Distances and volumina for graphs

It has long been realized that connected graphs have some sort of geometric structure, in that there is a natural distance function (or metric), namely, the shortest-path distance function. In fact, there are several other natural yet intrinsic distance functions, including: the resistance distance, correspondent “square-rooted” distance functions, and a so‐called “quasi‐Euclidean” distance function. Some of these distance functions are introduced here, and some are noted not only to satisfy the usual triangle inequality but also other relations such as the “tetrahedron inequality”. Granted some (intrinsic) distance function, there are different consequent graph-invariants. Here attention is directed to a sequence of graph invariants which may be interpreted as: the sum of a power of the distances between pairs of vertices of G, the sum of a power of the “areas” between triples of vertices of G, the sum of a power of the “volumes” between quartets of vertices of G, etc. The Cayley–Menger formula for n-volumes in Euclidean space is taken as the defining relation for so-called “n-volumina” in terms of graph distances, and several theorems are here established for the volumina-sum invariants (when the mentioned power is 2). This revised version was published online in July 2006 with corrections to the Cover Date.     

The physics of athermal nuclei in polymer crystallization

The lower temperature limit for sporadic “thermal” nucleation, as estimated in a previous paper (Janeschitz-Kriegl (1997) Colloid Polym Sci), can be verified by a variety of earlier experiments which are compiled in this paper. Below the said limit only “athermal” nuclei are of importance in samples containing no large numbers of hetero-nuclei. The number of athermal nuclei increases tremendously (by many decades) with decreasing temperature. Why these nuclei are dormant and “awake” only at “their” temperature is explained in terms of their growth conditions, which depend on the length of the incorporated (helical) sequences. Also the sluggishness of molecular processes, occurring in the temperature range of metastable conditions, where sporadic nucleation can occur is demonstrated by some of the recalled experiments. Except for very fast industrial processes, where flow plays a dominant role, this sluggishness makes a noticeable influence of the sporadic nucleation on structure formation very improbable. Received: 30 July 1998 Accepted in revised form: 5 September 1998     

Analysis of the topological dependency of the characteristic polynomial in its chebyshev expansion

The structural dependency (effect of branching and cyclisation) of an alternative form, the Chebyshev expansion, for the characteristic polynomial were investigated systematically. Closed forms of the Chebyshev expansion for an arbitrary star graph and a bicentric tree graph were obtained in terms of the “structure factor” expressed as the linear combination of the “step-down operator”. Several theorems were also derived for non-tree graphs. Usefulness and effectiveness of the Chebyshev expansion are illustrated with a number of examples. Relation with the topological index (Z _G ) was discussed. Operated for the U.S. Department of Energy by ISU under contract no. W-ENG-7405-82. Supported in part by the Office of Director     

Vertex topological indices and tree expressions,generalizations of continued fractions

We expand on the work of Hosoya to describe a generalization of continued fractions called “tree expressions.” Each rooted tree will be shown to correspond to a unique tree expression which can be evaluated as a rational number (not necessarily in lowest terms) whose numerator is equal to the Hosoya index of the entire tree and whose denominator is equal to the tree with the root deleted. In the development, we use Z(G) to define a natural candidate ζ(G, v) for a “vertex topological index” which is a value applied to each vertex of a graph, rather than a value assigned to the graph overall. Finally, we generalize the notion of tree expression to “labeled tree expressions” that correspond to labeled trees and show that such expressions can be evaluated as quotients of determinants of matrices that resemble adjacency matrices.     

Linearly polarized white fluorescence from shish-kebab type liquid crystalline poly(P-phenylenevinvlene)s with (P-phenylene)s as kebab

Liquid crystalline(LC) polymers with a shish-kebab-type moiety on their cross-conjugated(p-phenylene)s-poly(p-phenylenevinylene) s main chains were synthesized through Gilch polymerization in order to develop a kind of polymers available for linearly polarized white-light-emitting from single chain.In this system,the 2,5-bis(4’-alkoxyphenyl)benzene as the "kebabs" connects with poly(p-phenylenevinylene)(PPV) main chain backbone using its molecular gravity center and the PPV as the "shish" or "skewer"(the "shish-kebab").The polymers possess desirable properties such as excellent solubility and liquid crystalline properties.To drop the "kebabs" of the 2,5-bis(4’-alkoxyphenyl)benzene into the orientation microgroove of aligned polyimide film,not only the "shish" of polymer main chain can be aligned by the virtue of orientation of "kebabs" but also the uniform cross-conjugated structure between the "kebabs" and "shish" can be broken. Then,the alignment of the polymer main chain showed yellow light emission and was also accompanied by orientation of the LC side chains showing blue light emission,this gave rise to a notable linearly polarized white fluorescence.     

The effect of hydrogen ion production on the steady-state multiplicity of substrate-inhibited enzymatic reactions

The phenomenon of multiplicity is investigated for an isothermal continu ous stirred tank reactor (CSTR) in which an enzyme reaction producing hydrogen ions is taking place. The activity of the enzyme considered is sensitive to the hydrogen ion concentration and is inhibited by excess substrate. The enzyme is bound and the washout phenomenon is negligible. The investigation has uncovered a new type of hysteresis, consisting of a closed curve on the multiplicity diagram, and is disconnected from the rest of the multiplicity curve. This phenomenon has also been observed and analyzed by Uppal et al. (1) in their investigation of the non-isothermal, non-adiabatic (CSTR), and they have termed those closed curves “Isolas.” In the present paper we have elucidated the physical reason for the occurrence of those “Isolas” for the enzymatic reaction under consideration. We have also investigated the effect of different parameters on the appearance, disappearance, and size of the “Isolas.”     

“Osmiophilic particles”—a fungal agent with characteristic distribution in white-and brown-rotted wood

When pine wood decayed by white- and brown-rot fungi was observed in TEM after fixation and staining with glutaraldehyde/osmium tetroxide/ uranylacetate and embedding in Spurr’s ultralow viscosity resin electron dense particles, called “osmiophilic particles,” a typical distribution for the two decay types could be observed: in white-rotted wood the particles could be found in and around the hyphae and on the lumen surface of the wood cell wall, mostly aggregated to thick clusters. During the whole course of decay the wood cell walls were free of the particles, but they were present on the corroded surfaces. In brown-rotted wood the “osmiophilic particles” also could be found in and around the hyphae, but in contrast the particles were distributed over all the wood cell wall layers from the early to late stages of decay. The distribution of the “osmiophilic particles” coincides with the place where the major cell wall degradation takes place: in white-rot the cell walls are degraded from the lumen to the middle lamella; in brown-rot a depolymerization and degradation of the carbohydrates takes place all over the wood cell wall. Since the “osmiophilic particles” can be found where the degradation takes place, it can be concluded that they are causally connected with wood decay. The fact that they also were found in, and some of them also around, hyphae grown on malt-agar or Sabouraud-dextrose-agar proves that they are produced by the fungi and cannot be degradation products. The possibility that they could be preparative artifacts can be excluded because uncolonized wood was free of “osmiophilic particles.” Since the “osmiophilic particles” are produced by the fungi and can be found in places where wood is decaying, it can be further concluded that they are a fungal agent that is involved in wood degradation, probably fungal enzymes. The observation that the large “osmiophilic particles,” which may have a size of up to 20 nm, are composed of globular subunits of a diameter of 2—3 nm also speaks for their enzymatic nature. To find out which type of enzyme they might be, the white-rot fungusTrametes hirsuta was grown on wood pulp with 7% lignin, on delignified wood pulp containing cellulose and hemicellulose, and on filterpaper (pure cellulose). The hyphae on wood pulp containing 7% lignin were surrounded by thick sheaths of “osmiophilic particles,” whereas with the hyphae grown on delignified wood pulp and pure cellulose only a few particles could be found. This makes it clear that the production of the “osmiophilic particles” is induced by lignin.     

Classification and Representations of Low-Dimensional Nanomaterials: Terms and Symbols

A simple scheme, with special terms and symbols useful in categorizing various nanostructures, is introduced. Using “n-D in/on m-D” composite nanomaterials where n,m ≤ 2 as examples, we illustrate how these terms and symbols can be used to represent various hetero nanostructures. This simple nomenclature system also allows a systematization of a wide variety of multi-dimensional nanocomposite heterostructures.     

Integration of metrological principles and performance evaluation in a proficiency testing scheme in support of the Council Directive 98/83/EC

Proficiency testing as a means of external quality assessment plays the role of independent evidence of laboratories’ performance. To enable laboratories to fulfil the requirements stated in legislation, methodology for evaluation of laboratories’ performance in proficiency testing schemes should incorporate principles of measurement results which are fit for intended use and incorporate evaluation of laboratories’ performances based on independent reference value. A proficiency testing scheme was designed to support Drinking Water Directive (98/83/EC) specifically. The methodology for performance evaluation, which takes into account a “fitness for purpose”-based standard deviation for proficiency assessment, is proposed and discussed in terms of requirements of the Drinking Water Directive. A ζ′-score, modified by application of target uncertainty was developed in a way that fulfils requirements defined in the legislation. As an illustration, results are reported for nitrate concentration in water. The approach presented can also be applied to other fields of measurements.     

α,ω-Bis(3,6-dimethyl-2,4-dioxo-1,2,3,4-tetrahydropyrimidin-1-yl)alkanes and products of their cyclization, pyrimidinophanes: intra- and intermolecular interaction in crystals and in solutions

Reaction of α,ω-bis(3,6-dimethyl-2,4-dioxo-1,2,3,4-tetrahydropyrimidin-1-yl)alkanes with paraformaldehyde leads to pyrimidinophanes, which contain four 3,6-dimethyluracil fragments, connected to each other by the methylene chains. A comparative study of intra- and intermolecular interactions of “open” and macrocyclic uracil derivatives in the crystal state and in solution was performed. According to the NMR spectroscopy data, there is no self-association of “open” and macrocyclic compounds in chloroform solutions, whereas the X-ray data revealed the intermolecular π-π contacts between the 3,6-dimethyluracil fragments in the crystals of these compounds. Conclusions on the presence of intramolecular interactions in chloroform solutions of α,ω-bis(3,6-dimethyl-2,4-dioxo-1,2,3,4-tetrahydropyrimidin-1-yl)alkanes and pyrimidinophanes were made based on the UV spectra, which were interpreted in terms of hypo- and hyperchromic effects relatively to the model uracil derivative. These conclusions correlate with the X-ray data: there are no intramolecular π-π contacts between the 3,6-dimethyluracil fragments both in the crystals and in solutions of “open” compounds, positions of these fragments relatively to each other in the molecules of pyrimidinophanes are defined by the lengths of the polymethylene bridges. The intramolecular stacking effect between the opposite uracil rings is observed for the macrocycles with trimethylene and hexamethylene chains, whereas there is no such interactions in pyrimidinophanes with tetramethylene chains. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 119–131, January, 2008.     

Step wise and dissociative mechanisms of the electron transfer in electrochemical reactions involving organosilicon compounds: Molecular-thermodynamic approach1

Electrochemical reduction of organochlorosilanes and oxidation of hexaorganodisilanes may occur via dissociative and stepwise mechanisms, the choice between which is determined by the balance between fundamental structural parameters of elementoorganic molecules. The formation of radical anions of silyl-substituted chloromethane in the conditions of an electrochemical experiment is shown. The formation is due to α-silicon stabilization of the intermediate during the electron transfer. The role of conjugation and hyperconjugation in the organosilicon compounds’ reactivity is analyzed. When employing terms “ stepwise ” and “ dissociative ” mechanisms of the electron transfer, we follow tradition introduced and developed by J.-M. Saveant’s group [1] and recommended by the IUPAC Commission on Electrochemical Nomenclature [2]. The terms refer to an electrochemically reversible transfer of electron whose kinetics does not limit the process rate as a whole and to an electrochemically irreversible transfer which involves a bond cleavage in an elementary act of electron transfer. The term “ activation ” mechanism, which is sometimes applied to electrochemically irreversible processes, is more universal; however, it is somewhat not unique as compared with the term “ dissociative.” Coupled with “ associative,” the latter may be used for indicating processes that involve the formation of a bond in an elementary act of electron transfer.     

Standardization of pH measurements based on the ion interaction approach

The Pitzer method was used to calculate the pH values on the conventional and “true” scales for the TRIS—TRIS·HCl−NaCl−H₂O buffer system in the 0–40 °C temperature region and 0–4 NaCl molality interval. This buffer can be used as a standard for pH measurements in a wide range of ionic strengths. The conventional scale is used in cells without a salt bridge. The “true” scale is recommended for pH measurements using cells with a salt bridge. At the same concentrations of the buffer solution, the “true” scale is essentially transformed into the scale of the National Bureau of Standards (NBS) of the USA. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 676–680, April, 2000.     

Manifestation of electron-nuclear dynamics in <Superscript>59</Superscript>Co NQR spectra of a series of cobaltocenium derivatives

A coupling equation relating the quadrupole coupling constant (e² Qq _zz ) to the asymmetry parameter (η) of the electric field gradient for a series of cobaltocenium derivatives (⁵⁹Co NQR) is derived. The estimates of the correlation times of “slow” modulations of electron motions by tunneling processes lie in the range from 10⁻¹² to 10⁻¹⁴ s. This corresponds to the interval of the characteristic times of nuclear motions. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1919–1923, October, 2007.     

Comparability of measurement results for pesticide residues in foodstuffs: an open issue?

The dispersion of results from proficiency tests for the analysis of pesticide residues in foodstuffs suggests that improvements in the compatibility of measurement results are needed. Currently observed divergences can make the evaluation conclusion on foodstuffs compliance with certain legislation dependent on the consulted laboratory. This work discusses the origin and impact of this lack of compatibility, following the metrological concepts presented at the latest version of the “International Vocabulary of Metrology” (VIM3), thus allowing for a clear diagnostic of the problem. The reporting of results from different measurement methods uncorrected for the observed analyte recovery makes them traceable to different “operationally defined measurement procedures” (VIM3) and, therefore, not comparable. When results from different measurement methods are reported corrected for analyte recovery, R, and R is different for spiked and incurred residues, measurement results may be not compatible if this effect is not considered on the uncertainty budget. This discussion is illustrated with metrological models for any possible combination of “measurement performance” and “maximum residue level”. These models are complemented with experimental data of the analysis of pesticide residues in a sample of ginseng powder from a proficiency test. The adopted experimental design allowed the identification of additional threats to metrological compatibility in this field. Solutions to the faced problem are discussed for practicability and impact on regulatory issues. The use of a universal “reference measurement procedure” proves to be the most feasible way of ensuring comparability of measurements in this field.     

Low temperature carbene-to-carbene homologations

Since alkynes have higher symmetry than olefins, it is not easy to infer the mechanism of a triplet carbene’s addition to an alkyne by traditional product analysis studies. Specifically, no stereochemical information which might offer insight into the carbene’s spin state can be extracted from the cyclopropene products. In 1971, Hendrick, Baron, and Jones showed that diphenylcarbene reacts with terminal alkynes in solution to produce indenes via a “self-trapping” vinylcarbene. They also examined the diphenylcarbene reaction with disubstituted alkynes and found at most trace amounts of the “self-trapping” indene product. In this work, we report the direct observation by organic matrix EPR of the vinylcarbenes generated from triplet fluorenylidene and terminal alkynes. Our efforts to confirm the identities of these intermediates by independent synthesis, intermolecular trapping, and an intramolecular “self-trapping” method-halogen-migration-are also recounted. These findings are among the few instances in which fluorenylidene undergoes carbon-carbon bond formation rather than atom abstraction reactions in a low-temperature matrix, and in which the biradical adduct of a triplet carbene and a π-bonded substrate can be directly observed.     

Second-order energy components in basis-set-superposition-error-free intermolecular perturbation theory

 Recently a basis-set-superposition-error-free second-order perturbation theory was introduced based on the “chemical Hamiltonian approach” providing the full antisymmetry of all wave functions by using second quantization. Subsequently, the “Heitler–London” interaction energy corresponding to the sum of the zero- and first-order perturbational energy terms was decomposed into different physically meaningful components, like electrostatics, exchange and overlap effects. The first-order wave function obtained in the framework of this perturbation theory also consists of terms having clear physical significance: intramolecular correlation, polarization, charge transfer, dispersion and combined polarization–charge transfer excitations. The second-order energy, however, does not represent a simple sum of the respective contributions, owing to the intermolecular overlap. Here we propose an approximate energy decomposition scheme by defining some “partial Hylleraas functionals” corresponding to the different physically meaningful terms of the first-order wave functions. The sample calculations show that at large and intermediate intermolecular distances the total second-order intermolecular interaction energy contribution is practically equal to the sum of these “physical” terms, while at shorter distances the overlap-caused interferences become of increasing importance. Received: 18 June 2001 / Accepted: 28 August 2001 / Published online: 16 November 2001     

Revisiting the problem of correcting retention parameters for pressure and temperature in gas chromatography

Summary It has been shown [1, 2] that the compressibility correction factor equals the ratio of gas pressure at the column outlet to the average pressure in the column,j=p _o /p _c , and, therefore, by multiplying by this factor, all experimentally measured retention volumes and flow rates are converted from ambient pressure to the average pressure in the column. This makes retention volumes corrected in this way independent of pressure. In contrast, correcting retention times for gas compressibility has no physical meaning and terms such as “corrected retention time” and “net retention time” should not be used. Similarly, recalculating corrected retention volumes to a standard temperature of 273 K appears to provide a thermodynamically sound basis for comparison of data obtained at different temperatures. In reality, it distorts actual relationships and should not be used. Presented at: Balaton Symposium on High-Performance Separation Methods, Siófok, Hungary, September 3–5, 1997.     

Standardization in charged particle activation analysis

Standardization methods in activation analysis with charged particles are studied critically. Several approximate standardization methods that do not require knowledge of the excitation function are compared with the “numerical integration method” using excitation function data from the literature. It is shown that these methods yield accurate results if the threshold energy of the considered reaction is high and if sample and standard have a comparable Z value. A method that gives a rapid estimate of the maximum possible error is also presented. It is shown that for the “numerical integration method” the accuracy of the excitation function data has only a small influence on the overall accuracy. The influence of the accuracy of stopping power data and of possible deviations from Bragg's rule for light element standards is also considered. “Bevoegdverklaard navorser” of the NFWO.     

Lateral flow (immuno)assay: its strengths,weaknesses, opportunities and threats. A literature survey

Lateral flow (immuno)assays are currently used for qualitative, semiquantitative and to some extent quantitative monitoring in resource-poor or non-laboratory environments. Applications include tests on pathogens, drugs, hormones and metabolites in biomedical, phytosanitary, veterinary, feed/food and environmental settings. We describe principles of current formats, applications, limitations and perspectives for quantitative monitoring. We illustrate the potentials and limitations of analysis with lateral flow (immuno)assays using a literature survey and a SWOT analysis (acronym for “strengths, weaknesses, opportunities, threats”). Articles referred to in this survey were searched for on MEDLINE, Scopus and in references of reviewed papers. Search terms included “immunochromatography”, “sol particle immunoassay”, “lateral flow immunoassay” and “dipstick assay”.