The Orbit Rigidity Matrix of a Symmetric Framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions.     

Development and reproducibility of a novel high‐performance liquid‐chromatography monolithic column method for the detection and quantification of trans‐indolyl‐3‐acryloylglycine in human urine

Elevated levels of trans‐indolyl‐3‐acryloylglycine (IAcrGly) have been reported in the urine of people with various conditions including pervasive developmental disorders (PDDs) such as autism and Asperger syndrome. Reversed‐phase high‐performance liquid chromatography with ultra‐violet detection using traditional particle silica‐based columns subsequent to solid‐phase extraction (SPE) has been the preferred assay method; requiring long analytical run times, high flow rates and high solvent usage. Recent developments in monolithic HPLC column technology facilitated the development of a novel analytical method, for the detection and quantification of urinary IAcrGly. The revised method eliminates the requirement for SPE pre‐treatment, reduces sample run‐time and decreases solvent volumes. Five urine samples from people diagnosed with PDD were run in quadruplicate to test the intra‐ and inter‐day reliability of the new method based on retention time, peak area and peak height for IAcrGly. Detection was by UV with IAcrGly confirmation by MS/MS‐MS. Relative standard deviations showed significant improvement with the new method for all parameters. The new method represents a major advancement in the detection and quantification of IAcrGly by reducing time and cost of analysis whilst improving detection limits and reproducibility. Copyright © 2009 John Wiley & Sons, Ltd.     

Ueber die Bestimmung von Gerbs?ure

Ohne Zusammenfassung     

Rigidity and polarity

Any projective polarity in 3-space transforms a statically (or equivalently, infinitesimally) rigid bar-and-joint framework into a statically rigid hinged sheetwork — a set of plane-statically rigid sheets, joined in pairs along hinge lines. In the more general class of jointed sheetworks, which is closed under polarity, static rigidity is also preserved by the polarities. In particular, the class of infinitesimally (or statically) rigid polyhedra, built with joints at the vertices and bars triangulating the faces, is closed under polarity.Work supported, in part, by grants from N.S.E.R.C. (Canada) and F.C.A.C. (Quebec), and a visiting appointment at McGill University.     

Analysis of chromates for traces of Cr(III) by solvent extraction and inductively coupled plasma atomic emission spectrometry

Summary A method for the determination of quantities of 0.5–500 g of Cr(III) in the presence of chromates and dichromates is described. The samples are dissolved in an aqueous solution buffered at pH 7.0; the Cr(III) is selectively chelated with 2-thenoyltrifluoroacetone and extracted into xylene. The extracted chromium is analyzed using inductively coupled plasma emission spectrometry. Extraction of 1.0 g Cr(III) from 5.0 mg K₂Cr₂O₇ was accomplished and easily determined in a volume of 25 ml of xylene. The relative standard deviation for the determination of Cr(III) contents ranging from 4.0 × 10^–8 g/ml to 2.0 × 10^–8 g/ml was ± 0.079. Using a minimum signal to noise ratio of 101, the detection limits of the method were determined to be approximately 2.0 × 10^–8 g/ml xylene. Chloride, high surface area silica, and easily oxidized amorphous boron give rise to only minor interferences.

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Analyse von Cr(III)-Spuren in Chromaten durch Extraktion und ICP-Atomemissionsspektrometrie

Zusammenfassung Ein Verfahren wird beschrieben zur Bestimmung von 0,5–500 g Cr(III) in Gegenwart von Chromaten und Dichromaten. Die Proben werden in Pufferlösung pH 7,0 gelöst, und 2-Thenoyltrifluoraceton behandelt und Cr(III) selektiv mit Xylol extrahiert. Die Bestimmung erfolgt durch ICP-Spektrometrie. 1,0 g Cr(III) konnte von 5,0 mg K₂Cr₂O₇ getrennt und in einen Volumen von 25 ml Xylol bestimmt werden. Die relative Standardabweichung im Bereich von 4,0 · 10^–8 bis 2,0 · 10^–7 g Cr(III)/ml betrug ± 0,079. Bei einem Verhältnis SignalUntergrund = 101 wurden Nachweisgrenzen um 2,0 · 10^–8 g/ml gefunden. Störungen durch Chlorid, Siliciumdioxid und amorphes Bor sind gering.

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This work was supported by the U.S. Department of Energy (DOE) under contract number DE-AC04-76-DP00789

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A U.S. DOE facility     

Transition metal derivatives of 1,1′-dichloroferrocene

Complexes of the general formula [Cl₂Fc] _nML, (Cl₂Fc = C1C₅H₄FeC₅H₃Cl; ML = Fe(CO)₂C₅H₅, AuP(C₆H₅)₃, Mn(CO)₅ or Ir(CO)[P(C₆H₅)₃]₂ when n = 1; ML = Ti(C₅H₅)₂ when n = 2) have been prepared from a salt elimination reaction between 1,1′-dichloro-2-lithioferrocene and transition metal halide complexes. Spectroscopic properties of the compounds are reported. The titanium complex exists in meso and dl forms.     

Controlled Production of Fructose by an Exoinulinase from <Emphasis Type="Italic">Aspergillus Ficuum</Emphasis>

An exoinulinase has been isolated, purified and characterised from a commercially available broth of Aspergillus ficuum. The enzyme was purified 4.2-fold in a 21% yield with a specific activity of 12,300 U mg⁻¹(protein) after dialysis, ammonium sulphate fractionation and Sephacryl S-200 size exclusion and ion exchange chromatography. The molecular weight of this enzyme was estimated to be 63 kDa by SDS-PAGE. It exhibited a pH and temperature optima of 5.4 and 50 °C respectively and under such conditions the enzyme remained stable with 96% and 63.8% residual activity after incubation for 12 h and 72 h respectively. The respective K _m and V _max values were 4.75 mM and 833.3 μmol min⁻¹ ml⁻¹, respectively. Response surface methodological statistical analysis was evaluated for the maximal production of fructose from the hydrolysis of pure commercial chicory inulin. Incubation of the dialyzed crude exoinulinase (100 U/ml, 48 h, 50 °C, 150% inulin, pH 5.0) produced the highest amount of fructose (106.4 mg/ml) under static batch conditions. The purified exoinulinase was evaluated for fructose production and the highest amount (98 mg/ml) was produced after 12 h incubation at 50 °C, 150% inulin pH 5.0. The use of a crude exoinulinase preparation is economically desirable and the industrial production of fructose from inulin hydrolysis is biotechnologically feasible.     

Enhanced activity of chaperonin GroEL in the presence of platinum nanoparticles

The chaperonin protein GroEL was mixed with varying concentrations of K₂PtCl₄ followed by a 20-fold concentration of sodium borohydride to afford GroEL–platinum nanoparticle complexes in a ratio of between 1:25 and 1:2,000. Typical colour change, from colourless or pale yellow to brown, occurred that was dependent on the amount of platinum present. These complexes were characterised by UV/Vis, inductively coupled plasma optical emission spectroscopy, Fourier transform infra red, transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy. TEM analysis revealed that the size of nanoparticles increased as the molar ratio of platinum to GroEL increased with an average size diameter of 1.72–3.5 nm generated with GroEL–platinum molar ratios of 1:125–1:2,000. Fourier-transform infrared spectroscopy (FTIR) spectra showed no distinct changes in the structure of GroEL but confirmed that the nanoparticles were attached to the protein. The effect of platinum nanoparticles on the ATPase activity of GroEL showed an activity of 5.60 μmol min⁻¹ ml⁻¹ (87 % increase over a control) at the molar ratio of GroEL–platinum nanoparticles of 1:25.     

Novel Solventless Extraction Technique to Preserve Cannabinoid and Terpenoid Profiles of Fresh Cannabis Inflorescence

Despite its use by humans for thousands of years, the technology of cannabis usage and extraction is still evolving. Given that the primary pharmacological compounds of interest are cannabinoid and terpenoids found in greatest abundance in capitate glandular trichomes of unfertilized female inflorescences, it is surprising that older techniques of hashish making have received less technological advancement. The purpose of this study was to employ organically grown cannabis and to isolate pure trichomes from freshly picked flowers via exposure to vapor from solid CO₂, commonly known as “dry ice”, followed by their isolation via sifting through a 150 µ screens while maintaining the cold chain. Biochemical analysis was undertaken on fresh flower, frozen-sifted flower by-products, treated trichomes (Kryo-Kief™), dried flower, dried sifted flower by-product and dried kief. The dry ice process successfully concentrated cannabinoid content as high as 60.7%, with corresponding concentration and preservation of monoterpenoids encountered in fresh flower that are usually lost during the conventional cannabis drying and curing process. The resulting dried sifted flower by-product after dry ice processing remains a usable commodity. This approach may be of interest to pharmaceutical companies and supplement producers pursuing cannabis-based medicine development with an eye toward full synergy of ingredients harnessing the entourage effect.