The Representation Polyhedron of a Semiorder

Let a finite semiorder, or unit interval order, be given. When suitably defined, its numerical representations are the solutions of a system of linear inequalities. They thus form a convex polyhedron. We show that the facets of the representation polyhedron correspond to the noses and hollows of the semiorder. Our main result is to prove that the system defining the polyhedron is totally dual integral. As a consequence, the coordinates of the vertices and the components of the extreme rays of the polyhedron are all integral multiples of a common value. Total dual integrality is in turn derived from a particular property of the oriented cycles in the directed graph of noses and hollows of a strictly upper diagonal step tableau. Our approach delivers also a new proof for the existence of the minimal representation of a semiorder, a concept originally discovered by Pirlot (Theory Decis 28:109–141, 1990). Finding combinatorial interpretations of the vertices and extreme rays of the representation polyhedron is left for future work.     

In Situ Generated Gold Nanoparticles on Active Carbon as Reusable Highly Efficient Catalysts for a C −C Stille Coupling

Gold nanoparticle catalysts are important in many industrial production processes. Nevertheless, for traditional C ?C cross‐coupling reactions they have been rarely used and Pd catalysts usually give a superior performance. Herein we report that in situ formed gold metal nanoparticles are highly active catalysts for the cross coupling of allylstannanes and activated alkylbromides to form C ?C bonds. Turnover numbers up to 29 000 could be achieved in the presence of active carbon as solid support, which allowed for convenient catalyst recovery and reuse. The present study is a rare case where a gold metal catalyst is superior to Pd catalysts in a cross‐coupling reaction of an organic halide and an organometallic reagent.     

Phosphine-Catalyzed [3+2] Cycloaddition of Aza-Aurones and Allenoates: Enantioselective Synthesis of 2-Spirocyclopentyl-Indolin-3-Ones

An enantioselective phosphine-catalyzed [3+2] cycloaddition between aza-aurones and allenoates is here described. The reaction proceeded under mild reaction conditions to afford 2-spirocyclopentyl indolin-3-one derivatives as single γ-isomer and with high levels of stereocontrol.     

Crystal structure and cytotoxic activities of a bis(pyrrolyl-imine) gold(III) complex

A gold(III) complex with N,N′-ethylenebis(pyrrol-2-yl-methyleneamine) (H₂pyren) was synthesized and characterized by physicochemical and spectroscopic measurements. Density functional theory (DFT) studies and cytotoxic assays were performed. Infrared, mass spectrometry, and ¹H, ¹³C, and {¹⁵N,¹H} nuclear magnetic resonance analyses indicate that pyren is deprotonated and gold(III) is four coordinate in a square planar environment, with the pyrrole and imine nitrogens as donors. The structure was confirmed by powder X-ray diffraction and confirmed as a minimum of the potential energy surface by DFT. Cytotoxic activity of [Au(pyren)]⁺ was active against three tumorigenic cell lines with IC₅₀ values of 35 μM. Interaction studies with CT-DNA by fluorescence and competition with ethidium bromide (EB) showed a quenching of the emission band of DNA with a Stern–Volmer quenching constant value of (3.0 ± 0.1) × 10⁴ M^?1 and a decrease in fluorescence quenching of EB-DNA system, respectively, confirming that DNA is a possible target for the complex via an intercalative binding, which was confirmed by DNA conformational changes observed with circular dichroism spectroscopy.     

Novel functionalized pyridine-containing DTPA-like ligand. Synthesis, computational studies and characterization of the corresponding Gd(III) complex

A novel pyridine-containing DTPA-like ligand, carrying additional hydroxymethyl groups on the pyridine side-arms, was synthesized in 5 steps. The corresponding Gd(III) complex, potentially useful as an MRI contrast agent, was prepared and characterized in detail by relaxometric methods and its structure modeled by computational methods.     

In-channel atom-transfer radical polymerization of thermoset polyester microfluidic devices for bioanalytical applications

A new technique for polymer microchannel surface modification, called in-channel atom-transfer radical polymerization, has been developed and applied in the surface derivatization of thermoset polyester (TPE) microdevices with poly(ethylene glycol) (PEG). X-ray photoelectron spectroscopy, electroosmotic flow (EOF), and contact angle measurements indicate that PEG has been grafted on the TPE surface. Moreover, PEG-modified microchannels have much lower and more pH-stable EOF, more hydrophilic surfaces and reduced nonspecific protein adsorption. Capillary electrophoresis separation of amino acid and peptide mixtures in these PEG-modified TPE microchips had good reproducibility. Phosducin-like protein and phosphorylated phosducin-like protein were also separated to measure the phosphorylation efficiency. Our results indicate that PEG-grafted TPE microchips have broad potential application in biomolecular analysis.     

On the evaluation of the anisotropic-isotropic transition volume fraction for a semirigid polymer

It has been found that a method allowing the calculation of an anisotropic-isotropic transition volume fraction for a given semirigid polymer can be derived from the equations recently proposed by Blonski and coworkers to evaluate the equilibrium compositions of isotropic and anisotropic phases coexisting within ternary systems semirigid polymer/flexible polymer/solvent. By using the term anisotropic-isotropic transition volume fraction of a semirigid polymer we will refer to its smallest volume fraction giving an anisotropic character to liquid ternary phases also including a flexible polymer and a solvent. Its evaluation simplifies the construction of the corresponding ternary diagram and can also be seen as a fast and quantitative way of estimating the influence exerted by the semirigid polymer, through its intrinsic anisotropy, on ternary phases.     

NMR properties of sedimented solutes

This perspective paper is intended to give some insights into the recently proposed technique of NMR of solutes sedimented by ultracentrifugation in a rotor used for solid state NMR experiments. Sedimented "states" correspond to molecules with very little reorientational capability in extremely concentrated solutions. They provide solid state NMR spectra comparable in quality with those of the best microcrystalline samples. Here we report some experiments to look for chemicals which affect the properties of the sediment, and we show that it is possible to fill the rotor in a true ultracentrifuge and then record the spectra. The latter possibility opens new horizons for NMR of sedimented systems.     

Analysis of Bile Acids Profile in Human Serum by Ultrafiltration Clean-up and LC-MS/MS

Bile acids (BAs) are useful biomarkers for the diagnosis of many diseases. The pathologies related to bile acid synthesis are often expressed in the first years of life and may lead to serious liver injury. Here we present a sensitive and rapid method for the analysis of the main 14 bile acids in human serum by liquid chromatography-tandem mass spectrometry. The chromatographic separation is performed using a core–shell column which provides improved separation, highly desirable considering the small structural differences among the analytes. All isomeric BAs of interest were resolved in less than 9 min. Sample pretreatment consisted in ultrafiltration of serum after addition of methanol by means of centrifugal filter devices. The calculated LOQs ranged between 2 and 5 ng mL⁻¹ with linearity of the calibration curves in the 5–5,000 ng mL⁻¹ range for all the BAs. The extraction recoveries for all the analytes were higher than 80 %. Intra-day and inter-day coefficients of variation were all below 15 %. The method proposed has been validated and has been applied for the analysis of serum of pediatric patients. This simple procedure allowed minimal consumption of serum sample (about 100 μL) and a rapid assay, easily implementable in routine analysis.