There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

2 1 The innovative transport systems and the CityMobil project 10 1.1 The research questions 10 2 The state of art in the field of automatic transport systems 12 2.1 Case studies and demand studies for innovative transport systems 12 3 The design and implementation of surveys 14 3.1 Definition of experimental design 14 3.2 Questionnaire design and delivery 16 3.3 First analyses on the collected sample 18 4 Calibration of Logit Multionomial demand models 21 4.1 Methodology 21 4.2 Calibration of the “full” model. 22 4.3 Calibration of the “final” model 24 4.4 The demand analysis through the final Multinomial Logit model 25 5 The analysis of interaction between the demand and socioeconomic attributes 31 5.1 Methodology 31 5.2 Application of Mixed Logit models to the demand 31 5.3 Analysis of the interactions between demand and socioeconomic attributes through Mixed Logit models 32 5.4 Mixed Logit model and interaction between age and the demand for the CTS 38 5.5 Demand analysis with Mixed Logit model 39 6 Final analyses and conclusions 45 6.1 Comparison between the results of the analyses 45 6.2 Conclusions 48 6.3 Answers to the research questions and future developments 52

The European commission

We investigate whether income inequality affects subsequent growth in a cross-country sample for 1965-90, using the models of Barro (1997), Bleaney and Nishiyama (2002) and Sachs and Warner (1997), with negative results. We then investigate the evolution of income inequality over the same period and its correlation with growth. The dominating feature is inequality convergence across countries. This convergence has been significantly faster amongst developed countries. Growth does not appear to influence the evolution of inequality over time. Outline

https://www.econstor.eu/bitstream/10419/81822/1/02-28.pdf

Economic growth and income inequality

The topological and energetic properties of the electron density distribution ρ(r) of the isolated pairwise H⋯F interaction have been theoretically calculated at several geometries (0.8<d<2.5 A) and represented against the corresponding internuclear distances. From long to short geometries, the results presented here lead to three characteristic regions, which correspond to three different interaction states. While the extreme regions are associated to pure closed-shell (CS) and shared-shell (SS) interactions, the middle one has been related to the redistribution of ρ(r) between those electronic states. The analysis carried out with this system has permitted to associate the transit region between pure CS and SS interactions to internuclear geometries involved in the building of the H–F bonding molecular orbital. A comparative analysis between the formation of this orbital and the behavior of some characteristic ρ(r) properties has indicated their intrinsic correspondence, leading to the definition of a bond degree parameter [BD=HCP/ρCP; HCP and ρCP being the total electron energy density and the electron density value at the H⋯F (3,−1) critical point]. Along with the isolated pairwise H⋯F interaction, 79 X–H⋯F–Y (neutral, positively and negatively charged) complexes have been also theoretically considered and analyzed in terms of relevant topological and energetic properties of ρ(r) found at their H⋯F critical points. In particular, the interaction energies of X–H⋯F–Y pure CS interactions have been estimated by using the bond degree parameter. On the other hand, the [F⋯H⋯F]− proton transfer geometry has been related to the local maximum of the electron kinetic energy density (GCP)max.

From weak to strong interactions: A comprehensive analysis of the topological and energetic properties of the electron density distribution involving X–H⋯F–Y systems

Hydrogen bonding is an important interaction playing a key role in chemical, physical, and biochemical processes. One can mention numerous examples such as the role of hydrogen bonding in enzymatic catalysis, arrangement of molecules in crystals, crystal engineering, proton transfer reactions, and also its important role in life processes. Hence, its nature is often the subject of investigations and polemics. One of the first definitions of hydrogen bonding was formulated by Pauling who stated that “under certain conditions an atom of hydrogen is attracted by rather strong forces to two atoms, instead of only one, so that it may be considered to be acting as a bond between them. This is called the hydrogen bond”. Pauling also pointed out that the hydrogen atom is situated only between the most electronegative atoms and it usually interacts much stronger with one of them. The latter interaction is a typical covalent bond (A-H). The interaction between hydrogen and another electronegative atom is much weaker and mostly electrostatic in nature; it is a nonbonding interaction (H 3 3 3B). This system is often designated as AH 3 3 3B where the B-center (acceptor of proton) should possess at least one lone electron pair; A-H is called the protondonating bond. Pauling stated that sometimes the H 3 3 3B interaction possesses characteristics of the covalent bond. The [FHF] ion is an example where the proton is inserted between two negative fluorine ions, accurately in the middle of the F 3 3 3 F distance. Hence, both H 3 3 3 F interactions are equivalent. This is in line with an early conclusion of Lewis that “an atom of hydrogen may at times be attached to two electron pairs of two different atoms” and with the statement of Latimer and Rodebush that “the hydrogen nucleus held by two octets constitutes a weak bond”. The latter statements correspond to recent studies on proton bound homodimers, that is, systems where the proton is inserted between two closed-shell moieties and where it often interacts equivalently with both of them. Chan and co-workers analyzed recently what factors determine whether the protonbound homodimer has a symmetric or an asymmetric hydrogen bond. In the other study, it is discussed what conditions should be fulfilled for the proton situated accurately in the midpoint of the donor-acceptor distance. The high level calculations up to CCSD(T)/6-311þþ(3df,3pd)//CCSD/6-311þþ(3df,3pd) were performed on the [FHF] ion and systems with O-H 3 3 3O or N-H 3 3 3N hydrogen bonds. The latter study is supported by the experimental X-ray and neutron diffraction data because there are numerous crystal structures with short O-H 3 3 3O hydrogen bonds and the proton situated in the central position or nearly so. Also recently, homogeneous and heterogeneous short and strong hydrogen bonds (SSHBs) as well as the proton bound homodimers were analyzed theoretically at MP2/aug-ccpVDZ þ diffuse(2s,2p) level. Among various topics, the matter was raised if hydrogen bonding is an electrostatic or covalent interaction. The following question arises: what does the covalency of hydrogen bonding mean? The decomposition of the interaction energy is useful to analyze hydrogen bonding and particularly to answer the latter question. One of the first decomposition schemes introduced is one of Morokuma and Kitaura, where the interaction energy is calculated within the Hartree-Fock one-electron approximation and it is decomposed into the following components: the exchange energy, EEX (arising from repulsive forces), and the other components, which might be a result of attractive forces: the polarization energy, EPL, the charge transfer energy, ECT, and the electrostatic energy, EES. If a method is applied where the correlation of electrons is taken into account, then the correlation energy may be included. One of the most important attractive components of the correlation energy is the dispersive energy. Different H-bonded systems were analyzed early by Umeyama and Morokuma who stated that: “The energy components are strongly distance dependent. At a relatively small separation, ES, CT, and PL can all be important attractive components, competing against a large EX repulsion. At larger distances for the same complex the short-range attractions CT and PL are usually unimportant and ES is the only important attraction.” One can see that the “covalency of interaction”may be connected with short H 3 3 3B distances where terms other than the electrostatic attractive one are important.

What is the covalency of hydrogen bonding

The composition of high-altitude ice clouds is still a matter of intense discussion. The constituents in question are ice and nitric acid hydrates, but the exact phase composition of clouds and its formation mechanisms are still unknown. In this work, conclusive evidence for a long-predicted phase, alpha-nitric acid trihydrate (alpha-NAT), is presented. This phase was characterized by a combination of X-ray and neutron diffraction experiments, allowing a convincing structure solution. Furthermore, vibrational spectra (infrared and inelastic neutron scattering) were recorded and compared with theoretical calculations. A strong interaction between water ice and alpha-NAT was found, which explains the experimental spectra and the phase-transition kinetics. On the basis of these results, we propose a new three-step mechanism for NAT formation in high-altitude ice clouds.

Metastable Nitric Acid Trihydrate in Ice Clouds.

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/anie.201681061

Frontispiece: Metastable Nitric Acid Trihydrate in Ice Clouds

Back Cover: Spectroscopic Observation of Matrix‐Isolated Carbonic Acid Trapped from the Gas Phase (Angew. Chem. Int. Ed. 8/2011)

This work describes a simple agent model for the spread of an epidemic outburst, with special emphasis on mobility and geographical considerations, which we characterize via statistical mechanics and numerical simulations. As the mobility is decreased, a percolation phase transition is found separating a free-propagation phase in which the outburst spreads without finding spatial barriers and a localized phase in which the outburst dies off. Interestingly, the number of infected agents is subject to maximal fluctuations at the transition point, building upon the unpredictability of the evolution of an epidemic outburst. Our model also lends itself to testing vaccination schedules. Indeed, it has been suggested that if a vaccine is available but scarce it is convenient to carefully select the vaccination program to maximize the chances of halting the outburst. We discuss and evaluate several schemes, with special interest on how the percolation transition point can be shifted, allowing for higher mobility without epidemiological impact.

Effects of confinement and vaccination on an epidemic outburst: A statistical mechanics approach

The ion complexes NO 3 - (HNO 3 ) n , n = 1-3, have been studied by means of ab initio calculations at the B3LYP/aug-cc-pVTZ level of theory. These systems are the most abundant anionic clusters below approximately 30 km altitude in the stratosphere and also in the upper troposphere. These complexes display short strong hydrogen bonds, which should be considered to explain their abundance in the atmosphere. Equilibrium geometries, harmonic frequencies, relative energies, and thermochemical data have been calculated for these anions for the first time. The calculations indicate small differences of energy in the variation of the two nitrate groups from planarity to an almost perpendicular form for n = 1. Planar geometries are found for n = 2 and 3 to give rise to a highly symmetric C 3h NO 3 - (HNO 3 ) 3 . In all the cases, binding energies close to those of covalent compounds are estimated. When experimental data are available, good correlations are found with our results.

Óscar Gálvez

Papers

Metastable Nitric Acid Trihydrate in Ice Clouds.

Frontispiece: Metastable Nitric Acid Trihydrate in Ice Clouds

Back Cover: Spectroscopic Observation of Matrix‐Isolated Carbonic Acid Trapped from the Gas Phase (Angew. Chem. Int. Ed. 8/2011)

Effects of confinement and vaccination on an epidemic outburst: A statistical mechanics approach

Theoretical Study of Stratospheric Relevant Anions: Nitrate—Nitric Acid Complexes