Hamiltonian cycles in cubic 3-connected bipartite planar graphs

We show that 3-connected cubic bipartite planar graphs with fewer than 66 vertices are Hamiltonian.     

Hierarchical models and chaotic spin glasses

Renormalization-group studies in position space have led to the discovery of hierarchical models which are exactly solvable, exhibiting nonclassical critical behavior at finite temperature. Position-space renormalization-group approximations that had been widely and successfully used are in fact alternatively applicable as exact solutions of hierarchical models, this realizability guaranteeing important physical requirements. For example, a hierarchized version of the Sierpiriski gasket is presented, corresponding to a renormalization-group approximation which has quantitatively yielded the multicritical phase diagrams of submonolayers on graphite. Hierarchical models are now being studied directly as a testing ground for new concepts. For example, with the introduction of frustration, chaotic renormalization-group trajectories were obtained for the first time. Thus, strong and weak correlations are randomly intermingled at successive length scales, and a new microscopic picture and mechanism for a spin glass emerges. An upper critical dimension occurs via a boundary crisis mechanism in cluster-hierarchical variants developed to have well-behaved susceptibilities.     

Competitive Sorption of Copper and Nickel Ions from Aqueous Solution Using Peat

Bicomponent aqueous solutions of copper and nickel ions have been used to investigate the sorption of metal ions onto peat. Peat, a low cost sorbent, has shown a high capacity for the sorption of single component metal ions attributed to extensive carboxylic acids within its structure. Copper and nickel ions were selected as typical metals in the effluents of electroplating industries. The effects of competitive sorption in batch systems were studied at various metal ion concentrations. In this study the Butler and Ockrent model was modified using a coefficient, . Two models were developed based on the interaction coefficient . The first model incorporates a constant fixed factor for each metal ion into the Butler-Ockrent equation. The second model incorporates a variable factor into the Butler-Ockrent equation; this interaction factor varies as a function of sorbent surface coverage. Predicted equilibrium data are found to be in excellent agreement with experimental values using both modified models for various mole ratios of copper and nickel ions in competitive sorption.     

Regiospecific synthesis of quinizarin derivatives by cycloaddition

Cycloadditionof ($\text{E}$)-1,1,4-trimethaxy-1,3-butadiene (1) to naphthoquinones affords regiospecific syntheses of derivatives of 1,4-dihydroxyanthraquinone including the mould metabolites helminthosporin (21) and cynodontin (22).     

Determination of extractable perfluorooctanoic acid (PFOA) in water, sweat simulant, saliva simulant, and methanol from textile and carpet samples by LC/MS/MS

Methods were developed to quantify the amount of perfluorooctanoic acid (PFOA) extracted from textile and carpet samples through contact with water, methanol, and sweat and saliva simulants using LC/MS/MS. The limit of quantitation (LOQ) for samples extracted in water and sweat simulant is 1 ppb (ng PFOA (g sample)(-1)) while the limits of quantitation for samples extracted in saliva simulant and methanol were 3 ppb and 2.5 ppb, respectively. Method validation results are provided for a polyester control textile sample that was extracted in water on two different days by different analysts, which gave an overall recovery of 103% and standard deviation of 5.3% for 30 analyses. However, for routine application of these methods to a large number of sample sets differing in chemical and physical compositions, a complete validation for each sample type is not practical or possible since control samples for fortifications are often not available. Instead, suitable analytical methods and acceptance criteria are described which ensure accurate PFOA quantitation in each of the solvent extract types. During routine use of these methods, post-extraction spike recoveries for the different sample types and solvents are 100 +/- 15% using a dual isotopically labeled (13)C-PFOA internal standard to correct for matrix effects. A comparison of extraction solvent versus time using a wrist action shaker for textile and carpet samples demonstrates that the total extractable amount of PFOA is similar for each of the solvent types. However, as expected the rate of extraction in water and simulants is significantly less than that of methanol. Finally, a comparison of 2 h and 24 h wrist action shaker extractions with a 1.5 h pressurized fluid extraction (PFE) in methanol reveals that the 24 h wrist action shaker yields the highest results. The 2 h wrist action shaker results are similar to those of the 1.5 h PFE extraction.     

Comparison of antibody--antigen interactions on collagen measured by conventional immunological techniques and atomic force microscopy

We have developed a means of using atomic force microscopy (AFM) to repeatedly localize a small area of interest (4 x 4 microm(2)) within a 0.5-cm(2) area on a heterogeneous sample, to obtain and localize high-resolution images and force measurements on nonideal samples (i.e., samples that better reflect actual biological systems, not prepared on atomically flat surfaces). We demonstrate the repeated localization and measurement of unbinding forces associated with antibody--antigen (ab--ag) interactions, by applying AFM in air and in liquid to visualize and measure polyclonal ab--ag interactions, using chicken collagen as a model system. We demonstrate that molecular interactions, in the form of ab--ag complexes, can be visualized by AFM when secondary antibodies are conjugated to 20-nm colloidal gold particles. We then compare those results with established immunological techniques, to demonstrate broader application of AFM technology to other systems. Data from AFM studies are compared with results obtained using immunological methods traditionally employed to investigate ab--ag interactions, including enzyme-linked immunosorbent assay, immunoblotting, and in situ immunofluorescence. Finally, using functionalized AFM tips with a flexible tether [poly(ethylene glycol) 800] to which a derivatized antibody was attached, we analyzed force curve data to measure the unbinding force of collagen antibody from its antigen, obtaining a value of approximately 90 +/- 40 pN with a MatLab code written to automate the analyses of force curves obtained in force--volume mode. The methodology we developed for embedded collagen sections can be readily applied to the investigation of other receptor--ligand interactions.