Rational Ehrhart quasi-polynomials

Ehrhart?s famous theorem states that the number of integral points in a rational polytope is a quasi-polynomial in the integral dilation factor. We study the case of rational dilation factors. It turns out that the number of integral points can still be written as a rational quasi-polynomial. Furthermore, the coefficients of this rational quasi-polynomial are piecewise polynomial functions and related to each other by derivation.     

Continuous extension operators and convexity

Given a nonempty closed subset A of a Hilbert space X, we denote by L(A) the space of all bounded Lipschitz mappings from A into X, equipped with the supremum norm. We show that there is a continuous mapping F_c:L(A)?L(X) such that for each g∈L(A), F_c(g)|_A=g, , and . We also prove that the corresponding set-valued extension operator is lower semicontinuous.     

A genetic algorithm for the unrelated parallel machine scheduling problem with sequence dependent setup times

In this work a genetic algorithm is presented for the unrelated parallel machine scheduling problem in which machine and job sequence dependent setup times are considered. The proposed genetic algorithm includes a fast local search and a local search enhanced crossover operator. Two versions of the algorithm are obtained after extensive calibrations using the Design of Experiments (DOE) approach. We review, evaluate and compare the proposed algorithm against the best methods known from the literature. We also develop a benchmark of small and large instances to carry out the computational experiments. After an exhaustive computational and statistical analysis we can conclude that the proposed method shows an excellent performance overcoming the rest of the evaluated methods in a comprehensive benchmark set of instances.     

Contactless Conductivity Detection in Capillary Electrophoresis Employing Capillaries with Very Low Inner Diameters

The behaviour of a contactless conductivity detector was studied in its application to capillary electrophoresis employing quartz capillaries with inner diameters (i.d.) of 10 to 75 µm. The detector output signal was measured using KCl as the test electrolyte, within a KCl concentration range from 0 to 100 mmol/L, corresponding to specific conductivities from 0 to 1295 mS/m. When using capillaries with high inner diameters, then the signal‐to‐noise ratio is high in electrolytes of low conductivity. On the other hand, the use of capillaries with low i.d. values is useful in separations employing solutions of high conductivities. The advantages of capillaries with small i.d. values, combined with contactless conductivity detection, are demonstrated on separations of mixtures of inorganic ions and on separations of neutral mono‐ and disaccharides.     

Transition Metal Ions: Charge Carriers that Mediate the Electron Capture Dissociation Pathways of Peptides

Electron capture dissociation (ECD) of model peptides adducted with first row divalent transition metal ions, including Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺, were investigated. Model peptides with general sequence of ZGGGXGGGZ were used as probes to unveil the ECD mechanism of metalated peptides, where X is either V or W; and Z is either R or N. Peptides metalated with different divalent transition metal ions were found to generate different ECD tandem mass spectra. ECD spectra of peptides metalated by Mn²⁺ and Zn²⁺ were similar to those generated by ECD of peptides adducted with alkaline earth metal ions. Series of c-/z-type fragment ions with and without metal ions were observed. ECD of Fe²⁺, Co²⁺, and Ni²⁺ adducted peptides yielded abundant metalated a-/y-type fragment ions; whereas ECD of Cu²⁺ adducted peptides generated predominantly metalated b-/y-type fragment ions. From the present experimental results, it was postulated that electronic configuration of metal ions is an important factor in determining the ECD behavior of the metalated peptides. Due presumably to the stability of the electronic configuration, metal ions with fully-filled (i.e., Zn²⁺) and half filled (i.e., Mn²⁺) d-orbitals might not capture the incoming electron. Dissociation of the metal ions adducted peptides would proceed through the usual ECD channel(s) via “hot-hydrogen” or “superbase” intermediates, to form series of c-/z ^•- fragments. For other transition metal ions studied, reduction of the metal ions might occur preferentially. The energy liberated by the metal ion reduction would provide enough internal energy to generate the “slow-heating” type of fragment ions, i.e., metalated a-/y- fragments and metalated b-/y- fragments.     

Alkynylisocyanide gold mesogens as precursors of gold nanoparticles

Gold nanoparticles (Au NPs) have been synthesized using simple thermolysis, whether from the mesophase or from toluene solutions, of mesogenic alkynyl-isocyanide gold complexes [Au(C≡C-C(6)H(4)-C(m)H(2m+1))(C≡N-C(6)H(4)-O-C(n)H(2n+1))]. The thermal decomposition from the mesophase is much slower than from solution and produces a more heterogeneous size distribution of the nanoparticles. Working in toluene solution, the size of nanoparticles can be modulated from ~2 to ~20 nm by tuning the chain lengths of the ligands present in the precursor. Different experimental conditions have been analyzed to reveal the processes governing the formation of the gold nanoparticles. Experiments on the effect of adding ligands or bubbling oxygen support that the thermal decomposition is a bimolecular process that starts by decoordination of the isocyanide ligand, producing an oxidative coupling of the akynyl group to [R-C≡C-C≡C-R] and reduction of gold(I) to gold(0) as nanoparticles. The nanoparticles obtained behave as a catalyst in the oxidation of isocyanide (CNR) to isocyanate (OCNR), which in turn cooperates to catalyze the decomposition.     

Fluorescence detection by intensity changes for high-performance thin-layer chromatography separation of lipids using automated multiple development

Changes in emission of berberine cation, induced by non-covalent interactions with lipids on silica gel plates, can be used for detecting and quantifying lipids using fluorescence scanning densitometry in HPTLC analysis. This procedure, referred to as fluorescence detection by intensity changes (FDIC) has been used here in combination with automated multiple development (HPTLC/AMD), a gradient-based separation HPTLC technique, for separating, detecting and quantifying lipids from different families. Three different HPTLC/AMD gradient schemes have been developed for separating: neutral lipid families and steryl glycosides; different sphingolipids; and sphingosine-sphinganine mixtures. Fluorescent molar responses of studied lipids, and differences in response among different lipid families have been rationalized in the light of a previously proposed model of FDIC response, which is based on ion-induced dipole interactions between the fluorophore and the analyte. Likewise, computational calculations using molecular mechanics have also been a complementary useful tool to explain high FDIC responses of cholesteryl and steryl-derivatives, and moderate responses of sphingolipids. An explanation for the high FDIC response of cholesterol, whose limit of detection (LOD) is 5 ng, has been proposed. Advantages and limitations of FDIC application have also been discussed.     

Methods for determination of all binding parameters in systems with simultaneous borate and cyclodextrin complexation

Two novel methods for determination of binding constants in the systems with borate and cyclodextrin complexation were developed. The methods enable to determine all binding parameters in these systems and even the binding constants of interaction of a neutral analyte with a neutral cyclodextrin. The first method is based on nonlinear fitting of experimental data and further evaluation of fitting parameters. The second method requires a multiple regression. The methods provide identical results with low experimental error. Only one set of measurements is required for both methods. Thus the binding parameters can be mutually compared. The binding parameters for neutral analytes ((R,R)-(+)-hydrobenzoin and (S,S)-(-)-hydrobenzoin) and neutral cyclodextrin (heptakis(2,6-di-O-methyl)-β-cyclodextrin) were evaluated and the effect of individual types of interaction was revealed. The interaction of the analytes with cyclodextrin governs the chiral recognition, while the complexation of analyte with borate is responsible for electromigration. Very low values of the binding constants of mixed analyte-cyclodextrin-borate complexes indicate that this type of complexation has negligible effect on enantioseparation.     

Synthesis of potent and orally efficacious 11β-hydroxysteroid dehydrogenase type 1 inhibitor HSD-016

Cortisol and the glucocorticoid receptor (GR) signaling pathway has been linked to the development of diabetes and metabolic syndrome. In vivo, 11β-hydroxysteroid dehydrogenase type 1 (11β-HSD1) catalyzes the conversion of inactive cortisone to its active form, cortisol. Existing clinical data have supported 11β-HSD1 as a valid therapeutic target for type 2 diabetes. In our research program, (R)-1,1,1-trifluoro-2-(3-((R)-4-(4-fluoro-2-(trifluoromethyl)phenyl)-2-methylpiperazin-1-ylsulfonyl)phenyl)propan-2-ol (HSD-016) was discovered to be a potent, selective, and efficacious 11β-HSD1 inhibitor and advanced as a clinical candidate. Herein, a reliable and scalable synthesis of HSD-016 is described. Key transformations include an asymmetric synthesis of a chiral tertiary alcohol via Sharpless dihydroxylation, epoxide formation, and subsequent mild reduction. This route ensured multikilogram quantities of HSD-016 necessary for clinical studies.     

Glycoclusters presenting lactose on calix[4]arene cores display trypanocidal activity

A new series of water-soluble tetravalent glycoclusters incorporating β-lactosyl residues attached to a central calix[4]arene core was synthesised using azide-alkyne Cu(I)-catalysed cycloaddition (‘click chemistry’). Carbohydrate moieties were attached either to the upper or lower rim of rigid cone-shaped or partial cone macrocycles via 14-21 atom spacer arms. The glycoclusters with a C₄-symmetrical arrangement of β-lactosyl residues showed trypanocidal activity, with one of them showing comparable activity to established anti-trypanosomal drug benznidazole in in vitro anti-parasite assays.