Arbitrary Lagrangian Eulerian (ALE) methods have existed for several decades. However, three-dimensional multi-material arbitrary Lagrangian Eulerian (MMALE) methods for unstructured grids are relatively new. MMALE algorithms provide the framework to model sections of a simulation as either Lagrangian, ALE, or Eulerian. In addition, sections of a simulation can switch in time between mesh motio...

Let G = (V, A) be an Eulerian directed graph with an arclabeling. In this work we study the problem of finding an Eulerian circuit of lexicographically minimal label among all Eulerian circuits of the graph. We prove that this problem is NP-hard by showing a reduction from the Directed-Hamiltonian-Circuit problem. If the labeling of the arcs is such that arcs going out from the same vertex have...

Stembridge, J.R., Eulerian numbers, tableaux, and the Betti numbers of a toric variety, Discrete Mathematics 99 (1992) 307-320. Let Z denote the Coxeter complex of S,, and let X(X) denote the associated toric variety. Since the Betti numbers of the cohomology of X(Z) are Eulerian numbers, the additional presence of an &-module structure permits the definition of an isotypic refinement of these ...

Taylor series expansions of turbulent time correlation functions are applied to show that helicity influences Eulerian time correlations more strongly than Lagrangian time correlations: to second order in time, the hclicity effect on Lagrangian time correlations vanishes, but the helicity cffect on Eulerian time correlations is nonzero. Fourier analysis shows that the hclicity effect on Euleria...

In the present paper, we introduce Eulerian polynomials with parameters a and b and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Analytic Numbers Theory. Also, we give relations between Eulerian polynomials with parameters a and b, Bernstein polynomials, Poly-logarithm functions, Bernoulli and Euler numbers. Mo...