CuLn complexes with a single μ-oximato bridge

Two original dinuclear (LnYb, 3 and LnEr, 4) and one trinuclear Cu^IILn^IIICu^II (LnGd, 5) complexes derived from a polydentate non symmetrical Schiff base ligand H₂L have been prepared. The ligand possesses two functions (phenol and oxime) able to coordinate the Ln ions, but structural studies (X-ray diffraction and powder X-ray diffraction) show that the Cu^II and Ln^III ions are only bridged by the oximato (NO) pair. The missing phenoxo bridge is replaced by a surprising pseudo-bridge involving one oxygen atom of the nitrato anion linked to the Cu and Ln ions according to a η²: η¹: μ mode. Although this latter contact has no role from the magnetic point of view, it introduces a large deformation of the unique bridging network. The CuYb complex 3 and the trinuclear CuGdCu complex 5 present antiferromagnetic interactions, with a J_CuGd interaction equal to ?1.25 cm^?1 in 5. The genuine single bridge can be considered as responsible for the antiferromagnetic character of the interaction.     

Amorphous structure and electronic properties of the Ge1Sb2Te4 phase change material

Ge1Sb2Te4 is one of the most commonly used phase change materials, due to the large optical and electrical contrast between a metastable crystalline phase and the amorphous phase. We use ab initio molecular dynamics to generate an amorphous Ge1Sb2Te4 structure. By analysing the distance distributions, we show that the structure can be analysed in terms of 21% of tetrahedrally coordinated Ge atoms and 79% of 3-fold Ge atoms. These are involved in distorted octahedral shells with bond length correlations that are similar to the a-GeTe structure as a consequence of a Peierls-distortion. The electronic properties are shown to be in reasonable agreement with the experiment with an electronic gap of 0.45 eV with. The optical conductivity curve is also in agreement with the experiment, with a maximal conductivity at an energy of ～3 eV.     

Two minor phytoecdysteroids of the plant Silene viridiflora

Chemical investigations of Silene viridiflora (L.) yielded a new ecdysteroid, 20-hydroxyecdysone 20,22-monoacetonide-25-acetate (1), and a known ecdysteroid, 2-deoxypolypodine B-3-beta-D-glucoside (2). The elucidation of the chemical structures was established by 1D and 2D NMR experiments.     

Trumpet with near-perfect harmonicity: design and acoustic results

This paper presents a mathematical design methodology for determining the shape of a trumpet air column that has near-perfect harmonicity, whose components are discontinuity-free, and whose input impedance peak heights are balanced over the playing range. The simulation model employed assumes linear wave propagation and uses cylindrical element discretization with a plane wave approximation. Acoustic measurements are made using a test set-up with an estimated relative measurement error of ±3 cents. Comparisons of measured results are given for the presented design (Macaluso trumpet) and the same trumpet air column with the bell replaced by a commercially used generic trumpet bell of unknown shape (Generic trumpet). For acoustic resonance modes 2-13 (233-1515 Hz), the measured root-mean-square (rms) harmonicity deviation is 5 cents for the Macaluso trumpet, whereas it is 18 cents for the Generic trumpet. However, considering the estimated measurement uncertainty, each of those deviations is somewhat over-stated. For that same range of resonances, the rms deviation between measured and calculated resonance frequencies for the Macaluso trumpet is 3 cents, thus validating the presented simulation model and equations.     

Spectral Measures Associated with the Factorization of the Lebesgue Measure on a Set via Convolution

Let \(Q\) be a fundamental domain of some full-rank lattice in \({\mathbb {R}}^d\) and let \(\mu \) and \(\nu \) be two positive Borel measures on \({\mathbb {R}}^d\) such that the convolution \(\mu *\nu \) is a multiple of \(\chi _Q\) . We consider the problem as to whether or not both measures must be spectral (i.e. each of their respective associated \(L^2\) space admits an orthogonal basis of exponentials) and we show that this is the case when \(Q = [0,1]^d\) . This theorem yields a large class of examples of spectral measures which are either absolutely continuous, singularly continuous or purely discrete spectral measures. In addition, we propose a generalized Fuglede’s Conjecture for spectral measures on \({\mathbb {R}}^1\) and we show that it implies the classical Fuglede’s Conjecture on \({\mathbb {R}}^1\) .     

A sharp lower bound for the log canonical threshold

In this note, we prove a sharp lower bound for the log canonical threshold of a plurisubharmonic function ${\varphi}$ with an isolated singularity at 0 in an open subset of ${\mathbb{C}^n}$ . This threshold is defined as the supremum of constants c > 0 such that ${e^{-2c\varphi}}$ is integrable on a neighborhood of 0. We relate ${c(\varphi)}$ to the intermediate multiplicity numbers ${e_j(\varphi)}$ , defined as the Lelong numbers of ${(dd^c\varphi)^j}$ at 0 (so that in particular ${e_0(\varphi)=1}$ ). Our main result is that ${c(\varphi)\geqslant\sum_{j=0}^{n-1} e_j(\varphi)/e_{j+1}(\varphi)}$ . This inequality is shown to be sharp; it simultaneously improves the classical result ${c(\varphi)\geqslant 1/e_1(\varphi)}$ due to Skoda, as well as the lower estimate ${c(\varphi)\geqslant n/e_n(\varphi)^{1/n}}$ which has received crucial applications to birational geometry in recent years. The proof consists in a reduction to the toric case, i.e. singularities arising from monomial ideals.     

Studies on pyrrolidinones. On the application of copper-catalyzed arylation of methyl pyroglutamate to obtain a new benzo[de]quinoline scaffold

Optimized conditions for copper-catalyzed N-arylation of methyl pyroglutamate are described. These studies permitted the synthesis of methyl N-naphthylpyroglutamate, which was then cyclized to a ketone. The known dehydration of amidoketones by PPA was extended to this new scaffold to lead to a novel condensed benzo[de]quinoline with potential antioxidative activity.     

Phosphorus dendrimers as viewed by 31P NMR spectroscopy; synthesis and characterization

This review emphasizes the role of phosphorus for the elaboration of dendrimers and of various highly sophisticated dendritic structures, and the invaluable role played by ³¹P NMR for their characterization and to ascertain their purity. A few properties, highlighting the importance of phosphorus are reported at the end of this review.