Field Theoretic Cogalois Theory via Abstract Cogalois Theory

Abstract Cogalois Theory for arbitrary profinite groups was initiated by T. Albu and ?.A. Basarab [An Abstract Cogalois Theory for profinite groups, J. Pure. Appl. Algebra 200 (2005) 227-250]. The aim of this paper is twofold: firstly, to present the abstract group theoretic versions of various types of Kummer field extensions, and secondly, to show how some basic results of the (Field Theoretic) Cogalois Theory can be very easily deduced from their abstract versions.     

GI-graphs: a new class of graphs with many symmetries

The class of generalized Petersen graphs was introduced by Coxeter in the 1950s. Frucht, Graver and Watkins determined the automorphism groups of generalized Petersen graphs in 1971, and much later, Nedela and ?koviera and (independently) Lovre?i?-Sara?in characterised those which are Cayley graphs. In this paper we extend the class of generalized Petersen graphs to a class of GI-graphs. For any positive integer n and any sequence j ₀,j ₁,…,j _t?1 of integers mod n, the GI-graph GI(n;j ₀,j ₁,…,j _t?1) is a (t+1)-valent graph on the vertex set \(\mathbb{Z}_{t} \times\mathbb{Z}_{n}\) , with edges of two kinds:

• an edge from (s,v) to (s′,v), for all distinct \(s,s' \in \mathbb{Z}_{t}\) and all \(v \in\mathbb{Z}_{n}\) ,
• edges from (s,v) to (s,v+j _s ) and (s,v?j _s ), for all \(s \in\mathbb{Z}_{t}\) and \(v \in\mathbb{Z}_{n}\) .

By classifying different kinds of automorphisms, we describe the automorphism group of each GI-graph, and determine which GI-graphs are vertex-transitive and which are Cayley graphs. A GI-graph can be edge-transitive only when t≤3, or equivalently, for valence at most 4. We present a unit-distance drawing of a remarkable GI(7;1,2,3).     

New insights on surface‐enhanced Raman scattering based on controlled aggregation and spectroscopic studies,DFT calculations and symmetry analysis for 3,6‐bi‐2‐pyridyl‐1,2,4,5‐tetrazine adsorbed onto citrate‐stabilized gold nanoparticles

A systematic study on the surface‐enhanced Raman scattering (SERS) for 3,6‐bi‐2‐pyridyl‐1,2,4,5‐tetrazine (bptz) adsorbed onto citrate‐modified gold nanoparticles (cit‐AuNps) was carried out based on electronic and vibrational spectroscopy and density functional methods. The citrate/bptz exchange was carefully controlled by the stepwise addition of bptz to the cit‐AuNps, inducing flocculation and leading to the rise of a characteristic plasmon coupling band in the visible region. Such stepwise procedure led to a uniform decrease of the citrate SERS signals and to the rise of characteristic peaks of bptz, consistent with surface binding via the N heterocyclic atoms. In contrast, single addition of a large amount of bptz promoted complete aggregation of the nanoparticles, leading to a strong enhancement of the SERS signals. In this case, from the distinct Raman profiles involved, the formation of a new SERS environment became apparent, conjugating the influence of the local hot spots and charge‐transfer (CT) effects. The most strongly enhanced vibrations belong to a₁ and b₂ representations, and were interpreted in terms of the electromagnetic and the CT mechanisms: the latter involving significant contribution of vibronic coupling in the system. Copyright © 2010 John Wiley & Sons, Ltd.     

Linkage isomerism,kinetics and electrochemistry of ruthenium-edta complexes of benzotriazole

The [RuIII(edta)(benzotriazole)]− complex has been investigated in aqueous solution, by means of cyclic voltammetry, stopped-flow kinetics and spectroelectrochemistry. The formation reaction, starting from [RuIII(edta)H2O]− and benzotriazole, leads essentially to the N(1) coordinated isomer. In the case of the RuII species, the products exhibit an intramolecular isomerization equilibrium involving the N(1) and N(2) binding sites, with K12=0.33. A complete set of acid/base and association constants has been obtained for the RuII and RuIII complexes. The data are coherent with theoretical calculations, reflecting the importance of π-backbonding interactions in the reduced species. This revised version was published online in June 2006 with corrections to the Cover Date.     

Study of SNAr Reactions of Halobenzenes with Imidazole under Ultrasonic and Microwave Irradiation

Summary. Nucleophilic aromatic substitution reactions with imidazole of haloarenes having strongly electron-withdrawing groups were studied under ultrasonic and microwave irradiations. The course of the S_NAr reactions was found to be strongly dependent on the electron-withdrawing properties of the substituents as well as on the leaving ability of the halogen atom. Microwave irradiation allowed to shorten the reaction time and to increase the yields compared with ultrasonic irradiation.     

Transport parameters of I− and IO3 − determined in crushed granitic rock columns and groundwater system under dynamic flow conditions

Transport of two principal inorganic iodine anions separately in two crushed crystalline granitic rocks, gabbro and tonalite, have been investigated. The rocks were crushed and sieved, and finally a fraction between 0.25 and 0.80 mm was filled in 5 cm³ PET columns (medical syringes) of 5.40 cm length and 1.24 cm in inner diameter. NaI and NaIO₃ were dissolved in synthetic groundwater (SGW) in a concentration as low as 10^?4 mol/dm³. The SGW was pumped into the columns at a seepage velocity of 0.031 ± 0.001 cm/min using a multi-head peristaltic pump. Iodine concentration in the outflow SGW from the columns was determined by UV–Vis spectrophotometry at 510 nm absorption maximum in CHCl₃ using redox reactions. By the use of a dependence of concentration on the number of pore volumes from the outflow and the linear isotherm model, based on erfc-function, breakthrough curves were constructed and the principal transport parameters were calculated. The values of sorption and desorption retardation coefficients of about 1 for both iodide and iodate have been obtained, which show evidence of practically non-sorption behavior of these chemical forms of iodine in the tested granitic rocks. The values of hydrodynamic dispersion coefficients and corresponding Peclet numbers were about 0.0077 ± 0.0006 and 21.6 ± 1.8 cm²/min, respectively, for both anions and rocks under given conditions.     

Asymmetric Mannich reaction catalyzed by N-arylsulfonyl-l-proline amides

Proline-derived N-sulfonylcarboxamides efficiently catalyze the asymmetric Mannich reaction of cyclic ketones with N-(p-methoxyphenyl)-protected iminoglyoxylate. Both classical organic solvents and ionic liquids were used as the reaction media. With cyclohexanone, the reaction proceeded with high enantioselectivity (99% ee). Enamine intermediates were investigated by DFT calculations.