A time discretization scheme of a characteristics method for a fluid–rigid system with discontinuous density

We propose a new characteristics method for the time discretization of a fluid–rigid system in the case when the densities of the fluid and the solid are different. This method is based on a global weak formulation involving only terms defined on the whole fluid–rigid domain. The main idea is to construct a characteristic function which preserves the rigidity of the solid at the discrete time levels. A convergence result for this semi-discrete scheme is then given.     

Poly(butylene terephthalate)/phenoxy blends: Synergistic behavior in mechanical properties

The mechanical properties of miscible poly(butylene terephthalate) (PBT)/poly (hydroxy ether of bisphenol A) (phenoxy) blends obtained by melt mixing have been studied by means of the tensile test. The crystallinity of the blends has been studied by means of DSC and density measurements. A synergistic behavior, principally in the break properties, at high PBT contents in the blends is observed. As can be seen from the torque and density data, this synergistic behavior is related with the high level of miscibility which seems to exist at high PBT contents compared with that of the high phenoxy content region.     

Electron temperature and ion density measurements in a glow discharge of an Ar–N2 mixture

A DC glow discharge produced in N₂ gas can generate several species that are important in different applications, such as the modification of surface properties of materials. A low-pressure glow discharge apparatus was used for the the analysis of the Ar–N₂ mixture at a total pressure of 2.0 Torr, a power of 20 W and 40 l/min flow rate of gases. The emission bands were measured in the wavelength range of 200–1100 nm. The principal elements are N₂, N ₂⁺ and Ar I. The electron temperature was found in the range of 1.72–2.08 eV, and the ion density was in the order of 10¹⁰ cm^?3.     

Algebras with implication and fusion: a different point of view

This work uses well-known results on tensor products of lattices and semilattices developed by Fraser and Grätzer et al., and the duality for bounded distributive lattices introduced by Cignoli et al., in order to develop dual categorical equivalences involving bounded distributive lattices with fusion and implication, respectively. We show that these equivalences are essentially those developed by Cabrer and Celani as part of the PhD thesis of the former.     

An averaging method applied to a duffing equation

We approximate a Duffing equation by an averaged system. We solve the system explicitely and draw bifurcation diagrams in dependence of the forcing term. We discuss the goodness of the averaging method, relative to the behavior of the solutions in dependence of involved parameters, by comparing with results obtained in [6,10] for the original Duffing equation.     

Characterization of Lipschitz Continuous Difference of Convex Functions

We give a necessary and sufficient condition for a difference of convex (DC, for short) functions, defined on a normed space, to be Lipschitz continuous. Our criterion relies on the intersection of the ε-subdifferentials of the involved functions.     

On the Apéry sets of monomial curves

In this paper, we use the Apéry table of the numerical semigroup associated to an affine monomial curve in order to characterize arithmetic properties and invariants of its tangent cone. In particular, we precise the shape of the Apéry table of a numerical semigroup of embedding dimension 3, when the tangent cone of its monomial curve is Buchsbaum or 2-Buchsbaum, and give new proofs for two conjectures raised by Sapko (Commun. Algebra 29:4759–4773, 2001) and Shen (Commun. Algebra 39:1922–1940, 2001). We also provide a new simple proof in the case of monomial curves for Sally’s conjecture (Numbers of Generators of Ideals in Local Rings, 1978) that the Hilbert function of a one-dimensional Cohen-Macaulay ring with embedding dimension three is non-decreasing. Finally, we obtain that monomial curves of embedding dimension 4 whose tangent cones are Buchsbaum, and also monomial curves of any embedding dimensions whose numerical semigroups are balanced, have non-decreasing Hilbert functions. Numerous examples are provided to illustrate the results, most of them computed by using the NumericalSgps package of GAP (Delgado et al., NumericalSgps-a GAP package, 2006).