Sur un problème de capitulation du corps ℚ\sqrt {p_1 p_2 } , i dont le 2-groupe de classes est élémentaire

Let p ₁ ≡ p ₂ ≡ 1 (mod 8) be primes such that \(\left( {\tfrac{{p_1 }} {{p_2 }}} \right) = - 1\) and \(\left( {\tfrac{2} {{a + b}}} \right) = - 1\) , where p ₁ p ₂ = a ²+b ². Let \(i = \sqrt { - 1} \) , d = p ₁ p ₂, \(\Bbbk = \mathbb{Q}(\sqrt {d,} i),\Bbbk _2^{(1)} \) be the Hilbert 2-class field and \(\Bbbk ^{(*)} = \mathbb{Q}(\sqrt {p_1 } ,\sqrt {p_2 } ,i)\) be the genus field of \(\Bbbk \) . The 2-part \(C_{\Bbbk ,2} \) of the class group of \(\Bbbk \) is of type (2, 2, 2), so \(\Bbbk _2^{(1)} \) contains seven unramified quadratic extensions \(\mathbb{K}_j /\Bbbk \) and seven unramified biquadratic extensions \(\mathbb{L}_j /\Bbbk \) . Our goal is to determine the fourteen extensions, the group \(C_{\Bbbk ,2} \) and to study the capitulation problem of the 2-classes of \(\Bbbk \) .     

Phase transitions and electrical conduction in thermal energy storage compound (n-C12H25NH3)2CdCl4

Differential scanning calorimetry (DSC) and differential thermal analysis (DTA) are performed for the compound (n-C₁₂H₂₅NH₃)₂CdCl₄. The ac conductivity σ_(ω,T), and the complex dielectric permittivity ?*_(ω,T) are measured as a function of temperature (100 K < T < 375 K) and at some selected frequencies (3 → 100 kHz). Two structural phase transitions are detected at T = (330 ± 1) K and T = (343 ± 1) K as minor and major transitions, respectively. The analysis of the measured electrical parameters reveals that the frequency-dependent conductivity obeys the power law, and the quantum mechanical tunneling (QMT) model is the main conduction mechanism in the low-temperature phase (LTP; phase III). The role of hydrogen bond N–H…Cl as a trigger force for phase transitions has been discussed. While the LTP is of the order–disorder type, the high-temperature phase (HTP) or phase I seems to be conformational and represents the main transition.     

Adsorption and corrosion inhibition of mild steel in hydrochloric acid solution by verbena essential oil

The inhibitive action of verbena essential oil (VEO) on the corrosion of mild Steel in 1 M HCl solutions in the temperature range 298 to 328 K was measured by use of the weight-loss method, potentiodynamic polarization, and electrochemical impedance spectroscopy. Results showed that VEO inhibited corrosion of C38 steel in 1 M HCl solution and that inhibition efficiency increased with increasing concentration of inhibitor but decreased proportionally with temperature. Potentiodynamic polarization studies suggested VEO is a mixed-type inhibitor, with the anodic type predominating. Nyquist plots were depressed semicircles with their centre below the real axis. Adsorption of VEO by the C38 steel surface followed the Langmuir adsorption isotherm. Kinetic data for dissolution were investigated.     

Studies on the inhibitive effect of potassium ferrocyanide on the corrosion of steel in phosphoric acid

In this work, the effect of potassium ferrocyanide (Pf) on the corrosion of mild steel in solutions of phosphoric acid (H₃PO₄) has been investigated in relation to the concentration of the inhibitor by weight loss, potentiodynamic polarization and AC impedance (EIS) measurements. The results obtained revealed that this compound is good a mixed-type inhibitor. The effect of temperature on the corrosion behavior with the addition of optimal concentration of Pf was studied in the temperature range 298–328 K. The value of inhibition efficiency decreases slightly with the increase in temperature. Changes in impedance parameters (charge transfer resistance, R _t, and double layer capacitance, C _dl) were indicative of adsorption of Pf on the metal surface, leading to the formation of a protective film. Adsorption of Pf on the C38 steel surface was found to obey the Langmuir adsorption isotherm. Some thermodynamic functions of dissolution and adsorption processes were also determined.     

Ferromagnetism and ferroelectricity in Eu<Emphasis Type="Italic">X</Emphasis> (<Emphasis Type="Italic">X</Emphasis> = <Emphasis Type="Italic">O</Emphasis>, <Emphasis Type="Italic">S</Emphasis>): pressure effects

Ferromagnetism and ferroelectricity in Eu monochalcogenides have been investigated by ab initio density functional theory in the DFT+U approach. Exchange interaction parameters and Curie temperatures under pressure are studied and discussed using Heisenberg Hamiltonian with first and second-nearest-neighbor interactions. The calculations showed that the hydrostatic pressure perfectly improves the Curie temperature (EuO: T _C = 175 K; EuS: T _C = 33.8 K) and in the other hand it cannot induce the spontaneous polarization (P _s ). The effect of uniaxial and biaxial pressure is also studied. Although the uniaxial strains slightly increases the Curie temperature, it ensures the ferrolectricity in these systems by producing a spontaneous polarization of the order of P _s (EuO) = 57.50 μC/cm² and P _s (EuS) = 42.86 μC/cm² with pressures of 5% and 4%, respectively. The search for new model systems is a necessity to better understand the physics related to multiferroïc materials and to consider possible applications.     

Biopolymer-layered polysilicate micro/nanocomposite based on chitosan intercalated in magadiite

On the basis of their high adsorption and cation exchange capacity, swelling potential and low toxicity, layered sodium silicate magadiite (Na–magadiite) is an attractive solid for intercalation of polymers. This study envisages the intercalation of cationic biopolymer chitosan (Chit) in Na–magadiite to prepare a Chit/magadiite micro/nanocomposite. Characterisation of starting-magadiite, pure chitosan and Chit/magadiite were investigated using powder X-ray diffraction analysis (XRD), Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy and thermal analysis. XRD confirmed that the chitosan had been intercalated into the interlayer space of magadiite by increasing the basal spacing, d₀₀₁ from 15.6 Å to 21.45 Å. The presence of characteristic bands of biopolymer and layered silicate in Chit/magadiite were confirmed by FTIR analysis. The thermal stability of micro/nanocomposite was evaluated by thermogravimetry analysis. The results suggested the formation of electrostatic interactions by protonated amine groups with the negatively charged magadiite surface as well as intercalation in the form of a predominant monolayer arrangement of chitosan chains in layered silicate magadiite.     

Argan hulls extract: green inhibitor of mild steel corrosion in 1?M HCl solution

Argan hulls extract (AHE) was tested as corrosion inhibitor for mild steel in 1?M HCl. Weight loss measurements, potentiodynamic polarization, and electrochemical impedance spectroscopy (EIS) revealed that inhibiting action increased with increasing concentration of the inhibitor. The highest efficiency 97.3% was obtained at 5?g/L AHE. There was good agreement between gravimetric and electrochemical methods (potentiodynamic polarization and EIS). Results obtained from EIS measurements were analyzed to model the corrosion-inhibition process by use of the appropriate equivalent circuit model; a constant phase element was used. Polarization measurements show also that AHE acts as good mixed inhibitor. AHE is adsorbed on the steel surface in accordance with a Langmuir isotherm adsorption model.     

Generation of well‐defined clickable glycopolymers from aqueous RAFT polymerization of isomaltulose‐derived acrylamides

Original carbohydrate‐based acrylamides bearing one azide group in C‐2 or C‐6 position namely, 2‐[(2‐deoxy‐2‐azido‐α‐D ‐mannopyranosyloxy)ethanamido]‐ethyl acrylamide (II) and 2‐[(6‐deoxy‐6‐azido‐α‐D ‐glucopyranosyloxy)ethanamido]‐ethyl acrylamide (III), and their azide‐free analogue, 2‐[(α‐D ‐glucopyranosyloxy)ethanamido]‐ethyl acrylamide (I), have been designed. Whereas the reversible addition fragmentation chain transfer (RAFT) process ensured the preparation of well‐defined glycopolymers from I, the polymerization of monomers II and III proved to be challenging at temperatures compatible with a thermally initiated radical process, due to the presumed concomitant 1,3‐cycloaddition reactions between the azide and the acrylamide moieties. In contrast to III, for which no polymer could be obtained under any conditions, performing the RAFT polymerization of II at 30 °C clearly favored the radical polymerization and conferred a controlled character to the process, affording well‐defined azide‐functionalized glycopolymers and block copolymers. The presence of numerous azide moieties was finally exploited to introduce carbohydrates onto the glycopolymer backbone through copper catalyzed azide‐alkyne cycloaddition. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Electron–Phonon Superconductivity in Boron-Based Chalcogenide (X= S,Se) Monolayers

Electron–phonon mediated superconductivity is deeply investigated in two boron based monolayer materials, namely, $B_{3}S$, a metal exhibiting the ability to superconduct, and a new metal, $B_{3}Se$, presenting perfect kinetic stability. Calculations based on density functional perturbation theory combined with the maximally localized Wannier function also reveal that both materials exhibit anisotropic planar hexagonal structure like graphene. The key parameters involved in the superconductor behavior are all calculated. The electronic density in the Fermi surface is given to provide the environment for enhanced electron–phonon coupling. The longitudinal and transverse vibration modes of optical phonons mainly contribute to the electron–phonon coupling strength. Furthermore, the binding energy between the bosonic Cooper pair superfluid is quantified and determined. The critical temperature for the two materials is 20 and 10.5 K, respectively. The results obtained show the potential use of such materials for superconducting applications.     

A new synthesis of alkane and polyfluoroalkanesulfonyl chlorides

This study describes a new and advantageous procedure for the synthesis of alkanesulfonyl chlorides ( 2 ) by the reaction of alkyl thiocyanates ( 1 ) with sulfuryl chloride in a mixture of acetic acid and water. The alkanesulfonyl chlorides were obtained in good yields. © 2009 Wiley Periodicals, Inc. Heteroatom Chem 20:355–361, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20559