We give a complete classification of the factorial functions of Eulerian binomial posets. The factorial function B(n) either coincides with n!, the factorial function of the infinite Boolean algebra, or 2n−1, the factorial function of the infinite butterfly poset. We also classify the factorial functions for Eulerian Sheffer posets. An Eulerian Sheffer poset with binomial factorial function B(n...

This study reports the mutual transformations between the third-order Eulerian and Lagrangian solutions for the irrotational progressive gravity waves propagating on the uniform depth. Based on the fundamental principle of kinematics, the instantaneous Eulerian and Lagrangian velocities are identically equal, and using a successive Taylor series expansion to the path and the period of particle ...

A graph G is Eulerian-connected if for any u and v in V (G), G has a spanning (u. v)-trail. A graph G is edge-Eulerian-connected if for any e' and elf in E(G), G has a spanning (e', elf)-trail. For an integer r ~ 0, a graph is called r-Eulerian-connected if for any X s::: E(G) with IXI ~r, and for any u, v E V(G), G has a spanning (u, v)-trail T such that X s::: E(T). The r-edge-Eulerian­ conne...

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...

In this work, we present a Fully Eulerian framework for fluid-structure interaction (fsi) problems coupling the incompressible Navier-Stokes equations with a hyperelastic solid. The Fully Eulerian framework is a monolithic implicit variational formulation for the coupled problem. In contrast to the well-established Arbitrary Lagrangian Eulerian (ALE) coordinates, the Fully Eulerian framework fo...

We defined the symmetric TSP in lecture 6. The best known approximation algorithm for STSP is the 3/2 approximation algorithm of Christofides. The algorithm is very easy to describe, first choose a minimum cost spanning tree and then add that minimum cost Eulerian augmentation to the tree, that is the minimum cost set of edges to make the tree Eulerian. An undirected graph is Eulerian when ever...

Eulerian extension problems aim at making a given (directed) (multi-)graph Eulerian by adding a minimum-cost set of edges (arcs). These problems have natural applications in scheduling and routing and are closely related to the Chinese Postman and Rural Postman problems. Our main result is to show that the NP-hard Weighted Multigraph Eulerian Extension is fixed-parameter tractable with respect ...

The variational principle of barotropic Eulerian fluid dynamics is known to be quite cumbersome containing as much as eleven independent functions. This is much more than the the four functions (density and velocity) appearing in the Eulerian equations of motion. This fact may have discouraged applications of the variational method. In this paper a four function Eulerian variational principle i...

Dense slurry flow through centrifugal pump casing has been modeled using the Eulerian-Eulerian approach with Eulerian multiphase model in FLUENT 6.1. First order upwinding is considered for the discretization of momentum, k and ε terms. SIMPLE algorithm has been applied for dealing with pressurevelocity coupling. A mixture property based k-ε turbulence model has been used for modeling turbulenc...