On top-down splaying

The splay tree is a self-adjusting binary search tree which has a good amortized performance. This paper studies some properties of top-down splay trees. Different ways to charge for the primitive operations of top-down splaying are discussed. We also give some empirical results concerning the behaviour of different top-down restructuring algorithms.This work was supported by the Academy of Finland.     

Gas chromatographic optimization studies on the side chain and ring regioisomers of methylenedioxymethamphetamine

Gas chromatographic (GC) optimization studies are conducted for the 10 methylenedioxyphenethylamine regioisomeric substances related to the drug of abuse 3,4-methylenedioxymethamphetamine (MDMA, Ecstasy). These 10 compounds, having the same molecular weight and equivalent major mass spectral fragments, are not completely resolved using typical GC-mass spectrometry screening methods for illicit drugs. MDMA coelutes with at least one nondrug regioisomer under standard drug screening conditions. Separation of the 10 regioisomers is studied using stationary phases of varying polarities. Resolution optimization shows that very slow program rates give the best separation for the nonpolar stationary phases, requiring analysis times of as much as 85 min. Narrow-bore columns containing the same nonpolar stationary phases improve the analysis time to approximately 29 min. The polar stationary phase DB-35MS allows high-temperature programming rates, yielding complete resolution of all 10 compounds in less than 7 min. Temperature program optimization studies on the DB-35MS phase allow the separation time to be reduced to approximately 4.5 min.     

Scaled AMO calculations on the hydrogen molecule II. The 1s σ 2p σ 1∑ state

A scaled version of the AMO method is applied to the 1sσ2pσ ¹∑ state of the hydrogen molecule. A method to extend the domain of the mixing parameter λ to the whole complex plane is described and applied in the present calculation. All the parameters introduced have been varied completely. A considerable improvement in the computed energy values is found for large internuclear separations R. The comparison between our potential energy curve and the accurate curve calcualted by Kolos and Wolniewicz is studied and, for example, for R = 12 a.u. the energy difference is only 18% of that for R = 2.43 a.u. The equilibrium separation is found to be 2.140 a.u. in poor agreement with 2.429 a.u. obtained by the previously mentioned authors. In the separated atom limit, the state under consideration does not dissociate into H⁺ + H^?, although the ionic character of the wave function is dominating in the region 3 ≦ R ≦ 8 a.u. The connections with earlier calculations and methods, especially the scaled version of the MO –LCAO approximation, are also pointed out and discussed.     

Association of bound states of the coulomb potential with resonances of the coulomb potential perturbed by a barrier

In the present article we show how the bound states of the Coulomb potential may be associated with resonances that occur when this potential is perturbed by a barrier potential. The main idea is to trace the bound states on successive switching on of the barrier perturbation. It is found that those bound states that are localized inside the barrier are highly sensitive to variation with respect to the barrier height, whereas those that are localized outside are less sensitive. However, there are certain intervals for the barrier height when the role of being “a state localized inside the barrier” is shifted from one bound state to another. The result can be pictured as a “relay race,” where the “deliveries of the baton” are carried out over corresponding avoided crossings. The baton is ultimately handed over to a shape-type resonance state.     

Co-eluent effect in partition chromatography. Rhamnose-xylose separation with strong and weak cation-exchangers in aqueous ethanol

The effect of ethanol in aqueous eluent on the chromatographic separation was studied at 298 K. Two sugars, L-rhamnose and D-xylose, were separated by using strong and weak cation-exchangers as a stationary phase. The ionic form of the resins was Na+ or Ca2+. The separations were carried out with sugar feed concentrations up to 35 wt% and with both low (about 1%) and high (about 10%) feed volume to bed volume ratios. The separation of the sugars was improved by adding ethanol into the eluent. The separation was also significantly enhanced when the weak cation-exchangers with the greatest affinity for water were used instead of strong cation-exchangers as a separation medium for the sugars having different hydrophilicities. The experimental data were successfully explained with a rate-based column model, which accounted for the volume changes of the stationary phase. A thermodynamic sorption model was utilized in column calculations.     

Comparison of polydimethyl siloxane stationary phases with 5% and 50% phenyl substitution for the separation of organophosphorus and organonitrogen pesticides under optimized gas chromatographic conditions

The CGC analysis of 25 organophosphorus and organonitrogen pesticides was optimized on two different stationary phases, namely a 5% diphenyl dimethyl silicone (SE-54 type) and a 50% diphenyl dimethyl silicone (OV-17 type) by selecting the best temperature program conditions, using computer simulation.     

Rapid identification and quantitation of compounds with forensic interest using fast liquid chromatography-ion trap mass spectrometry and library searching

A fast liquid chromatography-electrospray tandem mass spectrometric (LC-ESI-MS-MS) method by using a monolithic column, gradient elution and ion trap mass spectrometer was developed for 14 forensically interesting and chemically different compounds. All compounds were eluted within 2.5 min and the total analysis time was 5 min including stabilisation time required for the next injection. All the compounds, basics, neutrals and acids were efficiently ionised by positive ion ESI. A laboratory library including MS-MS spectra and retention times was developed and tested. Results with 476 standard samples and 50 authentic samples showed that the compounds studied can be unambiguously identified with the library. A quantitative method was developed for the compounds using external calibration. The evaluation process showed good linearity of the method and reasonable repeatability. Limits of detection ranged from 10.0 to 50.0 ng/ml.     

Component reconstruction in the primary space of spectra and concentrations. Alternating regression and related direct methods

A set of methods that extract the spectral components in a chromatographic run is considered. The methods do not need libraries of previously known spectra or retention times. The methods have been developed for two-dimensional spectra but they can also be used for chromatographic analyses with a single-channel detector. The methods are direct; they do not use principal components as the starting point. Alternating regression (AR) remains in the primary space of spectra and concentrations during the calculations. Random numbers are used as the starting spectra. Regression is used to solve first for the concentrations, then for the spectra. The method uses two kinds of constraints: all spectra and concentrations are forced to be positive; and all concentration profiles are forced to a unimodal shape with a single local maximum. It is assumed that all observations are a linear sum of components. Compact alternating regression (CAR) is a new variant of the basic AR. The idea is to replace multiplication of a large matrix by two multiplications of smaller matrices. This typically speeds up the iterations by a factor of ten. AR and CAR have been successfully used with combined techniques such as gas chromatography—mass spectrometry and liquid chromatography with UV—visible detection. The reliability of the solution is checked by repeatedly injecting noise and performing the analysis several times. This produces estimates of confidence intervals. AR and CAR have recently been extended to handle single-dimensional signals. Examples are single-channel detectors such as the flame ionization detector in gas or liquid chromatography with a fixed-wavelength UV detector. A batch of samples is used as the observation matrix. As a result, one obtains both the concentrations and the elution shapes of individual chromatographic peaks.     

Immunochemical determination of dioxins in sediment and serum samples

Polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs) are considered highly toxic contaminants and the environmental and biological monitoring of these compounds is of great concern. Immunoassays may be used as screening methods to satisfy the growing demand for rapid and low cost analysis. In this work, we describe the application of an immunoassay that uses 2,3,7-trichloro-8-methyldibenzo-p-dioxin (TMDD) as a surrogate standard for 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) to sediment and human serum samples. Sample extraction and preparation methods were developed with the aim to establish the simplest, cost-effective and efficient removal of the matrix interferences in the enzyme-linked immunosorbent assay (ELISA). The overall method for sediments is based on a hexane extraction; clean up by a multilayered silica gel column and an activated carbon column; an organic solvent exchange with DMSO–Triton X-100 and ELISA measurement. The gas chromatography–high resolution mass spectrometry (GC–HRMS) validation studies (n = 13) revealed that the method is suitable for the toxic equivalents (TEQ) screening of dioxin in sediments with a method detection limit of about 100 pg g⁻¹ dry sediment with a precision of 13–33% R.S.D. The analysis of a large number of samples originating from different sources would be required to establish more precisely the screening level, as well as the number of false positives and negatives of dioxin TEQ by the immunoassay for sediments. The immunoassay method for sediment analysis offers improvement in speed, sample throughput, and cost in comparison to GC–HRMS. Dioxins were determined in serum samples after a simple liquid–liquid extraction and solvent exchange into DMSO–Triton X-100 without further dilution. The current method (approximate method LOQ of 200 pg ml⁻¹ serum) is not sufficiently sensitive for the determination of dioxins in serum to measure acceptable exposure limit.     

Effects of various washing procedures on the chromium content of human scalp hair

The effects of four wash procedures on the concentration of chromium in a pooled sample of human scalp hair are compared. The wash solutions examined are Triton X-100, sodium lauryl sulphate, acetone, and a mixture (1 + 1) of hexane and ethanol. The plateaux reached for hair chromium concentration are functions of the number of washings, and are characteristic for each wash solution. The wash procedure recommended involves two 20-min washes with aqueous 1% sodium lauryl sulphate solution after a hexane rinse.