Let G be a simple connected graph all of whose vertices have even degrees. An Eulerian circuit in G is a closed walk (see, for example, [2]) which uses every edge of G exactly once. Two Eulerian circuits are called equivalent if one is a cyclic permutation of the other. It is clear that the size of such an equivalence class equals the number of edges of graph G. Let EC(G) denote the number of e...

A random Eulerian triangulation is a random triangulation where an even number of triangles meet at any given vertex. We argue that the central charge increases by one if the fully packed O(n) model is defined on a random Eulerian triangulation instead of an ordinary random triangulation. Considering the case n → 0, this implies that the system of random Eulerian triangulations equipped with Ha...

For a graph G = (V,E) and a vertex v ∈ V , let T (v) be a local trace at v, i.e. T (v) is an Eulerian subgraph of G such that every walk W (v), with start vertex v can be extended to an Eulerian tour in T (v). We prove that every maximum edge-disjoint cycle packing Z∗ of G induces a maximum trace T (v) at v for every v ∈ V . Moreover, if G is Eulerian then sufficient conditions are given that g...

in the course of expansion in turbines steam nucleates to become a two-phase mixture, the liquid consisting of a very large number of extremely small droplets carried by the vapor. formation and subsequent behaviour of the liquid lowers the performance of turbine wet stages. the calculations were carried out assuming that the flow is two dimensional, compressible, turbulent and viscous. a class...

Let G be an eulerian digraph with a fixed edge coloring (not necessarily a proper edge coloring). A compatible circuit of G is an eulerian circuit such that every two consecutive edges in the circuit have different colors. We characterize the existence of compatible circuits for directed graphs avoiding certain vertices of outdegree three. Our result is analogous to a result of Kotzig for compa...

To assess the impact of dynamical formulation on climate simulations, a semi-Lagrangian and an Eulerian dynamical core have been used for 5-yr climate simulations with the same physical parameterizations. The comparison of the climate simulations is focused on various eddy statistics (the study of time-mean states from the simulations has been published in a previous paper). Significant differe...

This paper describes RHALE, a two and three-dimensional, multi-material, arbitrary Lagrangian-Eulerian (MMALE) shock physics code written in C++. RHALE is the successor to CTH, Sandia’s 3-D Eulerian shock physics code, and will be capable of solving problems that CTH cannot adequately address. RHALE employs a three step solution algorithm for the equations of motion: (1) a Lagrangian step capab...

R esum e. La description classique du probl eme de l'optique g eom etrique est La-grangienne. Le passage a la repr esentation Eul erienne est possible mais, en pr esence de caustiques, ne permet pas de calculer la solution Lagrangienne compl ete. On pr esente le contexte math ematique du probl eme ainsi que quelques outils num eriques d evelop-p es pour lever cette limitation. Abstract. The cla...

We present an infinite series of n-state Eulerian automata whose reset words have length at least (n − 3)/2. This improves the current lower bound on the length of shortest reset words in Eulerian automata. We conjecture that (n − 3)/2 also forms an upper bound for this class and we experimentally verify it for small automata by an exhaustive computation.

Since the properties of systems comprising many homogeneous agents may be expected to be independent of how the agents happen to be indexed, it should be possible to formulate and solve multiagent control problems in an index-free way. In this paper we provide such an approach, based on an indicator distribution representation, which results in integrodifferential dynamics that parallel and ext...