Perturbations for Delaunay and weighted Delaunay 3D triangulations

The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate. We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar. No flat tetrahedron exists in the defined triangulation. The perturbation scheme is easy to code. It is implemented in cgal, and guarantees that both vertex insertion and vertex removal are fully robust.     

Some Lower Bounds in the B. and M. Shapiro Conjecture for Flag Varieties

The B. and M. Shapiro conjecture stated that all solutions of the Schubert Calculus problems associated with real points on the rational normal curve should be real. For Grassmannians, it was proved by Mukhin, Tarasov, and Varchenko. For flag varieties, Sottile found a counterexample and suggested that all solutions should be real under certain monotonicity conditions. In this paper, we compute lower bounds on the number of real solutions for some special cases of the B. and M. Shapiro conjecture for flag varieties, when Sottile’s monotonicity conditions are not satisfied.     

NMR parameters in alkali, alkaline earth and rare earth fluorides from first principle calculations

(19)F isotropic chemical shifts for alkali, alkaline earth and rare earth of column 3 basic fluorides are measured and the corresponding isotropic chemical shieldings are calculated using the GIPAW method. When using the PBE exchange-correlation functional for the treatment of the cationic localized empty orbitals of Ca(2+), Sc(3+) (3d) and La(3+) (4f), a correction is needed to accurately calculate (19)F chemical shieldings. We show that the correlation between experimental isotropic chemical shifts and calculated isotropic chemical shieldings established for the studied compounds allows us to predict (19)F NMR spectra of crystalline compounds with a relatively good accuracy. In addition, we experimentally determine the quadrupolar parameters of (25)Mg in MgF(2) and calculate the electric field gradients of (25)Mg in MgF(2) and (139)La in LaF(3) using both PAW and LAPW methods. The orientation of the EFG components in the crystallographic frame, provided by DFT calculations, is analysed in terms of electron densities. It is shown that consideration of the quadrupolar charge deformation is essential for the analysis of slightly distorted environments or highly irregular polyhedra.     

Lower Bounds on Matrix Factorization Ranks via Noncommutative Polynomial Optimization

We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the positive semidefinite rank, and their symmetric analogs: the completely positive rank and the completely positive semidefinite rank. We study convergence properties of our hierarchies, compare them extensively to known lower bounds, and provide some (numerical) examples.

     

A Direct and Efficient Synthetic Method for Nitriles from Ketones

Cyclic cyano derivatives 3 were obtained by the reaction of Me₃SiCN / ZnI₂ with the cyclic ketones 2 which gave the trimethylsilyloxy nitriles 4. They were directly transformed to cyano derivatives 3 (70–80% yield) by the reductive reagent Me₃SiCl-NaI in acetonitrile in the presence of H₂O.     

A Simple and Efficient Procedure for the Preparation of Benzal Chlorides and Benzal Bromides

Benzal chlorides and benzal bromides were conveniently synthesized by reaction of aryl aldehydes with a Vilsmeier type reagent formed in situ by reduction of CC1₄ or CBr₄ in dimethylformamide (DMF) as solvent.     

Synthesis of Polyamides-11 with Sulfonamide End Groups

α,ω-Diaminooligoamides-11 were prepared and their structure was controlled by endgroup titration, elemental analysis, and infrared and ¹H NMR spectroscopy. A fundamental study of the reaction between αA,ω diaminooligoamides and p-toluenesulfonyl chloride in DMF showed that a side reaction takes place. This was carefully characterized. When the reaction was carried out in chlorobenzene (on models and on polymers), well-defined compounds were obtained which were characterized by different techniques.     

Pulsed amperometric detection (PAD) of diuretic drugs in herbal formulations using a gold electrode following ion-pair chromatographic separation

Herein, we present a new method based on separation by ion-pair chromatography with pulsed amperometric detection for evaluating various diuretics, including hydrochlorothiazide, chlorthalidone, furosemide, and amiloride, which are adulterants in herbal-based pharmaceutical formulations. The amperometric detection cycle (time?=?2 s) was performed at a gold electrode by applying a detection potential (E1) of +800 mV for 0.4 s and an oxidation potential (E2) of +1,000 mV for 0.40 s, followed by a reduction potential (E3) of ?200 mV for 1.20 s. The mobile phase for separating the diuretics was composed of 5 mmol L^?1 phosphate buffer and 0.3 mmol L^?1 sodium dodecyl sulfate in 50 % (v/v) methanol (pH 4.5). This method enabled the quantification of the drugs at low concentrations (i.e., 0.08 mg/capsule for hydrochlorothiazide, 0.01 mg/capsule for chlorthalidone, and 0.007 mg/capsule for furosemide). Twenty-six herbal formulations were analyzed, and eight samples (30.8 %) were found to contain diuretics that were added to the final composition (declared or not).