding a vertex-disjoint cycle cover (2-factor) of the graph .
The canonization theorem says that for given for some (the first one is called ) we have for every function with domain , for some , the question of when the equality (where and are from ) holds has the simplest answer: for some the equality holds iff . We improve the bound on so that fixing the number of exponentiation needed to calculate is best possible.
The paper deals with the decomposition and with the boundarz and hull construction of the so-called nondense point set. This problem and its applications have been frequently studied in computational geometry, raster graphics and, in particular, in the image processing (see e.g. [3], [6], [7], [8], [9], [10]). We solve a problem of the point set decomposition by means of certain relations in graph theory.
We prove that all finite simple groups of Lie type, with the exception of the Suzuki groups, can be made into a family of expanders in a uniform way. This confirms a conjecture of Babai, Kantor and Lubotzky from 1989, which has already been proved by Kassabov for sufficiently large rank. The bounded rank case is deduced here from a uniform result for which is obtained by combining results of Selberg and Drinfeld via an explicit construction of Ramanujan graphs by Lubotzky, Samuels and Vishne.
In this paper, we investigate the finite-time adaptive outer synchronization between two complex dynamical networks with nonidentical topological structures. We propose new adaptive controllers, with which we can synchronize two complex dynamical networks within finite time. Sufficient conditions for the finite-time adaptive outer synchronization are derived based on the finite-time stability theory. Finally, numerical examples are examined to demonstrate the effectiveness and feasibility of the...
In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.