New Metal Oxamates as Precursors of Low-Dimensional Heterobimetallics

The goal of this work was to synthesize new molecular bricks which could be used as precursors of heterobimetallic low-dimensional compounds. Along this line, four compounds have been synthesized and structurally characterized, namely (NBu(4))(2)[Ni(Cl(2)opba)] (1), (NBu(4))(2)[Cu(Cl(2)opba)] (2), (NBu(4))(5)[Mn(Cl(2)opba)(DMSO)(2)](4) (3), and Cu(en)(2)[Mn(Cl(2)opba)(H(2)O)(2)](2).2DMSO (4), with Cl(2)opba = (4,5-dichloro-o-phenylene)bis(oxamato), NBu(4) = tetra-n-butylammonium, en = ethylenediamine, and DMSO = dimethyl sulfoxide. Compounds 1 and 2 are isostructural; they crystallize in the monoclinic system, space group C2/c, Z = 4, with a = 18.708(2) ?, b = 17.525(2) ?, c = 14.763(9) ?, and beta = 92.03(4) degrees for 1 and a = 18.928(2) ?, b = 17.634(2) ?, c = 14.704(9) ?, and beta = 92.38(3) degrees for 2. 3 crystallizes in the tetragonal system, space group P&fourmacr;2(1)c, Z = 2, with a = 26.295(10) ? and c = 12.342(7) ?. The structure shows a random occupation of the metal site by Mn(III) and Mn(II) ions in 3/4 and 1/4 ratios, respectively. 4 crystallizes in the triclinic system, space group P&onemacr;, Z = 1, with a = 7.066(7) ?, b = 11.844(1) ?, c = 14.292(5) ?, alpha = 105.64(2) degrees, beta = 97.67(5) degrees, and gamma = 102.13(3) degrees. The structure consists of Mn(III)Cu(II)Mn(III) trinuclear species, with Cu-O-Mn bridges involving oxygen atoms of the oxamato groups already linked to the metal atom. The magnetic properties of compounds 1-4 have been investigated and quantitatively interpreted. For 3, this magnetic investigation has been performed on a single crystal, which allows us to determine unambiguously the sign of the axial zero-field splitting parameter for the Mn(III) ion. The potentialities of these new molecular bricks have been discussed.     

A Cut-Invariant Law of Large Numbers for Random Heaps

We consider the framework of Bernoulli measures for heap monoids. We introduce in this framework the notion of asynchronous stopping time, which generalizes the notion of stopping time for classical probabilistic processes. A strong Bernoulli property is proved. A notion of cut-invariance is formulated for convergent ergodic means. Then, a version of the strong law of large numbers is proved for heap monoids with Bernoulli measures. We study a sub-additive version of the law of large numbers in this framework.     

Phytochemical Investigation by Microwave‐Assisted Extraction of Essential Oil of the Leaves of Walnut Cultivated in Algeria

Walnut (Juglans regia L.) leaves are used traditionally as an herbal tea indicated for non‐insulin‐dependent diabetics. In recent years, the type‐II diabetes is occurring worldwide with increasing frequency. Thus, there is an urgent need to explore the new beneficial biomolecules on the human health. Our objective was to investigate, for the first time, the volatiles profile of Juglans regia L. leaves from Algiers region. The extraction of essential oil of fresh plant material was performed by microwave‐assisted hydrodistillation (MAHD), for the first time, a relatively recent method, then by the conventional hydrodistillation technique (HD) for comparison. The collected extracts were analyzed by GC‐FID and GC/MS using two capillary columns with different polarity. Extraction time of 1 h by MAHD provided higher yields (0.050±0.001% (w/w)) than by HD (0.030±0.006% (w/w)) after 3 h. A total of 38 compounds were identified using both techniques. Essential oils had similar qualitative but different quantitative composition in terms of chemical compounds. The MAHD method improved yield while reducing the extraction time. The sesquiterpenes were the dominant family in both MAHD and HD essential oils with β‐caryophyllene being the major constituent. Monoterpenes, including hydrocarbon and oxygenated, prevail in HD volatile fraction with β‐pinene and eucalyptol, respectively, as major components.     

Magnetic properties of 1d systems with a subtle stacking of copper(II) ions

In the last two decades, many studies have been reported on infinite Id networks of magnetically interacting metal ions. Until now, closed-form expressions for the partition function and related properties were mainly derived for the S = f Ising chain model (Ising, 1925), the XY model (Kastura, 1962) or for the classical limit S –t co with arbitrary spin dimensionality (Fischer, 1964). Recently, experimental and theoretical studies have focused on new Id systems made of alternating spin and/or Lande factors (Georges, Curely and Drillon, 1985; Drillon et al., 1983). This has motivated our interest in the behavior of new systems of copper(II) ions in which the magnetic sites form an exotic stacking in one direction of the crystal. Then, the specific behavior is related to the competition between different interactions, as occurs in the systems reported here, namely A₃Cu₃(PO₄)₄, with A = Ca, Sr, Cu₃(PO₄)₂ and Cu₂O(SO₄).     

Raman characterization of Pb2Na1−xLaxNb5−xFexO15 and Pb0.5(5−x)LaxNb5−xFexO15 (0≤x≤1) solid solutions

The ferroelectric compounds Pb₂Na_1−xLa_xNb_5−xFe_xO₁₅ and Pb_0.5(5−x)La_xNb_5−xFe_xO₁₅ (0≤x≤1) with the tungsten bronze type structure have been investigated using Raman spectroscopy. The evolution of the spectra as a function of composition at room temperature is reported. In the frequency range 200-1000 cm⁻¹ three main A₁ phonons around 240 (υ₁), 630 (υ₂) and 816 (υ₃) cm⁻¹ were observed. The broadening of the Raman lines for high values of x originates from a significant structural disorder. This is in good agreement with the relaxor character of these compositions. The lowest-frequency part of the spectra, below 180 cm⁻¹, reveals a structural change in the studied solid solutions. The behaviour of the Raman shift of the υ₁ mode confirms that in Pb₂Na_1−xLa_xNb_5−xFe_xO₁₅, a clear anomaly occurs in the vicinity of x=0.4.     

Sodium silver tricobalt bis(diphosphate) and sodium silver copper(II) diphosphate

The crystal structures of two new diphosphates, sodium silver tricobalt bis(diphosphate), (Na_1.42Ag_0.58)Co₃(P₂O₇)₂, and sodium silver copper(II) diphosphate, (Na_1.12Ag_0.88)CuP₂O₇, provide examples of the effect of mixing Na and Ag in the same site of known host phosphate compounds. The small differences in ionic radii of the two monocations do not lead to significant differences in the structural details. In the latter compound, the Cu atom lies on an inversion center.     

Control of the oscillator strength of the exciton in a single InGaN-GaN quantum dot

We report direct evidence for the control of the oscillator strength of the exciton state in a single quantum dot by the application of a vertical electric field. This is achieved through the study of the radiative lifetime of a single InGaN-GaN quantum dot in a p-i-n diode structure. Our results are in good quantitative agreement with theoretical predictions from an atomistic tight-binding model. Furthermore, the increase of the overlap between the electron and hole wave functions due to the applied field is shown experimentally to increase the attractive Coulomb interaction leading to a change in the sign of the biexcitonic binding energy.     

The characteristic class and ramification of an ℓ-adic étale sheaf

We introduce the characteristic class of an ℓ-adic étale sheaf using a cohomological pairing due to Verdier (SGA5). As a consequence of the Lefschetz–Verdier trace formula, its trace computes the Euler–Poincaré characteristic of the sheaf. We compare the characteristic class to two other invariants arising from ramification theory. One is the Swan class of Kato-Saito [17] and the other is the 0-cycle class defined by Kato for rank 1 sheaves in [16]. Dedicated to Luc Illusie, with admiration