In this paper, we give a combinatorial interpretation of the r-Whitney-Eulerian numbers by means of coloured signed permutations. This sequence is a generalization of the well-known Eulerian numbers and it is connected to r-Whitney numbers of the second kind. Using generating functions, we provide some combinatorial identities and the log-concavity property. Finally, we show some basic congruen...

We prove two conjectures of Shareshian and Wachs about Eulerian quasisymmetric functions and polynomials. The first states that the cycle type Eulerian quasisymmetric function Qλ,j is Schur-positive, and moreover that the sequence Qλ,j as j varies is Schur-unimodal. The second conjecture, which we prove using the first, states that the cycle type (q, p)-Eulerian polynomial A λ (q, p, q −1t) is ...

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 ...

d-spheres are defined graph theoretically and inductively as the empty graph in dimension d = −1 and d-dimensional graphs for which all unit spheres S(x) are (d−1)-spheres and such that for d ≥ 0 the removal of one vertex renders the graph contractible. Eulerian d-spheres are geometric d-spheres which can be colored with d + 1 colors. They are Eulerian graphs in the classical sense and for d ≥ ...

In this paper, a CFD model of syngas flow in slurry bubble column was developed. The model is based on an Eulerian-Eulerian approach and includes three phases: slurry of solid particles suspended in paraffin oil and syngas bubbles. Numerical calculations carried out for catalyst particles, bubble coalescence and breakup included bubble-fluid drag force and interfacial area effects. Also, the ef...

Designing a protocol to exchange a secret key is one of the most fundamental subjects in cryptography. Using a random deal of cards, pairs of card players (agents) can share secret keys that are information-theoretically secure against an eavesdropper. A key set protocol, which uses a random deal of cards, can perform an Eulerian secret key exchange, in which the pairs of players sharing secret...

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and eve...

A novel Eulerian Gaussian beam method was developed in [8] to compute the Schrödinger equation efficiently in the semiclassical regime. In this paper, we introduce an efficient semi-Eulerian implementation of this method. The new algorithm inherits the essence of the Eulerian Gaussian beam method where the Hessian is computed through the derivatives of the complexified level set functions inste...

Let G be an eulerian digraph with a fixed edge coloring (not necessarily a proper edge coloring). A compatible circuit of G is an eulerian circuit such that every two consecutive edges in the circuit have different colors. We characterize the existence of compatible circuits for directed graphs avoiding certain vertices of outdegree three. Our result is analogous to a result of Kotzig for compa...