Invariants of Combinatorial Line Arrangements and Rybnikov's Example

Following the general strategy proposed by G.Rybnikov, we present a proof of his well-known result, that is, the existence of two arrangements of lines having the same combinatorial type, but non-isomorphic fundamental groups. To do so, the Alexander Invariant and certain invariants of combinatorial line arrangements are presented and developed for combinatorics with only double and triple points. This is part of a more general project to better understand the relationship between topology and combinatorics of line arrangements.Comment: 27 pages, 2 eps figure

Volumetric Behavior and Vapor–Liquid Equilibrium of Dimethyl Disulfide + n-Alkanol Binary Mixtures

In this paper, we report densities at 303.15 and 323.15 K and at atmospheric pressure (p = 0.1 MPa) of the binary mixtures containing dimethyl disulfide and a linear alkanol (methanol, ethanol, 1-propanol or 1-butanol). The isothermal vapor–liquid equilibrium for these systems was also determined at the same temperatures while the pressure range for vapor–liquid equilibrium measurement depends on both the mixture and temperature considered. The vapor–liquid equilibrium data were found to be thermodynamically consistent. From these data experimental excess volumes and excess Gibbs functions were obtained and correlated with composition using the Redlich–Kister polynomial expansion and the Wilson equation, respectively. The values of both excess properties were positive. The excess volumes, unlike the excess Gibbs functions, increase with the length of the n-alkanol chain

Second Harmonic Generation Microscopy: A Tool for Quantitative Analysis of Tissues

Second harmonic generation (SHG) is a second‐order non‐linear optical process produced in birefringent crystals or in biological tissues with non‐centrosymmetric structure such as collagen or microtubules structures. SHG signal originates from two excitation photons which interact with the material and are “reconverted” to form a new emitted photon with half of wavelength. Although theoretically predicted by Maria Göpert‐Mayer in 1930s, the experimental SHG demonstration arrived with the invention of the laser in the 1960s. SHG was first obtained in ruby by using a high excitation oscillator. After that starting point, the harmonic generation reached an increasing interest and importance, based on its applications to characterize biological tissues using multiphoton microscopes. In particular, collagen has been one of the most often analyzed structures since it provides an efficient SHG signal. In late 1970s, it was discovered that SHG signal took place in three‐dimensional optical interaction at the focal point of a microscope objective with high numerical aperture. This finding allowed researchers to develop microscopes with 3D submicron resolution and an in depth analysis of biological specimens. Since SHG is a polarization‐sensitive non‐linear optical process, the implementation of polarization into multiphoton microscopes has allowed the study of both molecular architecture and fibrilar distribution of type‐I collagen fibers. The analysis of collagen‐based structures is particularly interesting since they represent 80% of the connective tissue of the human body. On the other hand, more recent techniques such as pulse compression of laser pulses or adaptive optics have been applied to SHG microscopy in order to improve the visualization of features. The combination of these techniques permit the reduction of the laser power required to produce efficient SHG signal and therefore photo‐toxicity and photo‐damage are avoided (critical parameters in biomedical applications). Some pathologies such as cancer or fibrosis are related to collagen disorders. These are thought to appear at molecular scale before the micrometric structure is affected. In this sense, SHG imaging has emerged as a powerful tool in biomedicine and it might serve as a non‐invasive early diagnosis technique

Nodal degenerations of plane curves and Galois covers

Globally irreducible nodes (i.e. nodes whose branches belong to the same irreducible component) have mild effects on the most common topological invariants of an algebraic curve. In other words, adding a globally irreducible node (simple nodal degeneration) to a curve should not change them a lot. In this paper we study the effect of nodal degeneration of curves on fundamental groups and show examples where simple nodal degenerations produce non-isomorphic fundamental groups and this can be detected in an algebraic way by means of Galois coverings.Comment: 16 pages, 3 figure

Volumetric and acoustic behaviour of myo-inositol in aqueous Natural Deep Eutectic Solvent solutions

A study of the interactions in aqueous systems containing a sweetener, myo-inositol, and a NAtural Deep Eutectic Solvent, reline or glyceline, is presented. Both NADESs include the same acceptor group, choline chloride, and different donor groups, urea and glycerol. For this purpose, the density and speed of sound were measured for dilute mixtures, and several related properties were calculated: the standard partial molar volume, the standard partial molar isentropic compression, the standard transfer properties, Hepler's constant, and the compressibility hydration number. The results were evaluated as a function of the temperature and composition, and they show the dominance of the ionic-hydrophilic and hydrophilic-hydrophilic interactions. Moreover, the glyceline disturbs the aqueous mixtures more than the reline

The NADES glyceline as a potential Green Solvent: A comprehensive study of its thermophysical properties and effect of water inclusion

In this paper, two Natural Deep Eutectic Solvents, glyceline (Gly) and glyceline-water (GlyW), containing choline chloride as acceptor H-bond compound and glycerol as donor H-bond group are studied. For glyceline the mole relation is 1 (choline chloride): 2 (glycerol) and for glyceline-water the mole relation is 1 (choline chloride): 1.99 (glycerol): 1.02 water. The ternary NADES has been synthetized and characterized chemically by NMR techniques for this work. Several thermophysical properties in a wide range of temperature (278.15–338.15)¿K and at atmospheric pressure (0.1¿MPa) have been measured for both compounds: density, , speed of sound, , refractive index, , surface tension,, isobaric molar heat capacity, , kinematic viscosity, , and electric conductivity,. Furthermore, some related properties have been also calculated: isobaric expansibility, , isentropic compressibility, , molar refraction, , entropy and enthalpy of surface formationper unit surface area ( and ), and dynamic viscosity, , and viscous flow and electrical conductivity activation energies. The results have been discussed in terms of the effect of temperature and the inclusion of water. We conclude that the compound containing water into the structure has a higher molar volume and a higher fluidity. The binary NADES (Gly) is a more structured liquid than ternary one (GlyW)

Influence of SO2 on CO2 storage for CCS technology: Evaluation of CO2/SO2 co-capture

In this work, we determined the influence of SO2 as an impurity in anthropogenic CO2 on carbon capture and storage (CCS) technology. We evaluated the impact on selected injection and storage parameters and the Joule-Thomson coefficient to assess the safety of long-term geological storage of CO2. For this purpose, we obtained new pressure-density-temperature-composition, vapor-liquid-equilibrium, and pressure-speed of sound-temperature-composition experimental data for CO2-rich mixtures containing SO2. To increase the general understanding of the impact of SO2, the compositions cover possible co-capture mixtures, SO2-enriched mixtures, and mixtures similar to industrial emissions. Temperatures and pressures were based on relevant geological storage site values. Our experimental results were used to validate the EOS-CG and PC-SAFT equations of state (EoSs) for CO2 + SO2 under the studied CCS conditions. On the understanding that the chemical reactivity effects due to SO2 have not been considered, we concluded that the presence of SO2 is profitable in most of the studied aspects, especially in the case of shallow reservoirs, and that CO2/SO2 co-capture may be considered as an alternative approach to reduce the costs of CO2 purification. Based on the assessment of the impact of 5 mol% SO2 in the injected fluid in seven saline aquifers, we determined that the reservoirs that would receive the most benefit were Sleipner, Nagaoka and Frio

Thermophysical characterization of the deep eutectic solvent choline chloride:ethylene glycol and one of its mixtures with water

The deep eutectic solvent ethaline, containing choline chloride as H-bond acceptor and ethylene glycol as H-bond donor and one of its mixture with water are studied in this work. Ethaline is anhydrous, with a 1:2 mol ratio. Hydrated ethaline, choline chloride:ethylene glycol:water, was studied in a 1:1.98:0.95 mol ratio. Several volumetric, acoustic, optical, thermal, surface, and transport properties were measured and calculated. The working temperature ranges from 278.15 to 338.15 K at pressure = 0.1 MPa. The effects of temperature, water inclusion, and the nature of the donor compound are evaluated. With regard to temperature, the system''s behaviour is as expected: a linear relation for the thermodynamic properties and agreement with the Vogel-Fulcher-Tammann equation for the transport properties. The water molecules hardly modify the ethaline structure. The choline chloride – ethylene glycol interactions are weaker than those for choline chloride - glycerol