A Six-Vertex Theorem for Bounding Normal Planar Curves

We prove that the number of vertices of a smooth normal planarcurve is at least 6, if it bounds a surface other than the disk.     

Determination of thiamine HCl and pyridoxine HCl in pharmaceutical preparations using UV-visible spectrophotometry and genetic algorithm based multivariate calibration methods

Simultaneous determination of binary mixtures pyridoxine hydrochloride and thiamine hydrochloride in a vitamin combination using UV-visible spectrophotometry and classical least squares (CLS) and three newly developed genetic algorithm (GA) based multivariate calibration methods was demonstrated. The three genetic multivariate calibration methods are Genetic Classical Least Squares (GCLS), Genetic Inverse Least Squares (GILS) and Genetic Regression (GR). The sample data set contains the UV-visible spectra of 30 synthetic mixtures (8 to 40 microg/ml) of these vitamins and 10 tablets containing 250 mg from each vitamin. The spectra cover the range from 200 to 330 nm in 0.1 nm intervals. Several calibration models were built with the four methods for the two components. Overall, the standard error of calibration (SEC) and the standard error of prediction (SEP) for the synthetic data were in the range of <0.01 and 0.43 microg/ml for all the four methods. The SEP values for the tablets were in the range of 2.91 and 11.51 mg/tablets. A comparison of genetic algorithm selected wavelengths for each component using GR method was also included.     

Synthesis of 5,6-O-Cyclohexylidene-1-amino-3-azahexane and Its Co(II), Ni(II), Cu(II) Complexes

5,6-O-Cyclohexylidene-1-amino-3-azahexane (L) is synthesized from 1-chloro-2,3-O-cyclohexylidenepropane, which is prepared by the reaction between epichlorohydrin and cyclohexanone. In this reaction, BF₃ · OEt₂ is used as a catalyst. Complexes of Co(II), Ni(II) and Cu(II) acetates with this ligand are prepared. The structures of the ligand and its complexes are proposed based on elemental analysis, IR and UV-VIS spectroscopy, magnetic susceptibility, conductometry, and ¹H and ¹³C NMR spectroscopy.     

Effect of electrolytes on the surface behavior of rhamnolipids R1 and R2

The surface behavior of solutions of the rhamnolipids, R1 and R2, were investigated in the absence and presence of an electrolyte (NaCl) through surface tension measurements and optical microscopy at pH 6.8. The NaCl concentrations studied are 0.05, 0.5 and 1 M. Electrolytes directly affect the carboxylate groups of the rhamnolipids. The solution/air interface has a net negative charge due to the dissociated carboxylate ions at pH 6.8 with strong repulsive electrostatic forces between the rhamnolipid molecules. This negative charge is shielded by the Na⁺ ions in the electrical double layer in the presence of NaCl, causing the formation of a close-packed monolayer, and a decrease in CMC, and surface tension values. The maximum compaction is observed at 0.5 M NaCl concentrations for R1 and R2 monolayers, with the R1 monolayer more compact than R2. The larger spaces left below the hydrophobic tails of R1 with respect to that of R2, due to the missing second rhamnosyl groups are thought to be responsible for the higher compaction. The rigidity of both R1 and R2 monolayers increases with the electrolyte concentration. The rigidity of the R1 monolayer is greater than that of R2 at all NaCl concentrations due to the lower hydrophilic character of R1. The variation of CMC values as a function of NaCl concentration obtained from the surface tension measurements and critical packing parameter (CPP) calculations show that spherical micelles, bilayer and rod like micelles are formed in the rhamnolipid solutions as a function of the NaCl concentration. The results of optical microscopy supported these aggregation states indicating lamellar nematic liquid crystal, cubic lamellar and hexagonal liquid crystal phases in R1 and R2 solutions depending on the NaCl concentration.     

Synthesis and determination of pKa values of some new 3,4-disubstituted-4,5-dihydro-1H-1,2,4-triazol-5-one derivatives in non-aqueous solvents

3-Alkyl(Aryl)-4-amino-4,5-dihydro-1H-1,2,4-triazol-5-ones (2) reacted with 2-furoyl chloride and thiophene-2-carbonyl chloride to afford the corresponding 3- alkyl(aryl)-4-(2-furoylamino)-4,5-dihydro-1H-1,2,4-triazol-5-ones (3) and 3-alkyl(aryl)- 4-(2-thienylcarbonylamino)-4,5-dihydro-1H-1,2,4-triazol-5-ones (4), respectively. The new compounds synthesized were characterized by using IR, 1H-NMR, 13C-NMR and UV spectral data together with elemental analysis. In addition, to investigate the effects of solvents and molecular structure upon acidity, compounds 3 and 4 were titrated potentiometrically with tetrabutylammonium hydroxide in four non-aqueous solvents (isopropyl alcohol, tert-butyl alcohol, N,N-dimethylformamide and acetonitrile). The half-neutralization potential values and the corresponding pKa values were determined for all cases.     

Ultrasensitive fluorescent probe for the hydrophobic range of solvent polarities

The new 3-hydroxychromone derivative 2-(6-diethylaminobenzo[b]furan-2-yl)-3-hydroxychromone (FA) displays a dramatic solvent-dependent transformation of fluorescence spectra in the range of low-polarity solvents. The two well-separated emission bands change their relative intensities so that the short-wavelength band being of a very low intensity in hexane becomes dominant in the more polar ethyl acetate and trichloromethane. We suggest the participation in this effect of excited-state intramolecular proton transfer, which is characteristic for other 3-hydroxychromone and 3-hydroxyflavone derivatives, in the range of solvents of much higher polarities. Because of these unique properties, a number of spectroscopic parameters (positions of absorption and two fluorescence maxima, the ratio of their intensities and the fluorescence quantum yield) can be measured in this solvent range with multiparametric analysis of the data. In terms of solvent polarity, the shifts in both emission bands and their intensity ratio demonstrate a good correlation with empirical polarity scales E_T^N, P_y and SPP, while the absorption spectra reveal some deviations for the tested oxygen-containing solvent molecules. A good cross-correlation is observed between fluorescence spectral shifts and the ratio of band intensities. The latter provides the means for a dramatic amplification of solvent response. Thus, a new approach for ultrasensitive scaling and probing the solvent polarity in the low-polararity range can be suggested. It involves very simple ratiometric measurements at two emission bands and can be posed for a variety of applications. We present examples of these applications for distinguishing of polarities between methylated benzene derivatives, for quantitative assay of polar impurities in low-polar solvents and for detection of the changes of solvent polarity as a function of temperature.     

Eta6-mesityl,eta1-imidazolinylidene-carbene-ruthenium(II) complexes: catalytic activity of their allenylidene derivatives in alkene metathesis and cycloisomerisation reactions

The reaction of electron-rich carbene-precursor olefins containing two imidazolinylidene moieties [(2,4,6-Me(3)C(6)H(2)CH(2))NCH(2)CH(2)N(R)Cdbond;](2) (2a: R=CH(2)CH(2)OMe, 2 b R=CH(2)Mes), bearing at least one 2,4,6-trimethylbenzyl (R=CH(2)Mes) group on the nitrogen atom, with [RuCl(2)(arene)](2) (arene=p-cymene, hexamethylbenzene) selectively leads to two types of complexes. The cleavage of the chloride bridges occurs first to yield the expected (carbene) (arene)ruthenium(II) complex 3. Then a further arene displacement reaction takes place to give the chelated eta(6)-mesityl,eta(1)-carbene-ruthenium complexes 4 and 5. An analogous eta(6)-arene,eta(1)-carbene complex with a benzimidazole frame 6 was isolated from an in situ reaction between [RuCl(2)(p-cymene)](2), the corresponding benzimidazolium salt and cesium carbonate. On heating, the RuCl(2)(imidazolinylidene) (p-cymene) complex 8, with p-methoxybenzyl pendent groups attached to the N atoms, leads to intramolecular p-cymene displacement and to the chelated eta(6)-arene,eta(1)-carbene complex 9. On reaction with AgOTf and the propargylic alcohol HCtbond;CCPh(2)OH, compounds 4-6 were transformed into the corresponding ruthenium allenylidene intermediates (4-->10, 5-->11, 6-->12). The in situ generated intermediates 10-12 were found to be active and selective catalysts for ring-closing metathesis (RCM) or cycloisomerisation reactions depending on the nature of the 1,6-dienes. Two complexes [RuCl(2)[eta(1)-CN(CH(2)C(6)H(2)Me(3)-2,4,6)CH(2)CH(2)N- (CH(2)CH(2)OMe)](C(6)Me(6))] 3 with a monodentate carbene ligand and [RuCl(2)[eta(1)-CN[CH(2)(eta(6)-C(6)H(2)Me(3)-2,4,6)]CH(2)CH(2)N-(CH(2)C(6)H(2)Me(3)-2,4,6)]] 5 with a chelating carbene-arene ligand were characterised by X-ray crystallography.     

cyc-DEP: Cyclic immunofluorescence profiling of particles collected using dielectrophoresis

Cancer is a highly heterogenous disease that requires precise detection tools and active surveillance methods. Liquid biopsy assays provide an agnostic way to follow the complex trajectory of cancer, providing better patient stratification tools for optimized treatment. Here, we present the development of a low-volume liquid biopsy assay called cyc-DEP (cyclic immunofluorescent imaging on dielectrophoretic chip) to profile biomarkers collected on a dielectrophoretic microfluidic chip platform. To enable on-chip cyclic imaging, we optimized a fluorophore quenching method and sequential rounds of on-chip staining with fluorescently conjugated primary antibodies. cyc-DEP allows for the quantification of a multiplex array of proteins using 25 µl of a patient plasma sample. We utilized nanoparticles from a prostate adenocarcinoma (LNCaP) cell line and a panel of six target proteins to develop our proof-of-concept technique. We then used cyc-DEP to quantify blood plasma levels of target proteins from healthy individuals, low-grade and high-grade prostate cancer patients (n = 3 each) in order to demonstrate that our platform is suitable for liquid biopsy analysis in its present form. To ensure accurate quantification of signal intensities and comparisons between different samples, we incorporated a signal intensity normalization method (fluorescent beads) and a custom signal intensity quantification algorithm that account for the distribution of signal across hundreds of collection regions on each chip. Our technique enabled a threefold improvement in multiplicity for detecting proteins associated with fluid samples, opening doors for early detection, and active surveillance through quantification of a multiplex array of biomarkers from low-volume liquid biopsies.     

Faithful qubit distribution assisted by one additional qubit against collective noise

We propose a distribution scheme of polarization states of a single photon over a collective-noise channel. By adding one extra photon with a fixed polarization, we can protect the state against collective noise via a parity-check measurement and postselection. While the scheme succeeds only probabilistically, it is simpler and more flexible than the schemes utilizing decoherence-free subspace. An application to the Bennett-Brassard 1984 protocol through a collective-noise channel, which is robust to the Trojan horse attack, is also given.