Comments on Salem polynomials

Archiv der Mathematik - We strengthen a sufficient condition, due to R.S. Vieira, for a (reciprocal) polynomial $$R(x)=(x-\alpha _{1})(x-\alpha _{1}^{-1})\cdots (x-\alpha _{s})(x-\alpha...     

In vitro antioxidant activities of five β-carboline alkaloids,molecular docking,and dynamic simulations

Structural Chemistry - Experimental and computational studies were performed to determine the antioxidant activities of harmine, harmaline, harmalol, harmane, and...     

CM fields with a reciprocal unit-primitive element

Let K be a noncyclotomic CM field. We show that the field $K\cap \mathbb{R}$ has a reciprocal unit-primitive element when K does. Also, we prove some related conditions that make the converse of this assertion true.     

The commutation relation <Emphasis Type="Italic">xy</Emphasis>=<Emphasis Type="Italic">qyx</Emphasis>+<Emphasis Type="Italic">hf</Emphasis>(<Emphasis Type="Italic">y</Emphasis>) and Newton’s binomial formula

Let x and y be two variables satisfying the commutation relation xy=qyx+hf(y), where f(y) is a polynomial. In this paper, using Young diagrams and generating functions techniques, we study the binomial formula (x+y) ⁿ and we present an identity for x ^m y. The connection to Operator Calculus is discussed and several special cases are treated explicitly.     

Virtual improvement of ice cream properties by computational homogenization of microstructures

Optimal shape design of microstructured materials has recently attracted a great deal of attention in materials science. The shape and the topology of the microstructure have a significant impact on the macroscopic properties. This paper presents different computational models of random microstructures, to virtually improve the physical properties of ice cream. Several sensory properties of this heterogeneous material issued from food industry are directly controlled by the elastic and thermal conducting ones. The material effective elastic and thermal conducting properties are obtained through direct large scale numerical simulations. The different formulations address the problem of finding the shape of the representative microstructural element for random heterogeneous media that increase the elastic moduli and thermal conductivity compared to existing products. The computational models are established using finite element method and images of virtual microstructures. In this paper we propose a new model of microstructures. This model is constructed with hexagonal prismatic rods and plates with volume fractions around 0.7 for the hard phase represented by hexagons of ice. A comparison between three two-phase elastic heterogeneous microstructures models is drawn. This illustrates the concept of design of microstructures using computational homogenization tools.     

Microstructure of the solid phase in fluidized beds for non-Stokes regimes

Experiments on two-dimensional fluidized beds of glass beads are presented for two fluids of typical Reynolds numbers of about 1 and a few hundred. The presence of inertial effects leads to the formation of wakes behind the particles and consequently to an anisotropy of the microstructure. The microstructures, studied by video imaging, are characterized by pair probability distribution functions and structure factors.     

Characteristics of flow from an oxy-fuel burner with separated jets: influence of jet injection angle

This paper presents an experimental study of flow development and structure on a separated jet burner in reacting and non-reacting flows. Effects of deflection jets in an aligned configuration of three round jets are emphasized. The idea is based on the confinement of a central jet of fuel by two side jets of oxygen to improve mixing, to control flame stability, and to reduce pollutant emissions. The fields of mean velocity and fluctuation intensity were measured using Particle Image Velocimetry. The deflection of jets has a considerable effect on the dynamic behavior and on the flame characteristics. Results showed that the deflection of jets favors mixing and accelerates merging and combining of jets to a single one. Measurements in reacting flow showed a high influence of combustion on dynamic fields. Compared to non-reactive case, in combustion, larger radial expansion and higher velocity were observed, particularly, above the stabilization point of the flame.     

On the sharp front-type solution of the Nagumo equation with nonlinear diffusion and convection

This paper is concerned with the Nagumo equation with nonlinear degenerate diffusion and convection which arises in several problems of population dynamics, chemical reactions and others. A sharp front-type solution with a minimum speed to this model equation is analysed using different methods. One of the methods is to solve the travelling wave equations and compute an exact solution which describes the sharp travelling wavefront. The second method is to solve numerically an initial-moving boundary-value problem for the partial differential equation and obtain an approximation for this sharp front-type solution.     

Counting derangements, involutions and unimodal elements in the wreath product Cr ? Sn

We count derangements, involutions and unimodal elements in the wreath product C _r ≀ S _n by the numbers of excedances, fixed points and 2-cycles. Properties of the generating functions, including combinatorial formulas, recurrence relations and real-rootedness are studied. The results obtained specialize to those on the symmetric group S _n and on the hyperoctahedral group B _n when r = 1, 2, respectively.