The KS-transformation revisited

We show that the Kustaanheimo-Stiefel (KS) regularizing transformation for the perturbed Kepler motion is so deeply rooted to the Keplerian orbital elements as to yield the position vector of a particle on the osculating orbit as the effect of a peculiar roto-dilatation in the physical Euclidean space. Adopting the conventional vector formulation, quaternions and spinors are also involved. A key role is played by (i): a simple hodographical approach to the integrals of the Kepler motion (angular momentum vector, Runge-Lenz vector); (ii) a polarized outlook on the attitude frame of the Kepler orbit; (iii) a simple kinematical expression for the orbital elements. The mechanical energy, the bilinear relation, the gauge transformation — fundamental in the KS-theory — are naturally arrived at, acquiring interesting kinematical interpretations.

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Sommario Si mostra come la trasformazione di Kustaanheimo e Stiefel (KS) per regolarizzare il moto kepleriano perturbato sia cosí legata agli elementi orbitali da condurre, tramite una particolare roto-omotetia nello spazio fisico euclideo, al vettore posizione di una particella sull'orbita osculatrice. Avvalendosi del consueto calcolo vettoriale, si introducono solo all'occorrenza quaternioni e spinori. Fondamentali risultano (i): l'introduzione per via odografica degli integrali primi caratteristici del moto kepleriano (momento della quantità di moto, vettore di Runge-Lenz); (ii) l'interpretazione polarizzata della terna di assi che dà la posizione dell'orbita nello spazio; (iii) le semplici espressioni cinematiche degli elementi orbitali. L'energia meccanica e la relazione bilineare, basilari nella teoria KS, acquistano interessanti interpretazioni cinematiche.

     

Biodiesel Production from Integration Between Reaction and Separation System: Reactive Distillation Process

Biodiesel is a clean burning fuel derived from a renewable feedstock such as vegetable oil or animal fat. It is biodegradable, non-inflammable, non-toxic, and produces lesser carbon monoxide, sulfur dioxide, and unburned hydrocarbons than petroleum-based fuel. The purpose of the present work is to present an efficient process using reactive distillation columns applied to biodiesel production. Reactive distillation is the simultaneous implementation of reaction and separation within a single unit of column. Nowadays, it is appropriately called “Intensified Process”. This combined operation is especially suited for the chemical reaction limited by equilibrium constraints, since one or more of the products of the reaction are continuously separated from the reactants. This work presents the biodiesel production from soybean oil and bioethanol by reactive distillation. Different variables affect the conventional biodiesel production process such as: catalyst concentration, reaction temperature, level of agitation, ethanol/soybean oil molar ratio, reaction time, and raw material type. In this study, the experimental design was used to optimize the following process variables: the catalyst concentration (from 0.5 wt.% to 1.5 wt.%), the ethanol/soybean oil molar ratio (from 3:1 to 9:1). The reactive column reflux rate was 83 ml/min, and the reaction time was 6 min.     

Unusual Reactions of (+)‐Car‐2‐ene and (+)‐Car‐3‐ene with Aldehydes on K10 Clay

The reactions of (+)‐car‐2‐ene ( 1 ) and (+)‐car‐3‐ene ( 2 ) with aldehydes in the presence of montmorillonite clay were studied for the first time (Schemes 3 and 5). The major products of these reactions are optically active, substituted hexahydroisobenzofurans, probably formed as a result of an attack of the protonated aldehyde at the cyclopropane ring. Quite unexpectedly, the products are cis‐configured at the ring‐fusion site; the fact was established by means of quantum‐chemical calculations and NMR data. It appeared that the behavior of the 2 : 3 mixture 1 / 2 in reactions with aldehydes in the presence of K10 clay differed substantially from the reactivities of the corresponding individual monoterpenes.     

Alkane Activation over Acidic Zeolites: The First Step

The heterogeneous acid‐catalyzed activation step of alkanes leading to the reaction intermediates (carbocationic or alkoxy species) was up to now the matter of a longstanding controversy. Gas chromatography and online mass spectroscopy measurements show that H₂ and methane are formed over H‐zeolites, whereas HD and CH₃D are formed over D‐zeolites as the primary products in the reaction with isobutane. These results indicate that σ‐bond protolysis by strong acid sites is the first step for hydrocarbon activation on these catalysts at mild temperatures (473 K), in analogy to the activation path occurring in liquid superacid media.     

Volatile profiling reveals intracellular metabolic changes in <Emphasis Type="Italic">Aspergillus parasiticus</Emphasis>: <Emphasis Type="Italic">veA</Emphasis> regulates branched chain amino acid and ethanol metabolism

Background  

Filamentous fungi in the genus Aspergillus produce a variety of natural products, including aflatoxin, the most potent naturally occurring carcinogen known. Aflatoxin biosynthesis, one of the most highly characterized secondary metabolic pathways, offers a model system to study secondary metabolism in eukaryotes. To control or customize biosynthesis of natural products we must understand how secondary metabolism integrates into the overall cellular metabolic network. By applying a metabolomics approach we analyzed volatile compounds synthesized by Aspergillus parasiticus in an attempt to define the association of secondary metabolism with other metabolic and cellular processes.     

Analysis of cocaine and benzoylecgonine in urine by using multisyringe flow injection analysis‐gas chromatography‐mass spectrometry system

In this paper, a method was described to determine cocaine (COC) and benzoylecgonine (BZE) in human urine samples by GC‐MS detection. The extraction of analytes from urine samples was achieved in an Oasis hydrophilic–lipophilic balance column (20 mm×3.9 mm id, dp=25 μm; Waters, USA), incorporated in a multisyringe flow injection system, used for the sample treatment. Finally, to improve the volatility of the BZE, an in‐line derivatization reaction with N,O‐bis (trimethylsilyl) trifluoroacetamide with 1% trimethylchlorosilane was made microwave‐assisted in order to reduce the reaction time. The results showed that the proposed method is a good alternative for the analysis of COC and BZE in urine samples because it offers advantages compared with those described in the literature, which include simplicity in the sample treatment, the sensitivity and selectivity necessary to determine the analytes of interest at low levels in the urine and high sample throughput.     

Quantifying surface coverage of colloidal silica by a cationic peptide using a combined centrifugation/time-resolved fluorescence anisotropy approach

Recent experimental studies have shown that time-resolved fluorescence anisotropy (TRFA) is a promising methodology for in situ characterization of the surface modification of aqueous silica nanocolloids. Here we provide a more fundamental insight into the principle of this approach and discuss how the adsorption parameters for a cationic peptide, Lys-Trp-Lys (denoted using the standard shortform KWK), onto Ludox nanoparticles (NPs) are linked to the rotational dynamics of rhodamine 6G (R6G) dispersed in the KWK/Ludox mixture. First, the adsorption isotherm of KWK on hydrophilic controlled pore glass (CPG-3000) was obtained using the traditional centrifugation method, which provides the total molar amount of KWK per unit surface area of the silica. Assuming that both CPG and Ludox particles possess identical surface properties when suspended in the same aqueous buffer, both materials should also have identical adsorption properties. Thus, the adsorbed amount of KWK per unit area at a given total KWK concentration, as determined by the centrifugation method, can be plotted against the fractions of R6G anisotropy decay components at the same KWK concentration to relate the anisotropy components to the absolute surface coverage. Using this approach, it was determined that the concentration of KWK at which the CPG surface was saturated corresponded to the condition g = 0 in the R6G decay, where g is the fraction of the nondecaying anisotropy component. This condition means that there is no R6G bound to the fraction of Ludox NPs with a radius R > 2.5 nm at maximum KWK coverage, consistent with the adsorbed peptide forming a continuous layer on the Ludox surface. Hence, the g value obtained from TRFA analysis can be used to assess the absolute surface coverage of monolayer coatings on colloidal nanoparticles.     

UV spectrophotometric determination of bioflavonoids from a semisolid pharmaceutical dosage form containing Trichilia catigua Adr. Juss and Ptychopetalum olacoides Bentham standardized extract: analytical method validation and statistical procedures

A precise, accurate, and sensitive UV spectrophotometric method was developed and validated for routine quantification of total bioflavonoids, expressed as rutin, from a topical oil-in-water pharmaceutical emulsion containing the extract of Trichilia catigua Adr. Juss and Ptychopetalum olacoides Bentham. The method was validated experimentally, and the data were treated rigorously by statistical analysis. The following analytical parameters were assessed: linearity, specificity, intra- and interrun precision measured as relative standard deviation (RSD, %), intra- and interrun accuracy (E, %), recovery (Rec., %), limit of detection (LOD, microg/mL), and limit of quantification (LOQ, microg/mL). The UV spectrophotometric method was linear (r = 0.9995) for standard rutin over the concentration range of 5.0-15.0 microg/mL with specificity for total bioflavonoids (expressed as rutin) at 361.0 nm with an absence of interferents from the complex matrix; RSD of < or = 1.79%, intrarun (E = 97.88 +/- 1.75 to 99.0 +/- 0.33%) and interrun (E = 98.38 +/- 1.12 to 100.79 +/- 1.30%) accuracy; Rec. = 98.64 +/- 0.42 to 100.74 +/- 0.41%; LOD = 0.20 microg/mL; and LOQ = 0.30 microg/mL.     

Direct monitoring of toxic compounds in air using a portable mass spectrometer

A portable tandem mass spectrometer, capable of performing atmospheric pressure chemical ionization (APCI) using a direct atmospheric inlet, is applied to the real-time monitoring of toxic compounds in air. Analytes of interest include dimethyl methylphosphonate, arsine, benzene, toluene, pyridine and vinyl acetate. The detection, identification and quantification of organic and inorganic compounds in air is demonstrated using short analysis times (<5 seconds) with detection limits in the low ppb (v/v) levels and linear dynamic ranges of several orders of magnitude. Highly specific detection and identification is achieved, even when the analyte is a trace component in a complex mixture including such interferents as fuels, lubricants, and cleaners. The effects of environmental conditions, including temperature and humidity, are delineated. Receiver operating characteristic (ROC) curves are presented to show the trade-off between false positive and false negative detection rates. Tandem mass spectrometry based both on collision-induced dissociation and on selective atmospheric pressure ion/molecule reactions is also used to increase selectivity and sensitivity.