A closed walk in a connected graph G that contains every edge of G exactly once is an Eulerian circuit. A graph is Eulerian if it contains an Eulerian circuit. It is well known that a connected graph G is Eulerian if and only if every vertex of G is even. An Eulerian walk in a connected graph G is a closed walk that contains every edge of G at least once, while an irregular Eulerian walk in G i...

Here presented is the interrelationship between Eulerian polynomials, Eulerian fractions and Euler-Frobenius polynomials, Euler-Frobenius fractions, Bsplines, respectively. The properties of Eulerian polynomials and Eulerian fractions and their applications in B-spline interpolation and evaluation of Riemann zeta function values at odd integers are given. The relation between Eulerian numbers a...

Recent years have witnessed significant improvements in the computer modeling of fluidized particle systems. Such models hold the potential to simulate complex systems and thus greatly reduce design efforts. As we approach the goal of simulating arbitrary systems, there exists a greater need to challenge the ability of the models to predict key features of operating beds. The simplest challenge...

[1] Fossil fuel combustion accounts for >50% of the global atmospheric emission of NOx, but this source is concentrated in the polluted continental boundary layer (CBL) and only a small fraction is exported as NOy (NOx and its oxidation products) to the global troposphere. Better quantification of this export efficiency is needed because of its implications for global tropospheric ozone. A rece...

Biofluid flows in bifurcating geometries has become paramount to the medical community. When addressing inhaled particulate matter in the lungs, it is essential to have an efficient computational model. High-order elements offer the opportunity to model nanoparticle deposition in a case by case basis with moderate computer processor times. This adds insight into cancer precipitation as well as ...

Using the existence of noncrossing Eulerian circuits in Eulerian plane graphs, we give a short constructive proof of the theorem of Heawood that Eulerian triangulations are 3-colorable.