The Schrödinger equation for the four-dimensional double singular oscillator is separable in Eulerian, doble polar and spheroidal coordinates in IR. It is shown that the coefficients for the expansion of double polar basis in terms of the Eulerian basis can be expressed through the Clebsch-Gordan coefficients of the group SU(2) analytically continued to real values of their arguments. The coeff...

Labeled graphs, in which edges are labeled by letters from some alphabet Σ, are extensively used to model many types of relations associated with actions, costs, owners, or other properties. Each path in a labeled graph induces a word in Σ∗ – the one obtained by concatenating the letters along the edges in the path. Classical graph-theory problems give rise to new problems that take these words...

A dual-eulerian graph is a plane graph which has an ordering defined on its edge set which forms simultaneously an Euler circuit in the graph and an euler circuit in the dual graph. Dual-eulerian graphs were defined and studied in the context of silicon optimization of cmos layouts. They are necessarily of low connectivity with exponentially many planar embeddings. We give a polynomial time alg...

2. Main result. By an eulerian digraph we mean a digraph in which the in-degree is equal to the out-degree at each vertex. Let ED ME ( n, t) be the number of labelled loop-free eulerian digraphs with n vertices in which the multiplicity of each edge is at most t. Allowing loops would multiply ED ME (n, t) by exactly (t + 1) n, since loops do not affect the eulerian property. For the case where ...

Not every graph has an Eulerian tour. But every finite, strongly connected graph has a multi-Eulerian tour, which we define as a closed path that uses each directed edge at least once, and uses edges e and f the same number of times whenever tail(e) = tail(f). This definition leads to a simple generalization of the BEST Theorem. We then show that the minimal length of a multi-Eulerian tour is b...

Granular flow simulation using CFD has received a lot of attention in recent years. In such cases, CFD is either, coupled with Discrete Element Method (DEM) techniques for appropriate incorporation of inter-particle collisions, or the Eulerian CFD approach is used in which granular particles are treated as they were fluid. In the present study, a CFD analysis was performed...

The standard algorithm for generating a random permutation gives rise to an obvious permutation statistic DIS that is readily seen to be Mahonian. We give evidence showing that it is not equal to any previously published statistic. Nor does its joint distribution with the standard Eulerian statistics des and exc appear to coincide with any known Euler-Mahonian pair. A general construction of Sk...

Parcel Eulerian–Lagrangian Hamiltonian formulations have recently been used in structure-preserving numerical schemes, asymptotic calculations, and in alternative explanations of fluid parcel (in)stabilities. A parcel formulation describes the dynamics of one fluid parcel with a Lagrangian kinetic energy but an Eulerian potential evaluated at the parcel’s position. In this paper, we derive the ...