Abstract In this paper, we explore the interrelationship between Eulerian numbers and B splines. Specifically, using B splines, we give the explicit formulas of the refined Eulerian numbers, and descents polynomials. Moreover, we prove that the coefficients of descent polynomials D d (t) are logconcave. This paper also provides a new approach to study Eulerian numbers and descent polynomials.

A novel 3D computational model was developed for the turbulent particulate two-phase flow simulation in rectangular channel. The is based on Eulerian approach applied to Reynolds-averaged Navier–Stokes modeling and statistical Probability Distribution Function method. uniqueness of method lies direct calculation normal transverse components Reynolds stresses both gas particles. Two cases were e...

In this paper, we evaluate the number of Eulerian circuits that can be obtained by an arbitrary rotation in a Markovian string, i.e., corresponding to a given Markovian type. Since all rotations do not result in an Eulerian circuit, but several of them, called Eulerian components; we also investigate the number of Eulerian components that result from a random rotation in a Markovian string. We ...

In this research the separation efficiency of deoiling hydrocyclone is evaluated using three-dimensional simulation of multiphase flow based on Eulerian-Eulerian finite volume method. The mixture approach of Reynolds Stress Model is also employed to capture the features of turbulent multiphase swirling flow. The obtained separation efficiency of Colman's design is compared with available experi...

recently, e. m'{a}v{c}ajov'{a} and m. v{s}koviera proved that every bidirected eulerian graph which admits a nowhere zero flow, admits a nowhere zero $4$-flow. this result shows the validity of bouchet's nowhere zero conjecture for eulerian bidirected graphs. in this paper we prove the same theorem in a different terminology and with a short and simple proof. more precisely, we p...

The main goal of this work is to establish a bijection between Dyck words and a family of Eulerian digraphs. We do so by providing two algorithms implementing such bijection in both directions. The connection between Dyck words and Eulerian digraphs exploits a novel combinatorial structure: a binary matrix, we call Dyck matrix, representing the cycles of an Eulerian digraph. 1. Background, and ...

An identity of Chung, Graham and Knuth involving binomial coefficients and Eulerian numbers motivates our study of a class of polynomials that we call binomial-Eulerian polynomials. These polynomials share several properties with the Eulerian polynomials. For one thing, they are h-polynomials of simplicial polytopes, which gives a geometric interpretation of the fact that they are palindromic a...

This paper defines the Stochastic Eulerian Tour Problem (SETP) and investigates several characteristics of this problem. Given an undirected Eulerian graph , a subset =) of the edges in E that require service, and a probability distribution for the number of edges in R that have to be visited in any given instance of the graph, the SETP seeks an a priori Eulerian tour of minimum expected length...