Navier–Stokes Equations on Weighted Graphs

Navier–Stokes equations arise in the study of incompressible fluid mechanics, star movement inside a galaxy, dynamics of airplane wings, etc. In the case of Newtonian incompressible fluids, we propose an adaptation of such equations to finite connected weighted graphs such that it produces an ordinary differential equation with solutions contained in a linear subspace, this subspace corresponding to the Newtonian conservation law. We discuss the particular case when the graph is the complete graph K _m , with constant weight, and provide a necessary and sufficient condition for it to have solutions.     

The seed of magnetic monopoles in the early inflationary universe from a 5D vacuum state

Starting from a 5D Riemann flat metric, we have induced an effective 4D Hermitian metric which has an antisymmetric part which is purely imaginary. We have worked an example in which both, non-metricity and cotorsion are zero. We obtained that the production of monopoles should be insignificant at the end of inflation and the tensor metric should come asymptotically diagonal and describing a nearly 4D de Sitter expansion.     

A survey on Cox rings

We survey the construction of the Cox ring of an algebraic variety X and study the birational geometry of X when its Cox ring is finitely generated. Basic notation. Throughout this paper k is an algebraically closed field.     

Synthesis of the potent immunostimulatory adjuvant QS-21A

QS-21A is one of the most promising new adjuvants for immune response potentiation and dose-sparing in vaccine therapy, given its exceedingly high level of potency and its favorable toxicity profile. Melanoma, breast cancer, small cell lung cancer, prostate cancer, HIV-1, and malaria are among the numerous maladies targeted in more than 80 recent and ongoing clinical trials involving QS-21A as a critical component for immune response augmentation in microgram doses. Herein is reported the first synthesis and structure verification of QS-21Aapi, applying novel glycosylation methodologies in the convergent modular construction of this rare and potent natural product immunostimulant.     

Ultrasound-assisted extraction of soy isoflavones

Efficiency in extracting four isoflavone derivatives (daidzin, glycitin, genistin and malonyl genistin) from freeze-dried ground soybeans was compared for mix-stirring extraction and ultrasound-assisted extraction, using different solvents and extraction temperatures with both. The efficiency of the extraction of soy isoflavones was improved by ultrasound but was dependent on the solvent employed. Optimization of the ratios of sample quantity to solvent volume and length of extraction time was also performed. Isoflavones can be quantitatively extracted from soybeans with 50% ethanol at 60 degrees C using ultrasound-assisted extraction in 20 min.     

Conformation of N,N′-bis (2,6-dimethylmorpholino), N″-dichloroacetyl phosphoric triamide: CHCl2C(O)NHP(O)[2,6(CH3)2(NC4H6O)]2. NMR and ab initio studies

Using phosphorus pentachloride as a substrate, a new carbacyclamidophosphate, N,N″-bis (2,6-dimethylmorpholino), N″-dichloroacetyl phosphoric triamide (1) has been synthesized and characterized by ¹H, ³¹P and ¹³C NMR, IR spectroscopy and elemental analysis. Due to the presence of methyl disubstituted morpholine rings and the dichloroacetamide group, several conformers can be considered for this molecule. The ³¹P{¹H} NMR spectra for the isomeric mixture of synthesized compound showed four signals with the ratio 67.1; 19.0; 12.2; 1.7, which indicates four independent conformers. The ¹H NMR spectra confirmed these results. The conformational space and the molecular geometry of the molecule in the gaseous phase have been studied using the B3LYP method of approximation, with 6-31G and 6-311++G^** basis sets.     

2,2′-biimidazole, 2,2′-bibenzimidazole and imidazoles as ligands in cationic rhodium(I) complexes

Summary Cationic rhodium(I) complexes of the type [Rh(diolefin)(L-L)]ClO₄ and [Rh(diolefin)L₂]ClO₄, (diolefin = 1,5-cyclooctadiene, 2,5-norbornadiene and tetrafluorobenzobarrelene; L-L = 2,2-biimidazole, 2,2-bibenzimidazole; L = pyrazole or imidazoles) are described. [Rh(CO)₂(L-L)]-C1O₄ complexes, which can be obtained by reaction of cyclooctadiene derivatives with CO, react with P-donor ligands in equimolar ratios to yield [Rh(CO)(P-donor)(L-L)]ClO₄ monocarbonyl derivatives. The catalytic activity of some of these complexes is considered.     

Indolylgold(I) derivatives and indole as π-arene ligands in cationic rhodium(I) complexes

The reaction of LAuIn (L = P(C₆H₅)₃, P(2-MeC₆H₄)₃ or P(4-MeC₆H₄)₃; In = indolyl group) with the solvated complexes [(diolefin)Rh(Me₂CO)_x]ClO₄ gives the novel heterometallic complexes [(diolefin)Rh(μ-In)AuL]ClO₄. The mononuclear arene derivatives [(diolefin)Rh(η⁶-HIn)]ClO₄ react with methanolic KOH to give the binuclear complexes [(diolefin)Rh(μ-OMe)]₂, while [(COD)Rh(η⁶-HIn)]ClO₄ reacts with KOH in water/acetone to give the hydroxo-bridged complex [(COD)Rh(μ-OH)]₂.     

Total assignment of 1H and 13C NMR data for the sesquiterpene lactone 15-deoxygoyazensolide

We describe a complete analysis of the 1H and 13C spectra of the anti-inflamatory, schistossomicidal and trypanosomicidal sesquiterpene lactone 15-deoxygoyazensolide. This lactone, with a structure similar to other important ones, was studied by NMR techniques such as COSY, HMQC, HMBC, Jres and NOE experiments. The comparison of the data with some computational results led to an unequivocal assignment of all hydrogen and carbon chemical shifts, even eliminating some previous ambiguities. We were able to determine all hydrogen coupling constants (J) and signal multiplicities and to confirm the stereochemistry. A new method for the determination of the relative position of the lactonization and the position of the ester group on a medium-sized ring by NMR was developed.