Hall’s and Kőnig’s theorem in graphs and hypergraphs

We investigate the relation between Hall’s theorem and K?nig’s theorem in graphs and hypergraphs. In particular, we characterize the graphs satisfying a deficiency version of Hall’s theorem, thereby showing that this class strictly contains all K?nig–Egerváry graphs. Furthermore, we give a generalization of Hall’s theorem to normal hypergraphs.     

Phase Transition and Level-Set Percolation for the Gaussian Free Field

We consider level-set percolation for the Gaussian free field on ${\mathbb{Z}^{d}}$ , d ≥ 3, and prove that, as h varies, there is a non-trivial percolation phase transition of the excursion set above level h for all dimensions d ≥ 3. So far, it was known that the corresponding critical level h _*(d) satisfies h _*(d) ≥ 0 for all d ≥ 3 and that h _*(3) is finite, see Bricmont et al. (J Stat Phys 48(5/6):1249–1268, 1987). We prove here that h _*(d) is finite for all d ≥ 3. In fact, we introduce a second critical parameter h _** ≥ h _*, show that h _**(d) is finite for all d ≥ 3, and that the connectivity function of the excursion set above level h has stretched exponential decay for all h > h _**. Finally, we prove that h _* is strictly positive in high dimension. It remains open whether h _* and h _** actually coincide and whether h _* > 0 for all d ≥ 3.     

Theoretical analysis of spin-resolved photoemission data from ferromagnetic Fe(001)

To interpret recent spin-, energy- and angle-resolved experimental photoemission spectra at photon energies ranging from 20 to 70 eV, one-step calculations on the basis of a non-relativistic Green function formalism have been performed together with a calculation of the corresponding bulk band structure and momentum-resolved layer-by-layer quasi-particle density of states. The theoretical spectra are in good agreement with the data. Individual features are explained in terms of bulk interband transitions and emission from a majority-spin surface resonance. Self-energy corrections are found to be important and in qualitative disagreement with recent microscopic theory.     

Sub‐millisecond transient vertical chevron formation during the electroclinic effect in the smectic A∗ phase

X‐ray diffraction studies are carried out in order to probe the smectic layer structure in liquid crystal devices filled with FLC mixture SCE8 and AFLC mixture CS4001, at a temperature just above the SmA?–SmC? phase transtion. The data gathered are time‐resolved in synchronization with a bipolar voltage pulse applied across the device. The layers are observed to move dynamically and reversibly with voltage application and removal, giving evidence for temporary vertical chevron formation due to the electroclinic effect on a timescale consistent with this phenomenon.     

SYNTHESIS,IDENTIFICATION AND SURFACE ACTIVITY OF 2-AMINE-2-DEOXY-3-O-n-OCTYL-D-GLUCOPYRANOSE HYDROCHLORIDE

The synthesis and identification of this product are described. Variations of surface tension of its aqueous solutions versus concentration (ranged between 3 and 95 mmol/L) and temperature (ranged between 20.0 and 47.5°C) are studied.

The isothermal plots of surface tension versus the logarithm of the concentration show a continous decrease, with a sharp change of slope at a concentration about 6.5 mmol/L, for all the studied temperatures. A second change of slope, less pronounced, appears for a higher concentration. This concentration value increases from 28 to 42 mmol/L when temperature is raised from 20.0 to 47.5°C.

The changes of slope can be attributed mainly to micellization of neutral amine molecules resulting from hydrolysis of surface active cations, which present a weak electrolytic character.     

Drop Size Distribution Bimodality and Its Effect on O/W Emulsion Viscosity

The research work on why and how distribution bimodality tends to reduce the viscosity of a particulate suspension is reviewed. The transfer of the corresponding concepts to emulsions requires some statistical tools, and becomes particularly easy with probability scale plotting which is reviewed. Viscosity reduction can be attained for different kinds of fine and coarse emulsion associations. The results are shown to depend on the characteristics of the base emulsions as well as on the way they are mixed.     

Studies of Nucleophilic Substitution Reactions of p‐Nitrophenyl Acetate with Some Dihydroxamate Ions in Cationic Micellar Media

Pseudo‐first‐order rate constants have been determined for the nucleophilic substitution reactions of p‐nitrophenyl acetate with oxalo, malono, and succinodihydroxamate ions (^?ONHC(O)(CH₂)_nC(O)NHO^?) in phosphate buffer (pH=7.9) at 27°C. The rate data of the reaction revealed that the nucleophilic reactivity sequence of these hydroxamate ions is generally ODHA>MDHA>SDHA. The k_obs value increases upon addition of cationic surfactants to the reaction medium which is typical behavior of micelle‐assisted bimolecular reactions. The pseudo‐phase ion exchange model has been successfully applied to determine binding constant.     

Distribution of arsenic species in environmental samples collected in Northern Chile

Gradient ion chromatographic separation coupled with ICP-MS was used to resolve and determine the most common arsenic species in environmental and biological samples of carrots, trout, soil, sediment and river water from Region II of Chile. The carrot and trout samples showed a concentration of 49 and 168 µg g^?1, respectively, of total As. Both concentrations are high considering the basal level. In the carrots, percentage of 45 and 31% of total As were found for As(III) and As(V) species, respectively. In the trout, the higher concentration related to AsB at 39% of the total As. As(III) and DMA were also present in relatively high concentrations. The River Loa and the soil in which the carrots are growing also present very high As(V) concentrations of 100 and 17 µg g^?1, respectively. The ratio between the concentration for the same As species found in the living organisms (carrots and trout) and the environment in which they grow (soil and water) can provide important information about the possible absorption or biotransformation of As species in living beings. As(III) and DMA are the species in which the greatest accumulation occurs with respect to the medium in which they are present, and biotransformation also appears to take place.     

Contact line extraction and length measurements in model sediments and sedimentary rocks

The mechanisms that govern the transport of colloids in the unsaturated zone of soils are still poorly understood, because of the complexity of processes that occur at pore scale. These mechanisms are of specific interest in quantifying water quality with respect to pathogen transport (e.g. Escherichia coli, Cryptosporidium) between the source (e.g. farms) and human users. Besides straining in pore throats and constrictions of smaller or equivalent size, the colloids can be retained at the interfaces between air, water, and grains. Theories competing to explain this mechanism claim that retention can be caused by adhesion at the air-water-interface (AWI) between sediment grains or by straining at the air-water-solid (AWS) contact line. Currently, there are no established methods for the estimation of pathogen retention in unsaturated media because of the intricate influence of AWI and AWS on transport and retention. What is known is that the geometric configuration and connectivity of the aqueous phase is an important factor in unsaturated transport. In this work we develop a computational method based on level set functions to identify and quantify the AWS contact line (in general the non-wetting-wetting-solid contact line) in any porous material. This is the first comprehensive report on contact line measurement for fluid configurations from both level-set method based fluid displacement simulation and imaged experiments. The method is applicable to any type of porous system, as long as the detailed pore scale geometry is available. We calculated the contact line length in model sediments (packs of spheres) as well as in real porous media, whose geometry is taken from high-resolution images of glass bead packs and sedimentary rocks. We observed a strong dependence of contact line length on the geometry of the sediment grains and the arrangement of the air and water phases. These measurements can help determine the relative contribution of the AWS line to pathogen retention.