The Eulerian mapping closure approach is developed for uncertainty propagation in computational uid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear ow. An analytical argument shows that uctuation of the concentration eld at one point in space is non-Gaussian and exhibits stretched exponential form. An Eu...

Any bipartite Eulerian graph, any Eulerian graph with evenly many vertices, and any bipartite graph with evenly many vertices and edges, has an even number of spanning trees. More generally, a graph has evenly many spanning trees if and only if it has an Eulerian edge cut. ∗Work supported in part by NSF grant CCR-9258355 and by matching funds from Xerox Corp.

We introduce new recurrences for the type B and type D Eulerian polynomials, and interpret them combinatorially. These recurrences are analogous to a well-known recurrence for the type A Eulerian polynomials. We also discuss their relationship to polynomials introduced by Savage and Visontai in connection to the real-rootedness of the corresponding Eulerian polynomials.

Here presented is constructive generalization of exponential Euler polynomial and exponential splines based on the interrelationship between the set of concepts of Eulerian polynomials, Eulerian numbers, and Eulerian fractions and the set of concepts related to spline functions. The applications of generalized exponential Euler polynomials in series transformations and expansions are also given.

Fleischner, H., G. Sabidussi and E. Wenger, Transforming eulerian trails, Discrete Mathematics 109 (1992) 103-116. In this paper a set of transformations (K-transformations) between eulerian trails is investigated. It is known that two arbitrary eulerian trails can be transformed into each other by a sequence of K-transformations. For compatible eulerran trails the set of K-transformations is a...

A graph is subeulerian if it is spanned by an eulerian supergraph. Boesch, Suffel and Tindell have characterized the class of subeulerian graphs and determined the minimum number of additional lines required to make a subeulerian graph eulerian. In this paper, we consider the related notion of a subsemi-eulerian graph, i.e. a graph which is spanned by a supergraph having an open trail containin...

The Stochastic Eulerian Tour Problem was introduced in 2008 [1] as a stochastic variant of the well-known Eulerian Tour Problem. In a follow-up paper the same authors investigated some heuristics for solving the Stochastic Eulerian Tour Problem [2]. After a thorough study of these two publications a few issues emerged. In this short research commentary we would like to discuss these issues. For...

A number of researchers studying permutation statistics on the symmetric group Sn have considered pairs (x, Y), where x is an Eulerian statistic and Y is a Mahonian statistic. Of special interest are pairs such as (des, maj), whose joint distribution on Sn is given by Carlitz’s q-Eulerian polynomials. We present a natural Eulerian statistic stc such that the pair (stc, inv) is equally distribut...

We introduce a new computational method for embedding Lagrangian sink particles into an Eulerian calculation. Simulations of gravitational collapse or accretion generally produce regions whose density greatly exceeds the mean density in the simulation. These dense regions require extremely small time steps to maintain numerical stability. Smoothed particle hydrodynamics (SPH) codes approach thi...

We completely characterize 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) = n! has...