Linear flows and Morse graphs: Topological consequences in low dimensions

The main aim of this paper is to show some specific connections between linear dynamic and graphs. Precisely, the Morse decomposition of a linear flow on the Grassmannians induces a directed graph. We apply the results appearing in Ayala et al. (2006, 2005)  and  and Colonius et al. (2002) [4] and compute the associated graphs for linear flows in dimensions two and three.     

A theoretical study of the bonding capabilities of the zinc-zinc double bond

The theoretical knowledge about the zinc-zinc bond has been recently expanded after the proposal of a zinc-zinc double bond in several [Zn₂(L)₄] compounds (Angew. Chem. Int. Ed. 2017 , 56, 10151-10155). Prompted by these results, we have selected the [Zn₂(CO)₄] species, isolobally related to ethylene, and theoretically investigated the possible η²-Zn₂-coordination to several first-row transition metal fragments. The [Zn₂(CO)₄] coordination to the metal fragment produces an elongation of the dizinc bond and a concomitant pyramidalization of the [Zn(CO)₂] unit. These structural parameters are indicative of π-backdonation from the metal to the coordinated dizinc moiety, as occurred with ethylene ligand. A quantum theory of atoms in molecules study of the Zn Zn bond shows a decrease of ρ_BCP, ∇²ρ_BCP ∫_Zn∩Znρ and delocalization indexes δ(Zn,Zn), relative to corresponding values in the parent [Zn₂(CO)₄] molecule. The Zn Zn and M Zn bonds in these [(η²-Zn₂(CO)₄)M(L)_n] complexes can be described as shared interactions with an important covalent component where the Zn Zn bond is preserved, albeit weakened, upon coordination.     

Focused microwave-assisted micellar extraction combined with solid-phase microextraction--gas chromatography/mass spectrometry to determine chlorophenols in wood samples

This work describes the utilization of the focused microwave-assisted micellar extraction in combination with the solid-phase microextraction (SPME) to determine chlorophenols in wood samples. The influence of the nature of the surfactant in the extraction process, the optimization of the variables of the focused-microwave system, and the effect of the ageing time of the samples in the extraction efficiency of the method, have been assessed in this study. The overall method using the non-ionic surfactant POLE as extracting medium allows us to determine chlorophenols in wood samples achieving an average extraction efficiency of 104.1%, limits of detection ranging from 2 to 120 ng g⁻¹, and intermediate precision values ranging between 3.5 and 13.2%. The proposed method is also characterized by short analysis times (around 5 min for the microwaves extraction step) and by avoiding the use of organic solvents.     

Scaling violation and shadowing corrections at HERA

We study the value of shadowing corrections (SC) in the HERA kinematic region in the Glauber–Mueller approach. Since the Glauber–Mueller approach was proven in perturbative quantum chromodynamics (QCD) in the double-logarithmic approximation (DLA), we develop the DLA approach for the deep inelastic structure function which takes into account the SC. Our estimates show small SC for in the HERA kinematic region while they turn out to be sizable for the gluon structure function. We compare our estimates with those for gluon distribution in leading order (LO) and next to leading order (NLO) in the DGLAP evolution equations. Received: 21 September 1998 /Published online: 14 January 1999     

Poly(ε-caprolactone) modified by functional groups: Preparation and chemical–physical investigation

Functionalization of polymers is a particular relevant approach in the field of biodegradable polymers, where modifications are often required to allow these materials to replace more conventional, not biodegradable polymers in a wider range of applications. This article will report on functionalization of poly(ε-caprolactone) with unsaturated monomers bearing either anhydride groups (PCL-g-(MA-GMA)) or tertiary amines (PCL-g-DMAEA), obtained through radical grafting in a Brabender mixer. Crystallization kinetics parameters have been determined with several techniques (rheology, optical microscopy and differential scanning calorimetry) and the results obtained are in good agreement. It was observed that the crystallization rate significantly increases in the case of the modified polymers.     

Variational formulation of the material failure process in solids by embedded discontinuities model

This work presents a variational formulation of the material failure process, idealized as strain or displacement discontinuities, by weak, strong, or discrete embedded discontinuities into a continuum. It is shown that the solution of the proposed variational formulation may be approximated by different types of finite elements with embedded discontinuities. The developed displacement approximation of a finite element split by the discontinuity leads to a symmetric stiffness matrix, which considers not only the continuity of tractions but also the rigid body relative motions of the portions in which the element is split. The variational formulation of a continuum with more than one discontinuity in its interior is developed. It is shown that this formulation may lead to finite elements with embedded discontinuities that can be classified as displacement, force, mixed, and hybrid models. To show the effectiveness of the proposed formulation, the classical example of a bar under tension is solved using one and 2D finite element approximations. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009