Characteristic p multizeta values were initially studied by Thakur, who defined them as analogues of classical multiple zeta values of Euler. In the present paper we establish an effective criterion for Eulerian multizeta values, which characterizes when a multizeta value is a rational multiple of a power of the Carlitz period. The resulting “t-motivic”algorithm can tell whether any given multi...

We consider the problem of sampling from the uniform distribution on the set of Eulerian orientations of subgraphs of the triangular lattice. Although it is known that this can be achieved in polynomial time for any graph, the algorithm studied here is more natural in the context of planar Eulerian graphs. We analyse the mixing time of a Markov chain on the Eulerian orientations of a planar gra...

This paper describes a motion blur technique which can be applied to rendering fluid simulations that are carried out in the Eulerian framework. Existing motion blur techniques can be applied to rigid bodies, deformable solids, clothes, and several other kinds of objects, and produce satisfactory results. As there is no specific reason to discriminate fluids from the above objects, one may cons...

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...

The combinatorial Hopf algebra on building sets BSet extends the chromatic Hopf algebra of simple graphs. The image of a building set under canonical morphism to quasi-symmetric functions is the chromatic symmetric function of the corresponding hypergraph. By passing from graphs to building sets, we construct a sequence of symmetric functions associated to a graph. From the generalized DehnSomm...

With the increase of computer power and advancement of modeling software, the study of turbulent gas-particle flow problems using computational fluid dynamics (CFD) techniques is gradually becoming attractive in the engineering field. Two basic CFD approaches are used to simulate the gas-particle flow, i.e. the Eulerian-Lagrangian model and the EulerianEulerian model. The aim of this thesis is ...

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 ...