A short report on my lecture at the Conference in Honor of W. Killing in Münster on December 7, 2007, together with some remarks on the preceding paper by ArjehM. Cohen. I reported on Euler’s famous paper Remarques sur un beau rapport entre les series des puissances tant direct que reciproques, Académie des sciences de Berlin, Lu en 1749, Opera Omnia Serie I, Bd. 15, pp. 70-90. In modern termin...

We show that each Eulerian representation of n is the restriction of a representation of n+1. We describe the new representations, giving character formulae, and identify the one which restricts to the rst Eulerian representation as the tree representation.

Three Eulerian models are implemented on a network graph model of air traffic flow. The underlying network is constructed using one year of ASDI/ETMS data. The three models are applied to high altitude traffic for a full Air Route Traffic Control Center of the National Airspace System and surrounding airspace. Simulations are carried out for a full day of data, to assess the predictive capabili...

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...

This study is concerned with the prediction of particles’ velocity in a dilute turbulent gas-solidboundary layer flow using a fully Eulerian two-fluid model. The closures required for equationsdescribing the particulate phase are derived from the kinetic theory of granular flows. Gas phaseturbulence is modeled by one-equation model and solid phase turbulence by MLH theory. Resultsof one-way and...

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...

The purpose of this paper is to evaluate the accuracy of the mesoscopic approach proposed by Février et al. [P. Février, O. Simonin, K.D. Squires, Partitioning of particle velocities in gas–solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study, J. Fluid Mech. 533 (2005) 1–46] by comparison against the Lagrangian...

In the present study, a hybrid Eulerian-Lagrangian methodology is utilized for large eddy simulation (LES) of premixed fuel/air flow over a three-dimensional backward facing step (BFS). The fluid dynamic features are obtained by solving the Eulerian filtered compressible transport equations while the species are predicted by using the filtered mass density function method (FMDF).  Some scalar f...

In this paper we study finite Eulerian posets which are binomial or Sheffer. These important classes of posets are related to the theory of generating functions and to geometry. The results of this paper are organized as follows: (1) We completely determine the structure of Eulerian binomial posets and, as a conclusion, we are able to classify factorial functions of Eulerian binomial posets; (2...