Reducing trigonometric functions by using spokes on a carousel

In this note, a simple and quick method is shown for reducing some trigonometric expressions by using a diagram called a ‘carousel’. These expressions can be reduced using other methods, such as: (i) reduction formulae for sum/difference of angles; and (ii) graph shifting techniques.     

Location of services and the impact on healthcare quality: insights from a simulation of a musculoskeletal physiotherapy service

Many healthcare systems are being redesigned to deliver local care with more services within the community. Relocation may enhance access but other aspects of healthcare quality should also be considered, notably waiting times and equity of care. This study examined a musculoskeletal physiotherapy service using a discrete-event simulation with simple heuristics to model patient behaviour. This combination provided an effective mechanism for incorporating the individuality of the patients in the flows along the patient pathways, subject to the varying availabilities of key resources. In particular, it captured the feedback that is critical in system performance, especially where waiting times are important. The model recognised the heterogeneity of patient attitudes and demonstrated how the behaviour of a relatively small proportion can affect the experience of all patients. The study suggested that, with careful operational management, more care could be delivered locally while exploiting many of the benefits of a centralised service.     

Hydride ion transfer from ruthenium(II) complexes in water: kinetics and mechanism

Reactions of hydride complexes of ruthenium(II) with hydride acceptors have been examined for Ru(terpy)(bpy)H(+), Ru(terpy)(dmb)H(+), and Ru(η(6)-C(6)Me(6))(bpy)(H)(+) in aqueous media at 25 °C (terpy = 2,2';6',2'-terpyridine, bpy = 2,2'-bipyridine, dmb = 4,4'-dimethyl-2,2'-bipyridine). The acceptors include CO(2), CO, CH(2)O, and H(3)O(+). CO reacts with Ru(terpy)(dmb)H(+) with a rate constant of 1.2 (0.2) × 10(1) M(-1) s(-1), but for Ru(η(6)-C(6)Me(6))(bpy)(H)(+), the reaction was very slow, k ≤ 0.1 M(-1) s(-1). Ru(terpy)(bpy)H(+) and Ru(η(6)-C(6)Me(6))(bpy)(H)(+) react with CH(2)O with rate constants of (6 ± 4) × 10(6) and 1.1 × 10(3) M(-1) s(-1), respectively. The reaction of Ru(η(6)-C(6)Me(6))(bpy)(H)(+) with acid exhibits straightforward, second-order kinetics, with the rate proportional to [Ru(η(6)-C(6)Me(6))(bpy)(H)(+)] and [H(3)O(+)] and k = 2.2 × 10(1) M(-1) s(-1) (μ = 0.1 M, Na(2)SO(4) medium). However, for the case of Ru(terpy)(bpy)H(+), the protonation step is very rapid, and only the formation of the product Ru(terpy)(bpy)(H(2)O)(2+) (presumably via a dihydrogen or dihydride complex) is observed with a k(obs) of ca. 4 s(-1). The hydricities of HCO(2)(-), HCO(-), and H(3)CO(-) in water are estimated as +1.48, -0.76, and +1.57 eV/molecule (+34, -17.5, +36 kcal/mol), respectively. Theoretical studies of the reactions with CO(2) reveal a "product-like" transition state with short C-H and long M-H distances. (Reactant) Ru-H stretched 0.68 ?; (product) C-H stretched only 0.04 ?. The role of water solvent was explored by including one, two, or three water molecules in the calculation.     

Some new selective stationary phases for RP-HPLC

At the present time, more complex analyses of apolar compounds with similar chemical structures or of polar compounds, especially basic ones, having diverse properties require more selective stationary phases having better stabilities. This paper describes several new stationary phases with directed selectivities that were prepared by immobilizing two different phenyl group-containing siloxanes and a trifluoropropyl-containing siloxane onto chromatographic silica and, in the case of the fluorinated siloxane, onto zirconized silica, using thermal treatment or microware radiation. The chromatographic properties and stabilities of these new phases were determined and several applications were evaluated. The phenyl-containing phases showed excellent characteristics related to the separation of several different types of aromatic compounds while the fluorinated phases, which present a more polar character, revealed selectivity for the separation of positional isomers as well as for a mixture of basic pharmaceuticals. Stability tests indicate that immobilization of the polysiloxanes increases column lifetimes by making the stationary phases less susceptible to dissolution, while the phases immobilized with microwave radiation were somewhat more stable than those immobilized by thermal treatments.     

Molecularly imprinted silica as a selective SPE sorbent for triazine herbicides

A molecularly imprinted organically modified silica was prepared through a simple sol‐gel procedure and evaluated as a specific sorbent for SPE of triazine herbicides. The material proved to be highly selective for the template molecule, atrazine, as well as for other structurally related species such as simazine and propazine. The performance of this material was shown to be comparable with commercial acrylate‐based molecularly imprinted polymers. The molecularly imprinted silica was applied for the determination of trace levels of the target triazine analytes in sugar cane juice (locally called “garapa”).     

Current trends in quantitative proteomics

It was inevitable that as soon as mass spectrometrists were able to tell biologists which proteins were in their samples, the next question would be how much of these proteins were present. This has turned out to be a much more challenging question. In this review, we describe the multiple ways that mass spectrometry has attempted to address this issue, both for relative quantitation and for absolute quantitation of proteins. There is no single method that will work for every problem or for every sample. What we present here is a variety of techniques, with guidelines that we hope will assist the researcher in selecting the most appropriate technique for the particular biological problem that needs to be addressed. We need to emphasize that this is a very active area of proteomics research—new quantitative methods are continuously being introduced and some ‘pitfalls’ of older methods are just being discovered. However, even though there is no perfect technique—and a better technique may be developed tomorrow—valuable information on biomarkers and pathways can be obtained using these currently available methods Copyright © 2009 John Wiley & Sons, Ltd.     

Determination of organochlorine pesticides in water samples by dispersive liquid-liquid microextraction coupled to gas chromatography-mass spectrometry

A rapid and simple dispersive liquid-liquid microextraction (DLLME) has been developed to preconcentrate eighteen organochlorine pesticides (OCPs) from water samples prior to analysis by gas chromatography-mass spectrometry (GC-MS). The studied variables were extraction solvent type and volume, disperser solvent type and volume, aqueous sample volume and temperature. The optimum experimental conditions of the proposed DLLME method were: a mixture of 10 μL tetrachloroethylene (extraction solvent) and 1 mL acetone (disperser solvent) exposed for 30 s to 10 mL of the aqueous sample at room temperature (20 °C). Centrifugation of cloudy solution was carried out at 2300 rpm for 3 min to allow phases separation. Finally, 2 μL of extractant was recovered and injected into the GC-MS instrument. Under the optimum conditions, the enrichment factors ranged between 46 and 316. The calculated calibration curves gave a high-level linearity for all target analytes with correlation coefficients ranging between 0.9967 and 0.9999. The repeatability of the proposed method, expressed as relative standard deviation, varied between 5% and 15% (n = 8), and the detection limits were in the range of 1-25 ng L⁻¹. The LOD values obtained are able to detect these OCPs in aqueous matrices as required by EPA methods 525.2 and 625. Analysis of spiked real water samples revealed that the matrix had no effect on extraction for river, surface and tap waters; however, urban wastewater sample shown a little effect for five out of eighteen analytes.     

Integer equal flows

The integer equal flow problem is an NP-hard network flow problem, in which all arcs in given sets R₁,…,R_ℓ must carry equal flow. We show that this problem is effectively inapproximable, even if the cardinality of each set R_k is two. When ℓ is fixed, it is solvable in polynomial time.     

Singular value decomposition of torsional angles of analogs of the dopamine reuptake inhibitor GBR 12909

Analysis of large, flexible molecules, such as the dopamine reuptake inhibitor GBR 12909 (1), is complicated by the fact that they can take on a wide range of closely related conformations. The first step in the analysis is to classify the conformers into groups. Here, Singular Value Decomposition (SVD) was used to group conformations of GBR 12909 analogs by the similarity of their nonring torsional angles. The significance of the present work, the first application of SVD to the analysis of very flexible molecules, lies in the development of a novel scaling technique for circular data and in the grouping of molecular conformations using a technique that is independent of molecular alignment. Over 700 conformers each of a piperazine (2) and piperidine (3) analog of 1 were studied. Analysis of the score and loading plots showed that the conformers of 2 separate into three large groups due to torsional angles on the naphthalene side of the molecule, whereas those of 3 separate into nine groups due to torsional angles on the bisphenyl side of the molecule. These differences are due to nitrogen inversion at the unprotonated piperazinyl nitrogen of 2, which results in a different ensemble of conformers than those of 3, where no inversion is possible at the corresponding piperidinyl carbon.     

Hierarchical clustering analysis of flexible GBR 12909 dialkyl piperazine and piperidine analogs

Pharmacophore modeling of large, drug-like molecules, such as the dopamine reuptake inhibitor GBR 12909, is complicated by their flexibility. A comprehensive hierarchical clustering study of two GBR 12909 analogs was performed to identify representative conformers for input to three-dimensional quantitative structure–activity relationship studies of closely-related analogs. Two data sets of more than 700 conformers each produced by random search conformational analysis of a piperazine and a piperidine GBR 12909 analog were studied. Several clustering studies were carried out based on different feature sets that include the important pharmacophore elements. The distance maps, the plot of the effective number of clusters versus actual number of clusters, and the novel derived clustering statistic, percentage change in the effective number of clusters, were shown to be useful in determining the appropriate clustering level.Six clusters were chosen for each analog, each representing a different region of the torsional angle space that determines the relative orientation of the pharmacophore elements. Conformers of each cluster that are representative of these regions were identified and compared for each analog. This study illustrates the utility of using hierarchical clustering for the classification of conformers of highly flexible molecules in terms of the three-dimensional spatial orientation of key pharmacophore elements.