The number of critical elements of discrete Morse functions on non-compact surfaces

This paper is focused on looking for links between the topology of a connected and non-compact surface with finitely many ends and any proper discrete Morse function which can be defined on it. More precisely, we study the non-compact surfaces which admit a proper discrete Morse function with a given number of critical elements. In particular, given any of these surfaces, we obtain an optimal discrete Morse function on it, that is, with the minimum possible number of critical elements.     

Characterizing equivalent discrete Morse functions

We get a characterization theorem for equivalent discrete Morse functions defined on simplicial complexes in terms of their gradient vector field. As a consequence, we also characterize them in the 1-dimensional case by using critical elements. The authors are partially supported by the P.A.I. project (Junta de Andalucia, SPAIN, 2009/FQM-189 and 327) and by the MEC-FEDER grants MTM2007-61284 and MTM2007-65726 (MEC, SPAIN, 2007).     

A differential equation approach to implicit sweeping processes

In this paper, we study an implicit version of the sweeping process. Based on methods of convex analysis, we prove the equivalence of the implicit sweeping process with a differential equation, which enables us to show the existence and uniqueness of the solution to the implicit sweeping process in a very general framework. Moreover, this equivalence allows us to give a characterization of nonsmooth Lyapunov pairs and invariance for implicit sweeping processes. The results of the paper are illustrated with two applications to quasistatic evolution variational inequalities and electrical circuits.     

One-dimensional and two-dimensional quantum systems on carbon nanotube bundles

We report the first measurement of the structure of 4He atoms adsorbed on bundles of single-walled carbon nanotubes. Neutron diffraction techniques and nanotube samples closed at the end were used. At low coverage, 4He forms a 1D, single line lattice along the grooves between two nanotubes on the surface of the nanotube bundles. As coverage is increased, additional lines of 1D lattices form along the grooves. This is followed by an incommensurate, 2D monolayer covering the whole nanotube bundle surface. The lattice constants of these 1D and 2D systems are largely independent of filling once a single 1D line is formed. No occupation of the interstitial channels between nanotubes is observed in the present sample.     

The two-dimensional liquid-vapor coexistence line of methane adsorbed on graphite

We measured the specific heat of two-dimensional films of CH₄ adsorbed on graphite for several coverages and we observed broad peaks at the liquid-vapor transition. The critical temperature is estimated to be 70 ± 1 K, somewhat lower than reported in previous measurements. At intermediate coverages the liquid-vapor boundary is very flat indicating that it could be described by a 2D Ising model. We measured also for some coverages the triple temperature at 56.2 K and the commensurate-incommensurate transition at about 50 K, both in reasonable agreement with previous measurements.     

Advances in methodology for the validation of methods according to the International Organization for Standardization. Application to the determination of benzoic and sorbic acids in soft drinks by high-performance liquid chromatography

Robust chemometric techniques such as least median of squares regression, H15 Huber estimator and Lenth's method are fundamental tools in the validation of analytical methods since they contribute the strategies needed to estimate efficiently parameters such as robustness, linear range, selectivity, accuracy (trueness and precision) and the capability of detection. In addition, the capability of discrimination defined as a generalisation of the capability of detection for any nominal concentration is evaluated. The new strategy proposed is applied to the validation of a chromatographic method for use in systematic analysis.     

Structural study of tropane-3-spiro-4'-imidazol-5'-one

Tropane-3-spiro-4'-imidazol-5'-one has been synthesized and its crystal and molecular structures determined by X-ray diffraction, IR, Raman, ¹H-NMR and ¹³C-NMR methods. The tautomeric equilibrium between this structure and the corresponding conjugated form in different solvents is also studied from IR and UV data. The imidazoline ring, the spiranic C(3, 4'), the N(8) and the methyl C(9) atoms are situated in a plane. The piperidine ring adopts a distorted chair conformation in the crystalline form and in solution. The flattening of the C(1), C(2), C(3, 4'), C(4), C(5) part of the chair and the opposite puckering are noticeably large. In order to complete the results, some spectroscopic measurements have also been made for the tropane-3-spiro-4'-imidazol-5'-one hydrochloride.     

Evolution Inclusions Governed by Time-Dependent Maximal Monotone Operators with a Full Domain

In this paper, we study the existence of solutions for evolution inclusions governed by time-dependent maximal monotone operators with a full domain. Without assumptions concerning time-regularity on the time-dependent maximal monotone operators, and by using the Moreau-Yosida regularization technique, we establish the existence of solutions in Hilbert spaces. The theoretical result is applied to prove the existence of solutions for semicoercive sweeping processes with velocity constraint.

     

Total reflection X ray fluorescence in environmental and geochemical studies: unveiling solute provenance in streams during a rain episode

Rural population uses water for irrigation, animal watering and for their own consumption, therefore water contamination is a major concern and a priority for its inhabitants. Unveiling the presence and source of contaminants can help to understand the dynamic of pollutants and therefore define management politics to address the issue. One way to elucidate the origin of contaminants in surface water is by studying rain episodes, relating water discharge with changes in solute concentration. Total Reflection x‐ray Fluorescence (TXRF) was used as the main analytical technique. The study was based on the analysis of samples originating from a Pampean stream (Buenos Aires, Argentina). Solutes (As, P, Ca, Fe, K, Zn, Br) were monitored before, during and after a storm event. During the monitoring it was observed that As was diluted at the beginning of the episode and concentration increased slowly after the rain ceased. The pattern of As is consistent with Ca, K and Fe behavior, revealing a groundwater source. Instead, P concentration increased in the early hours, it was diluted later and finally increased. This behavior indicates that the source of this analyte is superficial and sub superficial water, implying a runoff origin. The simultaneous determination of these analytes by TXRF allowed comparing solute behavior under the same episode, allowing reveal their provenance. Copyright © 2016 John Wiley & Sons, Ltd.