The cosine functional equation for nilpotent groups

Aequationes mathematicae -     

Thermodynamic stability of chemical species in multiple reaction systems

A general thermodynamic and stoichiometric method, recently developed by us to study subtle forms of stability/instability relations among chemical species, such as resonance and strain energies (Fishtik, I.; Datta, R. J. Phys. Chem. A 2004, 108, 5727-5739), is extended to stability relations in multiple chemical reaction systems. Namely, a new definition as well as a new algorithm of evaluation of the stabilities of chemical species, referred to as the overall stabilities, is proposed. It is further shown that the overall stabilities may be partitioned into a sum of contributions associated with a complete set of stoichiometrically unique response reactions (RERs). This finding reveals that the conventional stability analysis is stoichiometrically and thermodynamically inconsistent in that it involves only a part of RERs.     

Determination of persistent organohalogenated pollutants in human hair reference material (BCR 397): an interlaboratory study

A human powdered hair material (BCR 397) was tested for its content in persistent organic pollutants (POPs), such as polychlorinated biphenyls (PCBs), organochlorine pesticides (OCPs) and polybrominated diphenyl ethers (PBDEs). Using different methods, three laboratories (two from Canada and one from Belgium) analysed a powdered hair sample to evaluate some methodologies and to obtain consensus values for selected POPs. Measured values for all PCB congeners and p,p-DDE were within a relative standard deviation (RSD) of 15%. These first results contribute to the accuracy and precision for POPs quantification in hair and render test results more comparable among different laboratories.     

Computer generation of acyclic graphs based on local vertex invariants and topological indices. Derived canonical labelling and coding of trees and alkanes

A new procedure (GENLOIS) is presented for generating trees or certain classes of trees such as 4-trees (graphs representing alkanes), identity trees, homeomorphical irreducible trees, rooted trees, trees labelled on a certain vertex (primary, secondary, tertiary, etc.). The present method differs from previous procedures by differentiating among the vertices of a given parent graph by means of local vertex invariants (LOVIs). New graphs are efficiently generated by adding points and/or edges only to non-equivalent vertices of the parent graph. Redundant generation of graphs is minimized and checked by means of highly discriminating, recently devised topological indices based either on LOVIs or on the information content of LOVIs. All trees onN + 1 (N + 1 < 17) points could thus be generated from the complete set of trees onN points. A unique cooperative labelling for trees results as a consequence of the generation scheme. This labelling can be translated into a code for which canonical rules were recently stated by A.T. Balaban. This coding appears to be one of the best procedures for encoding, retrieving or ordering the molecular structure of trees (or alkanes).Dedicated to Professor Alexandru T. Balaban on the occasion of his 60th anniversary.     

Mass spectrometric detection in narrow-bore (0.10 mm i.d.) capillary chromatography fast, sensitive and selective analysis of polychlorinated biphenyls

The combination of narrow-bore capillary gas chromatography with bench-top quadrupole mass spectrometric detection was evaluated for the determination of polychlorinated biphenyls (PCBs). The qualitative and quantitative performances of the system are illustrated by several analyses (PCB standards and human milk extracts). Capillary columns with different internal diameters (0.10, 0.18 and 0.22 mm, respectively) were compared for their ability to separate PCB congeners and the analysis time. Short run times (less than 7 min) were sufficient for complete separation of PCB congeners on a 0.10-mm internal diameter (I.D.) capillary column without any loss of resolution when compared with a 0.22 mm I.D. column. Good qualitative and quantitative data acquisition was possible with quadrupole mass spectrometer for run times of 8 min, but incomplete peak reading was observed when run times were reduced to 3-4 min. Selected ion monitoring and dwell times of 10 ms are necessary to obtain detection limits for individual PCB congeners as low as 0.4 pg microl(-1) for standard solutions and 0.2 ng g(-1) fat for milk extracts. By using cold splitless injection, relatively high volumes (1 microl) for narrow-bore capillaries could be injected without any peak distortion.     

A solid-state NMR study of the fast and slow dynamics of collagen fibrils at varying hydration levels

We report solid-state NMR investigations of the effect of temperature and hydration on the molecular mobility of collagen isolated from bovine achilles tendon. (13)C cross-polarization magic angle spinning (MAS) experiments were performed on samples at natural abundance, using NMR methods that detect motionally averaged dipolar interactions and chemical shift anisotropies and also slow reorientational processes. Fast motions with correlation times much shorter than 40 micro s scale dipolar couplings and chemical shift anisotropies of the carbon sites in collagen. These motionally averaged anisotropic interactions provide a measure of the amplitudes of the segmental motions expressed by a molecular order parameter. The data reveal that increasing hydration has a much stronger effect on the amplitude of the molecular processes than increasing temperature. In particular, the Cgamma carbons of the hydroxyproline residues exhibit a strong dependence of the amplitude of motion on the hydration level. This could be correlated with the effect of hydration on the hydrogen bonding structure in collagen, for which this residue is known to play a crucial role. The applicability of 1D MAS exchange experiments to investigate motions on the millisecond time-scale is discussed and first results are presented. Slow motions with correlation times of the order of milliseconds have also been detected for hydrated collagen.     

Molecular topology. IV. Regressive vertex degrees (new graph invariants) and derived topological indices

New local graph invariants, “regressive vertex degrees” (which are slightly augmented vertex degrees) are introduced on the basis of decreasing contributions of more remote vertexes to the classical vertex degrees. Several such invariants are proposed (BR, ER, SR) where t (either t = 1 or t = 2) is an operator expressing the attenuation with increasing topological distance, according to formula (1) or (2). With the aid of these new local invariants, new topological indices (global graph invariants), Y (namely BY, EY or SY) are introduced and exemplified. Their ability to express the branching and to order alkanes is investigated. An appendix gives some recursive relationships for computing these indices.     

Monolayers of photosystem II on gold electrodes with enhanced sensor response—effect of porosity and protein layer arrangement

Mass transport of the bulk of the analyte to the electrode and through the bioactive layer can be significantly improved by use of the nanoelectrode array and defined arrangement of protein film. This phenomenon has been studied by (i) atomic-force microscopy, (ii) electrochemical measurements of PSII activity, and (iii) digital simulations for an oriented monolayer of histidine-tagged photosystem II (PSII) immobilized on nitrilotriacetic acid (NTA)-modified gold electrodes. The output signal of the electrochemical biosensor is controlled by (i) mass transport from the bioactive layer to electrode and (ii) mass transport between the bulk of the analyte and the electrode. Mass transport through the bioactive layer was electrochemically studied for PSII self-assembled on gold screen-printed electrodes. A densely packed monolayer of PSII has a significant shielding effect toward the diffusion of redox mediator duroquinone (DQ). Mass transport to the planar electrode surface was improved by co-immobilization of bovine-serum albumin (BSA) as spacer biomolecule in the monolayer of PSII. Correlation between the electrochemical properties and surface arrangement of the resulting protein films was clearly observable and confirmed the improved mass-transport properties of structured enzyme monolayers. On the basis of this observation, the application of a bottom-up approach for improvement of electrode performance was proposed and digitally simulated for an infinite array of electrodes ranging in diameter from 50 nm to 5 m. The nanoelectrode array, with the optimum time window selected for measurements, enables enhancement of mass transport between the bulk of the analyte and the macroelectrode by a factor of up to 50 in comparison with classical planar electrodes. Use of a time window enables minimization of crosstalk between individual electrodes in the array. The measurements require methods which suppress the double-layer capacity.     

Joule-Thomson coefficient in systems with multiple chemical equilibria

Multiple chemical equilibria under adiabatic conditionsH, P = const. are considered. It is shown that in this case the Joule-Thomson coefficient may also be expressed in terms of response equilibria, which were previously introduced in the study of equilibria achieved underT, P = const. Nevertheless, our approach reveals some noteworthy differences between the isothermic and adiabatic equilibria.     

Gas chromatography–ion trap tandem mass spectrometry method for the analysis of methoxylated polybrominated diphenyl ethers in fish

Gas chromatography coupled to ion trap tandem mass spectrometry (GC–ITMS-MS) is proposed for the analysis of methoxylated polybrominated diphenyl ethers (MeO-PBDEs) in fish and shellfish. MS–MS operating parameters related to the isolation and fragmentation of the precursor ions were optimized to achieve maximum sensitivity and selectivity. This new method allows the determination of both MeO-PBDEs and PBDEs in a single run. Low limits of detection (0.4–2.5 pg injected) and high precision (RSD < 13%) were achieved. A sample treatment based on a selective pressurized liquid extraction (PLE) using Florisil as fat retainer was applied for the analysis of these compounds in fish samples. Method limits of quantification ranged from 0.11 to 0.95 ng g⁻¹ lipid weight for MeO-PBDEs and between 0.18 and 0.50 ng g⁻¹ lipid weight for PBDEs. In addition, good repeatability of the whole method was achieved (RSD < 15%). The suitability of the method was evaluated by analyzing a certified reference material (SRM 1945, whale blubber) with satisfactory results. The developed method was applied to the simultaneous analysis of MeO-PBDEs and PBDEs in fish and shellfish samples from the Mediterranean Sea.