Continued fractions in local fields, II

The present paper is a continuation of an earlier work by the author. We propose some new definitions of -adic continued fractions. At the end of the paper we give numerical examples illustrating these definitions. It turns out that for every if then has a periodic continued fraction expansion. The same is not true in for some larger values of

     

Numerical analysis of a quadratic matrix equation

The quadratic matrix equation AX²+ BX + C = 0in n x nmatricesarises in applications and is of intrinsic interest as oneof the simplest nonlinear matrix equations. We give a completecharacterization of solutions in terms of the generalized Schurdecomposition and describe and compare various numerical solutiontechniques. In particular, we give a thorough treatment offunctional iteration methods based on Bernoulli’s method.Other methods considered include Newton’s method with exact line searches, symbolic solution and continued fractions.We show that functional iteration applied to the quadraticmatrix equation can provide an efficient way to solve the associated quadratic eigenvalue problem (²A + B + C)x = 0.     

Mathematical modelling of selected characterisation procedures for oil fractions

Models of two important characterisation procedures for oil and oil fractions, ASTM D86 (ASTM = American Society for Testing of Materials) and EFV (Equilibrium Flash Vaporization), were presented. The purpose was to provide a basis for the construction of substitute mixtures of real components used in modelling and simulation of chemical engineering processes instead of original complex mixtures. It was shown how to deal with a possible problem of higher index of differential-algebraic model of the ASTM D86. A number of examples proved the adequacy of the presented models. Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.     

pePC-SAFT: Modeling of polyelectrolyte systems: 1. Vapor–liquid equilibria

A molecular thermodynamic model for polyelectrolyte systems—called pePC-SAFT—is proposed. The effect of charged monomers within the polyelectrolyte chain is explicitly taken into account in the reference term by replacing the hard-chain contribution of the PC-SAFT model by a charged-hard-chain contribution. Moreover, counterion condensation is accounted for to determine the effective number of charges along the polyion as well as of free counterions. The electrostatic contribution of the free counterions is described by a Debye–Hückel term.     

Synthesis and optical characterization of novel azacrown ethers containing an acridinone or an N-methylacridinone unit as potential fluorescent chemosensors

Four new achiral and four new chiral monoazacrown ethers containing an acridinone or an N-methylacridinone fluorescent signalling unit were prepared by reacting chloromethyl-substituted acridinone derivatives with achiral monoazacrown ethers with different cavity sizes and enantiopure monoaza-18-crown-6 ethers having two methyl and two isobutyl groups on their chiral centres, respectively. The operation of these chemosensors is based on the photoinduced electron transfer (PET) process, thus they show fluorescence enhancement in the presence of cationic guests. Their fluorescent behaviour as well as their complexation properties towards selected metal ions and the enantiomers of α-(1-naphthyl)ethylammonium perchlorate and potassium mandelate were examined.     

Application of thiophilic chromatography to deplete serum immunoglobulins in sample preparation for bidimensional electrophoresis

Serum is a typical sample for non-invasive studies in clinical research. Its proteome characterization is challenging, since requires extensive protein depletion. Methods used nowadays for removal of high-abundance proteins are expensive or show quite often a low loading capacity, which has strong repercussions on the number of samples and replicates per analysis.In order to deplete immunoglobulins (Igs) and albumin (HSA) from 1 mL serum samples, we have developed a protocol based on a combination of thiophilic chromatography, not previously used in clinical proteomics, and a HSA-specific resin. Ig/HSA-depleted samples, immunoglobulinome and albuminone were analyzed by 2-DE. Thiophilic chromatography, coupled with HSA-depletion, allows a good 2-DE resolution as well as the visualization of new spots. Moreover, it yields enough protein to evaluate technical variability and facilitate subsequent protein identification. To validate the protocol, we carried out a preliminary comparative study between triplicate Igs/HSA-depleted serum samples from healthy control individuals and recently diagnosed/untreated rheumatoid arthritis (RA) patients. RA patients showed several acute phase proteins, as well as additional serum proteins, differentially and significantly regulated.Therefore, thiophilic chromatography can be used as an efficient and economical method in 2-DE to deplete immunoglobulins from large human serum samples before a more extensive fractioning.     

Amplification of chirality as a pathway to biological homochirality

Amplification of enantiomeric enrichment is a key feature for the chemical evolution of biological homochirality from the origin of chirality. The aggregations of the enantiomers by diastereomeric interactions enable the modification of their enantiomeric excess during some chemical processes. Fluorine-containing chiral compounds possess large amplification effect via distillation, sublimation and achiral chromatography by self-disproportionation. Asymmetric amplifications in enantioselective catalysis occur by the differential formation and reactivity between homochiral and heterochiral aggregate in solution.We described the amplification of ee in asymmetric autocatalysis of 5-pyrimidyl alkanol in the reaction between diisopropylzinc and pyrimidine-5-carbaldehdye. During the reactions extremely low ee (ca. 0.00005% ee) can be amplified to achieve more than 99.5% ee. Since the proposed origins of chirality such as CPL, quartz, chiral organic crystals of achiral compounds and statistical fluctuation of ee can initiate the asymmetric autocatalysis with amplification of ee, the proposed origin of chirality can be linked with enantiopure organic compound in conjunction with amplification of ee by asymmetric autocatalysis. In addition, we described that the carbon isotopically chiral compound triggers the asymmetric autocatalysis of 5-pyrimiodyl alkanol to afford the enantioenriched product with the absolute configuration correlated with that of carbon isotope chirality, that is, isotope chirality including hydrogen isotopes can control the enantioselectivity of asymmetric addition of alkyl metal reagent to aldehyde.     

Different approaches of impregnation for resolution of enantiomers of atenolol,propranolol and salbutamol using Cu(II)-l-amino acid complexes for ligand exchange on commercial thin layer chromatographic plates

Atenolol and propranolol (the β-blocking agents) and salbutamol (broncho- and vasodilator) were resolved into their enantiomers by adopting different modes of loading/impregnating the Cu(II) complexes of l-proline (l-Pro), l-phenylalanine (l-Phe), l-histidine (l-His), N,N-dimethyl-l-phenylalanine (N,N-Me₂-l-Phe), and l-tryptophan (l-Trp) on commercial precoated normal phase plates. The three different approaches were (A) using the Cu(II)-l-amino acid complex as chiral mobile phase additive, (B) ascending development of plain commercial plates in the solutions of Cu complex, and (C) using a solution of Cu(II) acetate as mobile phase additive for the commercial TLC plates impregnated with ascending development of plates in the solutions of amino acid. Spots were located using iodine vapour. The results obtained for the three methods have been compared for their efficiency and the issue of involvement of the Cu(II) cation for the best performance of the three methods has been discussed with respect to the same mobile phase. The detection limit is 0.18 μg for each enantiomer.     

Thorough evaluation of the validity of conventional enantio-gas chromatography in the analysis of volatile chiral compounds in mandarin essential oil: A comparative investigation with multidimensional gas chromatography

The present research is focused on the determination of the enantiomeric distribution of chiral compounds, contained in mandarin essential oils, by means of conventional chiral gas chromatography with flame ionization detection (enantio-GC-FID); the results attained were compared with those derived from heart-cutting multidimensional GC-mass spectrometry (MDGC/MS), to evaluate the reliability of the monodimensional technique as a tool for quality control. The Deans-switch MDGC system was equipped with two GC ovens, which were connected via a heated transfer line, a flame ionization detector (FID1) in the first dimension and a quadrupole MS as second-dimension detector. The a priori knowledge of potential co-elutions concerning target compounds (an enantiomer and an interfering compound), when using enantio-GC-FID, could enable the use of corrected enantiomer excess values. Correction factors could be calculated through a preliminary GC-FID analysis (using an apolar column), considering the peak areas of the known interferences. The method used for the calculation of a so-called “coelution correction factor” is described, along with some examples.     

Development of a method based on on-line reversed phase liquid chromatography and gas chromatography coupled by means of an adsorption–desorption interface for the analysis of selected chiral volatile compounds in methyl jasmonate treated strawberries

A method based on the use of the through oven transfer adsorption–desorption (TOTAD) interface in on-line coupling between reversed phase liquid chromatography and gas chromatography (RPLC–GC) for the determination of chiral volatile compounds was developed. In particular, the method was applied to the study of the influence of methyl jasmonate (MJ) treatment on the production and enantiomeric composition of selected aroma compounds in strawberry. The compounds studied were ethyl 2-methylbutanoate, linalool and 4-hydroxy-2,5-dimethyl-3(2H)-furanone (i.e. furaneol), which were examined on days 3, 6 and 9 after treatment. The method developed resulted in relative standard deviations (RSDs) of 21.6%, 8.1% and 9.8% and limits of detection (LD) of 0.04, 0.07 and 0.02 mg/l for ethyl 2-methylbutanoate, linalool and furaneol, respectively. The application of the RPLC–TOTAD–GC method allowed higher levels of ethyl 2-methylbutanoate, linalool and furaneol to be detected, particularly after 9 days of treatment. Besides, MJ demonstrated to affect the enantiomeric distribution of ethyl 2-methylbutanoate. On the contrary, the enantiomeric composition of linalool and furaneol kept constant in both control and MJ-treated strawberries throughout the study. These results are discussed.