Cyclicity of the unramified Iwasawa module

For a number field k and a prime number p, let k _?? be the cyclotomic Z _p -extension of k with finite layers k _n . We study the finiteness of the Galois group X _?? over k _?? of the maximal abelian unramified p-extension of k _?? when it is assumed to be cyclic. We then focus our attention to the case where p?=?2 and k is a real quadratic field and give the rank of the 2-primary part of the class group of k _n . As a consequence, we determine the complete list of real quadratic number fields for which X _?? is cyclic non trivial. We then apply these results to the study of Greenberg??s conjecture for infinite families of real quadratic fields thus generalizing previous results obtained by Ozaki and Taya.     

A positive proportion of some quadratic number fields with infinite Hilbert 2-class field tower

We show that a positive proportion of real and imaginary quadratic number fields with 2-class rank equal to 2 have 4-rank equal to 1 or 2 and infinite Hilbert 2-class field tower.     

On the Hilbert 2-class field tower of some abelian 2-extensions over the field of rational numbers

It is well known by results of Golod and Shafarevich that the Hilbert 2-class field tower of any real quadratic number field, in which the discriminant is not a sum of two squares and divisible by eight primes, is infinite. The aim of this article is to extend this result to any real abelian 2-extension over the field of rational numbers. So using genus theory, units of biquadratic number fields and norm residue symbol, we prove that for every real abelian 2-extension over ? in which eight primes ramify and one of theses primes ≡ ?1 (mod 4), the Hilbert 2-class field tower is infinite.     

Two conformers of ethyl pivalate studied by microwave spectroscopy

The rotational spectra of two conformers of ethyl pivalate, (CH₃)₃C-COO-C₂H₅ have been recorded by molecular beam FT microwave spectroscopy. The analysis yielded a set of three rotational constants and five quartic centrifugal distortion constants for each conformer. The conformers were identified by comparing the experimental rotational constants with those obtained by ab initio calculations at MP2/6-311++G∗∗ level. One conformer has C_s symmetry, the other one forms a pair of enantiomers with C₁ symmetry. Additionally, the torsional potentials of the tert-butyl group and of the methyl groups were obtained by ab initio methods.     

Mechanisms,Anti-Quorum-Sensing Actions,and Clinical Trials of Medicinal Plant Bioactive Compounds against Bacteria: A Comprehensive Review

Bacterial strains have developed an ability to resist antibiotics via numerous mechanisms. Recently, researchers conducted several studies to identify natural bioactive compounds, particularly secondary metabolites of medicinal plants, such as terpenoids, flavonoids, and phenolic acids, as antibacterial agents. These molecules exert several mechanisms of action at different structural, cellular, and molecular levels, which could make them candidates or lead compounds for developing natural antibiotics. Research findings revealed that these bioactive compounds can inhibit the synthesis of DNA and proteins, block oxidative respiration, increase membrane permeability, and decrease membrane integrity. Furthermore, recent investigations showed that some bacterial strains resist these different mechanisms of antibacterial agents. Researchers demonstrated that this resistance to antibiotics is linked to a microbial cell-to-cell communication system called quorum sensing (QS). Consequently, inhibition of QS or quorum quenching is a promising strategy to not only overcome the resistance problems but also to treat infections. In this respect, various bioactive molecules, including terpenoids, flavonoids, and phenolic acids, exhibit numerous anti-QS mechanisms via the inhibition of auto-inducer releases, sequestration of QS-mediated molecules, and deregulation of QS gene expression. However, clinical applications of these molecules have not been fully covered, which limits their use against infectious diseases. Accordingly, the aim of the present work was to discuss the role of the QS system in bacteria and its involvement in virulence and resistance to antibiotics. In addition, the present review summarizes the most recent and relevant literature pertaining to the anti-quorum sensing of secondary metabolites and its relationship to antibacterial activity.     

Comparison of fullerene and large argon clusters for the molecular depth profiling of amino acid multilayers

A major challenge regarding the characterization of multilayer films is to perform high-resolution molecular depth profiling of, in particular, organic materials. This experimental work compares the performance of C₆₀ ⁺ and Ar₁₇₀₀ ⁺ for the depth profiling of model multilayer organic films. In particular, the conditions under which the original interface widths (depth resolution) were preserved were investigated as a function of the sputtering energy. The multilayer samples consisted of three thin δ-layers (~8 nm) of the amino acid tyrosine embedded between four thicker layers (~93 nm) of the amino acid phenylalanine, all evaporated on to a silicon substrate under high vacuum. When C₆₀ ⁺ was used for sputtering, the interface quality degraded with depth through an increase of the apparent width and a decay of the signal intensity. Due to the continuous sputtering yield decline with increasing the C₆₀ ⁺ dose, the second and third δ-layers were shifted with respect to the first one; this deterioration was more pronounced at 10 keV, when the third δ-layer, and a fortiori the silicon substrate, could not be reached even after prolonged sputtering. When large argon clusters, Ar₁₇₀₀ ⁺, were used for sputtering, a stable molecular signal and constant sputtering yield were achieved throughout the erosion process. The depth resolution parameters calculated for all δ-layers were very similar irrespective of the impact energy. The experimental interface widths of approximately 10 nm were barely larger than the theoretical thickness of 8 nm for the evaporated δ-layers.

A remark on the capitulation problem

We determine explicitly an infinite family of imaginary cyclic number fields k, such that the 2-class group of k is elementary with arbitrary large 2-rank and capitulates in an unramified quadratic extension K. The infinitely many number fields k and K have the same Hilbert 2-class field and an infinite Hilbert 2-class field tower.     

Continuum of compensation points in the mixed spin Ising ferrimagnet with four-spin interaction and next-nearest neighbor coupling

We investigate the magnetic properties of the mixed spin-1/2 and spin-1 Ising ferrimagnetic system with four-spin interaction J₄ and next-nearest neighbor (NNN) coupling J′. We perform exact ground-state calculations and use the finite cluster approximation, based on a single cluster theory, to derive the state equations for the two-dimensional square lattice. The main attention has been paid to the study of the phase diagram for both the transition and compensation temperatures. We find a number of characteristic behaviors. The model with only NNNs induces one compensation point while the four-spin interaction does not. The investigation of the model with both interactions shows a number of characteristic behaviors. In particular, the presence of the four-spin interaction, according to J₄ and J′, may lead to one, two or possibly a continuum of compensation points. This phenomenon may have important applications in technology such as thermomagnetic writing and erasing at the compensation point.