Sommerfeld’s fine structure constant approximated as a series representation in e and $$\pi $$

Sommerfeld in 1916 introduced the dimensionless fine structure constant, \(\alpha \), in to the context of atomic physics, in the course of working out the relativistic theory of the H atom, under the old quantum theory of Bohr. He was able to account for the fine structural detail of the atomic line spectrum of H by introducing this dimensionless constant which emerged naturally from his relativistic theory of the H atom. Since this time, the fine structure constant has emerged in several other contexts within experimental and theoretical physics. It has attained a status of being a mysterious number in physics that defies understanding as to its experimentally verified magnitude and identity. Being physically dimensionless, such a number invites a suggestion (or approximation) of its value in terms of mathematical constants in some formulation. Feynman most famously has conjectured that it might be possible to account for \(\alpha \) in some type of series or product expression in “e”, the base of natural logarithms, and “\(\pi \)” the familiar circular constant. Here we propose an infinite series in the product \(\mathrm{e} \cdot \pi \) that converges, within a few terms, to better than 9999 parts in 10,000 of the true value of \(\alpha \).     

Reaction of β-arylidennaphthylamines with 4-hydroxycoumarin. A correction in structural assignment of the product. III

The reaction of 4-hydroxycoumarin with β-arylidennaphthylamines constitutes a convenient synthetic route to the hitherto unknown 2H-benzo[f][1]benzopyrano[4,3-b]quinolin-2-one, VI . The X-ray crystallography data conform with the present benzopyrano[4,3-b]quinolin-2-one ring system and disprove the benzopyrano[3,4-c]quinolin-2-one structure previously assigned for such reaction products.     

From Salts to Ionic Liquids by Systematic Structural Modifications: A Rational Approach Towards the Efficient Modular Synthesis of Enantiopure Imidazolium Salts

This paper reports a simple and robust modular synthetic strategy that leads to a large variety of configurationally and structurally diverse imidazole‐based chiral ionic liquids (CILs) by lipase‐catalyzed resolution. The intimate microscopic interactions of the supramolecular ionic network of these imidazolium chiral salts at the molecular level are investigated both spectroscopically (NMR, FT‐IR‐ATR) and theoretically, and a topological analysis of the experimental electron densities obtained by X‐ray dif fr action of single crystals is performed. Our results support the key role played by the relative configuration of the ‐OR group on the hydrogen‐bonding pattern and its strong influence on the final physical properties of the imidazolium salt. We also obtained a reasonable correlation between the observed melting point and the non‐covalent interactions. The spectroscopic data and the topological analysis reflect the key role played by hydrogen bonds between the OH and imidazolium C2H groups in both cation–anion and cation–cation interactions, with the presence of an OH group leading to an additional inter‐cation interaction. This interaction significantly affects the properties of stereoisomeric salts. Even more interestingly, we also studied the effect of the chirality by comparing enantiopure CILs with their racemic mixtures and found that, with the exception of trans‐Cy6‐OH‐Im‐Bn‐Br, the melting points of the racemic mixtures are higher than those of the corresponding enantiomerically pure forms. For stereoisomeric examples, we have successfully explained the differences in melting temperatures in light of the corresponding structural data. Chirality should therefore be taken into account as a highly attractive design vector in the preparation of ILs with specifically desired properties.     

Superacid-promoted reactions of alpha-ketoamides and related systems

The superacid-promoted reactions of alpha-hydroxy and alpha-ketoamides have been studied. Ionization of these compounds leads to varied aryl-substituted oxyindole products. In some cases, electrocyclization can lead to substituted fluorene products. Dicationic, superelectrophilic intermediates are proposed as intermediates leading to the products from alpha-hydroxy and alpha-ketoamides.     

Theoretical study of the surface reactivity of alkaline earth oxides: local density of states evaluation of the local softness

The local softness of MgO, CaO, SrO, and BaO (100) surfaces has been studied using a model based on the local density of states. In all the species, the local softness (chemical reactivity) of oxygen atoms at the surface is enhanced as compared to the bulk. The results for the local and the global softness are in agreement with the ionic pattern of the metal-oxygen bond of the series.     

Hydrogeochemical and isotopic characterisation of groundwater in a sand-dune phreatic aquifer on the northeastern coast of the province of Buenos Aires,Argentina

This contribution presents the hydrochemical and isotopic characterisation of the phreatic aquifer located in the Partido de la Costa, province of Buenos Aires, Argentina. In the sand-dune barrier geomorphological environment, groundwater is mainly a low-salinity Ca-HCO₃ and Na-HCO₃-type, being in general suitable for drinking, whereas in the continental plain (silty clay sediments), groundwater is a Na-Cl type with high salinity and unsuitable for human consumption. The general isotopic composition of the area ranges from?6.8 to?4.3 ‰ for δ¹⁸O and from?39 to?21 ‰ for δ²H, showing that rainwater rapidly infiltrates into the sandy substrate and reaches the water table almost without significant modification in its isotopic composition. These analyses, combined with other chemical parameters, made it possible to corroborate that in the eastern area of the phreatic aquifer, there is no contamination from marine salt water.     

Theory of twist liquids: Gauging an anyonic symmetry

Topological phases in (2+1)$(2+1)$-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric–magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static point-like objects that permute the labels of orbiting anyons. Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids  , which are generically non-Abelian. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. We explicitly demonstrate the gauging of the Z₂${\mathbb{Z}}_2$-symmetric toric code, SO(2N)₁$SO{\left(2N\right)}_1$ and SU(3)₁$SU{\left(3\right)}_1$ state as well as the S₃$S_3$-symmetric SO(8)₁$SO{\left(8\right)}_1$ state and a non-Abelian chiral state we call the “4-Potts” state.     

On counting interval lengths of interval graphs

Given an interval graph G, the interval count problem is that of computing the minimum number IC(G) of interval lengths needed to represent G. Although the problem of deciding whether IC(G)=1 is equivalent to that of recognizing unit-interval graphs, which is a well-known problem having several efficient recognition approaches, very little is known about deciding efficiently whether IC(G)=k for fixed k≥2. We provide efficient computations of the interval count of generalizations of threshold graphs.     

Quantum transport in randomly diluted quantum percolation clusters in two dimensions

We study the hopping transport of a quantum particle through finite, randomly diluted percolation clusters in two dimensions. We investigate how the transmission coefficient T behaves as a function of the energy E of the particle, the occupation concentration p of the disordered cluster, the size of the underlying lattice, and the type of connection chosen between the cluster and the input and output leads. We investigate both the point-to-point contacts and the busbar type of connection. For highly diluted clusters we find the behavior of the transmission to be independent of the type of connection. As the amount of dilution is decreased we find sharp variations in transmission. These variations are the remnants of the resonances at the ordered, zero-dilution, limit. For particles with energies within 0.25≤E≤1.75 (relative to the hopping integral) and with underlying square lattices of size 20×20, the configurations begin transmitting near p_α=0.60 with T against p curves following a common pattern as the amount of dilution is decreased. Near p_β=0.90 this pattern is broken and the transmission begins to vary with the energy. In the asymptotic limit of very large clusters we find the systems to be totally reflecting in almost all cases. A few clear exceptions we find are when the amount of dilution is very low, when the particle has energy close to a resonance value at the ordered limit, and when the particle has energy at the middle of the band. These three cases, however, may not exhaust all possible exceptions.     

Thermal Immobilization of Poly(Butylacrylate) on Glass-Ceramic Rod for Preparation of Solid Phase Microextraction Fibers

The efficiency of a glass-ceramic rod as a base for the preparation of SPME fibers using thermal immobilization was investigated. Glass-ceramic and fused silica rods were thermally immobilized with poly(butylacrylate) and their absorption capacity was compared. The absorption capacity between the fiber obtained for thermal immobilization of poly(butylacrylate) on glass-ceramic surface and commercially PA fiber was also compared. In this study the target analytes were phthalate esters and phenols. The results obtained for extraction of phenols from aqueous solutions using the headspace mode demonstrated the superiority of glass-ceramic in relation the silica gel rod as a base for SPME fiber. The direct SPME extraction of phthalate esters from aqueous solutions using commercial PA fiber and that obtained for thermal immobilization of poly(butylacrylate) on glass-ceramic rod presented similar results. The repeatability and the reproducibility among extractions using fibers developed in our laboratory were achieved.