Maxima in hypercubes

We derive a Berry‐Esseen bound, essentially of the order of the square of the standard deviation, for the number of maxima in random samples from (0,1)^d. The bound is, although not optimal, the first of its kind for the number of maxima in dimensions higher than two. The proof uses Poisson processes and Stein's method. We also propose a new method for computing the variance and derive an asymptotic expansion. The methods of proof we propose are of some generality and applicable to other regions such as d‐dimensional simplex. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Liquid Chromatography with Pulsed Amperometric Detection for Speciation of Mercury

Liquid chromatography with pulsed amperometric detection (PAD) at an Au electrode was successfully applied for speciation of mercury: inorganic mercury, methylmercury and ethylmercury. The optimized conditions for triple-step potential waveforms utilized in PAD were: E₁ 1800 mV, t₁ 50 ms; E₂ 300 mV, t₂ 3850 ms; E₃ 750 mV, t₃ 100 ms; mercury oxidation was monitored at E₃. With the eluent of HClO₄ (0.10 M) + KCl (1.0 mM) + CH₃CN (1.0%) at a flow rate 0.80 mL/min, three mercury species were fully separated in 6 min on a glass column (3 mm × 10 cm) packed with Chemcosorb C₁₈ (5 μm). However, the first peak (inorganic mercury) was commonly overlapped by the solvent front. The relative standard deviations (n = 6) for methylmercury (15 ppb) and ethylmercury (30 ppb) were 4.2% and 2.8%, respectively. The linear range tested was 2 – 500 ppb (r = 0.9998) for methylmercury, and was 4 – 1000 ppb (r = 1.000) for ethylmercury. The detection limits (S/N = 3) were 1.2 ppb and 1.8 ppb for methylmercury and ethylmercury, respectively. The results of determination of the mercury-containing species thimerosat in three commercial contact-lens solutions agreed satisfactorily with the expected values.     

Simultaneous Determination of Carbohydrates and Amino Acids by Capillary Zone Electrophoresis with Constant Potential Amperometric Detection at a Copper Electrode

Capillary zone electrophoresis with end-column amperometric detection at a copper microdisk electrode (100 μm in diameter) was successfully applied for simultaneous determination of carbohydrates and amino acids. Under the separation voltage of 27 kV and the separation electrolyte of 80 mM NaOH in a 75 cm fused silica capillary (10 μm i.d. × 375 μmU o.d.), complete separation of a standard mixture containing 9 carbohydrates and 12 amino acids was achieved in less than 25 min. With the electrokinetical injection of 5.4 s at 27 kV and the detection potential of 0.62 V vs. Ag/AgCl, the detection limits (S/N = 3) were 0.22–0.65 ppm (1.2–1.9 μM) for carbohydrates and 0.31–6.5 ppm (2.3–39 μM) for amino acids, respectively. The calculated numbers of theoretical plates were between 41,000 and 190,000. The use of this method for analysis of carbohydrates and amino acids in a urine sample was demonstrated.     

Natural Bond Orbital Rationalizations of NMR Observations for Metal‐Ligand Bonding (II): Rehybridization of Phosphorus Arising from Coordination of Methyl‐Phenyl‐Phosphines

Carbonyls' 2π orbital populations, [2π], in W(CO)₅L {L = PPh₃, PPh₂Me, PPhMe₂} have been determined by NMR spin‐lattice relaxation techniques. Experimental values of axial [2π], compared with those reported for PMe₃ and P(OMe)₃, reveal that PMe₃ is a slightly better π‐acid than PPh₃. Through space interactions between carbonyl and phenyl groups are insignificant since values of [2π] do not vary significantly in the series of phosphines, going from PMep₃ to PPh₃. Natural bond orbital (NBO) studies indicate that π‐accepting capabilities for these phosphines are primarily governed by the nature of P‐C anti‐bonding, σ*_P‐C. Compared with PPh₃, the better π‐accepting σ*_P‐C, as well as the better s‐donating lone‐pair LP(P), in PMe₃ can both be explained by the higher extents of rehybridization of the coordinated phosphorus atom. Based on this rehybridization argument, the NBO predicted order of increasing π‐acidic strengths PPh₃ < PPh₂Me < PPhMe₂ < PMe₃, which cannot be clearly distinguished by NMR experiments, is ascribed to the same NBO trend of σ‐donating capabilities in a synergistic manner. Effects of coordination on P‐Y (Y = C, O, F) bonding strengths in phosphines (or phosphites) are depending on two conflicting effects: rehybridization of LP(P) and the hyperconjugative‐like d_π → σ*_P‐Y back‐donation.     

Synthesis of Polynucleotide Modified Gold Nanoparticles as a High Potent Anti‐Cancer Drug Carrier

Gold nanoparticles have been developed for the photoacoustic imaging, delivery of genes and laser induced photothermal therapy. In this study, we have developed oligonucleotide conjugated gold nanoparticles as the carrier for simultaneous DNA and anti‐cancer nucleoside delivery. The polynucleotidenanoparticle complex presented higher capacity in carrying 5‐FU anti‐cancer compounds than the original gold particles. The hydrodynamic size of the gold nanoparticles increased from 25 to 35 nm with an increase in the negative surface charge from ?9.58 to 21.66 mV after polynucleotide conjugation and drug loading. A positive association between environmental pH and drug release was observed in PBS, which implied their potential use in the controlled localized drug release in the lower GI tract. The MTT assay revealed dose dependent cytotoxicity to colon cancer cell line than free compounds. These results suggest the potential use of this new polynucleotide‐gold nanoparticles complex as the environmental controlled anti‐cancer nanocapsule, especially suitable for per oral colon cancer chemotherapy.     

Preparation of 1H‐1,2,3‐Triazoles by Cuprous Ion Mediated Cycloaddition of Terminal Alkyne and Sodium Azide

1H‐1,2,3‐triazoles can be prepared in good yield by the reaction of terminal alkyne and sodium azide in the presence of cuprous chloride at a temperature higher than 70°C. The alkyne is unactivated and the reaction has to be carried out under inert gas. At room temperature, the reaction first gives a Cu(I)‐azide complex which is converted to a Cu‐alkyne complex when the temperature is raised to higher than 70°C. The reaction of Cu(I)‐alkyne complex and azide ion dissociated from or coordinated to Cu(I) then gives 1H‐1,2,3‐triazoles.