Understanding the properties of isospectral points and pairs in graphs: The concept of orthogonal relation

The mathematical property orthogonal relationship is used in proving the fact that isospectrality, isocodality and isocoefficiency of vertices within a graph are all equivalent. The same is true for isospectrality, strict isocodality and strict isocoefficiency of pairs (including edges) within a graph, whereas the weak versions of the latter properties are necessary but not sufficient for isospectrality of pairs. Similarly, necessary and sufficient conditions for isospectrality of vertices and pairs in different graphs are derived. In all these proofs, the concept of orthogonal relation plays a major role in that it allows the use of tools of elementary linear algebra.     

Meeting the need for reference measurements

Summary Reference materials do fulfil a very useful function in that they provide means to check, verify and calibrate measurement procedures and instrumentation. However, the material is often idealized compared to real life samples: it is either (very) pure or does not correspond in concentration level or matrix to the real life case. It is shown how this situation could be remedied if real life samples with carefully assessed reference values could be made available regularly as unknowns to measurement laboratories. Comparison of the latter's measurements with the reference values then would provide a picture of the real performance of the particular measurement community in general and of each participating laboratory in particular. The opinion is expressed that isotope-specific methods have now matured to the stage that, if they are correctly applied under rigorous control and based on highly skilled expertise, they can provide such reference values against which laboratories can then evaluate their routine performance in regular Interlaboratory Measurement Evaluation Programmes (IMEPs).

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Wie der Notwendigkeit von Referenzmessungen entsprochen werden kann

     

Plutonium in soils, bottom sediments and lichen near peaceful nuclear explosion sites in the Republic of Sakha (Yakutia)

During the 1974–1987 period 12 paceful nuclear explosions were conducted in the Republic of Sakha (Yakutia). For the first time^239,240Pu and²³⁸Pu concentrations were determined in samples of soils, bottom sediments and lichen taken at the Craton-3 and Crystal nuclear explosion sites. At the Craton-3^239,240Pu concentrations in the range 6.2 mBq/g to 5.9 Bq/g samples of soil and^239,240Pu concentrations up to 7.4 Bq/g in samples of lichen were observed.^239,240Pu concentration measurements in bottom sediments of a stream washing out the banking around the borehole of Craton-3 show that plutonium migrates in the direction of the Markha river. At the Crystal site local plutonium concentrations up to 35 Bq/g in soil and 1.8 Bq/g in lichen were observed.     

Structure-reactivity problem in cycloaddition reactions to form heterocyclic compounds

The steric and electronic effects of substituents in both diene and dienophile components have been considered as the main factors that control the electronic character of (4+2)-cycloaddition leading to transitions between normal, neutral, and inverse Diels-Alder reactions.Institut für Organische Chemie der Universität Regensburg, Universitätsstr. 31, D-93040 Regensburg, Germany. Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1307–1322, October, 1995. Original article submitted August 15, 1995.     

Determination of total,and bound Se in sera by INAA

In this study we report on the comparison between the total selenium in serum (total Se) with that which is apparently bound to high molecular weight (>12,000 D) species, presumably proteins (bound Se). Nine hundred seventy seven (977) serum samples arising out of a population-based epidemiological study were prepared in duplicate for the determination of total Se by pipeting directly into irradiation vials; and separate duplicate aliquots were dialyzed against DI water for the determination of bound Se. All samples were analyzed by neutron activation analysis via^77mSe (17.4 s). A small dialyzable Se component (6%) (free Se), defined as the difference between the total Se minus the bound Se, was identified.     

The diagram lattice as structural principle A. New aspects for representations and group algebra of the symmetric group B. Definition of classification character,mixing character,statistical order,statistical disorder; A general principle for the time evolution of irreversible processes

It is the aim of this paper to demonstrate the significance of the diagram lattice. This lattice was defined in order to achieve structural insight into the phenomenon of chirality in chemistry. In this context, Theorie der Chiralitätsfunktionen [1] may serve as reference. In the introduction of the present paper a summary of the relevant theorems and definitions is given and a few examples of the diagram lattice are graphically illustrated. Parts A and B can be read independently and presuppose knowledge only of the introduction. Part A is of special interest for mathematicians, Part B and [1] for physicists and chemists.In Part A theorems on the representations of the group _n and certain subgroups of it and on the structure of the group algebra are developed. In Part B the concept classification character with the two complementary aspects of identification and distinction is derived. With the interpretation mixing character the partial order relation gains an interpretation through a mixing process, which can be expressed by a bistochastic matrix. This results in another equivalent definition of the diagram lattice. Interpreted as mixing character of a statistical distribution a diagram represents statistical order and statistical disorder by its row partition and column partition respectively. These concepts and the corresponding lattice structure lead to the hypothesis of growing mixing character as a criterion for the time evolution of isolated systems. The criterion of increasing entropy provides a much weaker condition. A discussion of the master equation leads to a proof of the principle of growing mixing character.[/p]     

Studies of solvent effects

The effect of water on the conformational preferences of acetylcholine has been studied within the discrete, the continuum and the combined discrete-continuum models described in parts I and II of this series. All the models lead to the conclusion that the trans-gauche form which is, following refined quantum-mechanical computations, the intrinsically preferred one and the one observed in the crystal of acetylcholine and of a number of analogues should remain also the preferred conformation in water. This result agrees with NMR studies. The results of the empirical discrete model used here compare favorably to those obtained by an ab initio super-molecule treatment. The continuum model utilized here represents a net improvement above such models utilized in other works.     

Zur Literaturdokumentation in der Analytischen Chemie

Zusammenfassung Der in den Referatezeitschriften Chemical Abstracts, Analytical Abstracts und Fresenius Zeitschrift für Analytische Chemie erkennbare alphabetischsystematische Aufbau der Indexregister wird dargestellt und beurteilt. Die Beispiele stammen aus den Indexabschnitten Atomabsorptionsspektrometrie (Methode), Phenole (Stoff) und Boden (Material). Unter Berücksichtigung der Ergebnisse werden Vorschläge zur benutzerfreundlichen Gestaltung eines analytisch-chemischen Indexsystems nach einer 3-W-Regel (Fragen nach WAS, WIE und WORIN, WOZU?) gemacht und diese Anforderungen an einer Stichprobe von 47 Referaten von Veröffentlichungen aus 21 verschiedenen Zeitschriften in den Indices der Referatzeitschriften überprüft. Die Recall-Raten nach den vorgegebenen Schlüsselwörtern für jede Teilfrage der 3-W-Regel liegen zwischen 3 und 51% und für die Frage nach der Methode mit 3–14% am niedrigsten.

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Literature documentation in analytical chemistryIII. Structure and valuation of index systems

Summary The recognizable alphabetic-sytematic structure of the indices in the abstract journals Chemical Abstracts, Analytical Abstracts and Fresenius Zeitschrift für Analytische Chemie is described and criticized. The examples are taken from the index sections atomic absorption spectrometry (method), phenols (substance) and soil (material). In consideration of the results and taking into account the needs of the user suggestions for the construction of an analytical-chemical index system according to a 3-Wprinciple (questions for what, in what way and wherein, whereto) are given, and these requirements are proved by a random sample of 47 abstracts from publications of 21 diverse journals taken from the indices of the abstract journals. The recall ratios resulting from the pretended key words for every sectional question of the 3-W-priciple are between 3 and 51%; for the question as to the method they are most inferior with 3–14%.

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Teil II siehe Fresenius Z Anal Chem 304:28 (1980)     

Chemical shifts of aqueous nonelectrolyte solutions: Influence of the polar and nonpolar groups on the water proton shifts at 0°C

Hydroxyl-proton chemical shifts of alcohol mixtures and aqueous solutions containing some nonelectrolytes (alcohols, ketones, cyclic ethers, and amines) have been measured at 60 MHz and at 0°C. Methyl-proton resonance of the solutes was used as the internal reference and the water-proton shifts in solutions were measured with respect to pure water. Downfield shifts for some alcohols (particularly tertiary butanol and iso-propanol), cyclic ethers, and amines in the water-rich region were confirmed For alcohols and some other nonelectrolytes in water, the observed shifts were decomposed to component contributions arising from the polar group effect, solute proton effect, and nonpolar group effect. Polar effects are found to contribute a substantial fraction of the observed downfield shifts. After subtracting these polar contributions, however, there still remains certain amounts of downfield shifts which may be attributed to the effect of nonpolar groups on the water structure. The downfield shifts are found to be relatively large when the solutes have branched alkyl groups with nearly spherical shape and with diameters of about 5 Å. Strikingly large downfield shifts of water proton resonance were found for some secondary amines and tertiary diamines with globular shape. However, in view of the extrapolation technique employed in evaluating the polar group effect, the downfield nonpolar group effect we estimated should be considered as the upper limits.Work done at Professor Hertz's laboratory in Karlsruhe on a sabbatical leave from Clark University.     

Philosophical aspects of chemometrical strategy in Analytical Chemistry

Summary This paper discusses the philosophical aspects of the three main chemometrical strategies in analytical chemistry: statistical data treatment, optimization and modelling, pattern recognition. It is possible by a more general consideration of these approaches to find a proper place of different philosophical categories such as form and content, induction and deduction, concrete and general in analytical chemistry. The philosophical aspect of the considerations allows a deeper penetration into the theoretical basis of chemical analysis.

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Philosophische Betrachtungen zu chemometrischen Strategien in der Analytischen Chemie

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Presented at the First International Symposium on History and Philosophy in Analytical Chemistry, Vienna, November 22–23, 1985     

Similarity and dissimilarity in posets

The relevance of partially ordered sets (or posets) in a wide diversity of contexts in chemistry is emphasized, and the utility of distance functions (or metrics) on such posets is noted. First a notion of scale similarity is introduced to make comparisons within certain so-called scaled posets, for which there is formulated natural comparators, which in turn lead to associated distance functions. Beyond taking note of several chemically relevant examples of these scaled posets and their consequent associated similarity measures, a second chemically relevant class of so-called shifted posets is similarly developed, with examples. Even further extension of some aspects of the current approach is indicated, and finally the multi-posetic character of chemical periodic law is suggested.     

An investigation of micro-brownian motions in polydimethylsiloxane by complementary incoherent-neutron-scattering and nuclear-magnetic-resonance experiments below room temperature

Two different experimental methods, neutron scattering and nuclear magnetic resonance are used to investigate the random methyl group and segmental rotational jump motions in polydimethylsiloxane. It is shown that nuclear magnetic relaxation and line width experiments are complementary to incoherent neutron scattering fixed-window experiments, the principle of the fixed-window experiments being discussed in somewhat detail. Satisfactory agreement of these experimental techniques is achieved as to the determination of the two model parameters of the motional processes in question, i. e. the activation energy and the preexponential factor of the Arrhenius ansatz made for the correlation time or jump time, respectively.Contribution partly presented during the meeting of the Macromolecular Club, June 8–10, 1983 in Uppsala, the spring conference of the Deutsche Physikalische Gesellschaft, March 12–17, 1984 in Münster and the Fourth International Seminar on Polymer Physics, October 22–26, 1984 in Eyba (GDR).     

FT-IR/PAS investigation of solid fuels and catalysts

Coal and catalysts are examples of substances of great technical importance, whose knowledge has advanced for many years empirically. They are considered as disordered and complex materials. FT-IR/PAS suggests models closer to the real systems as the samples can be examined as they are: coal with the same sampling procedure as for ASTM analysis and catalysts during catalysis without manipulation. Some examples are reported.     

Multivariate Statistical Assessment of Air Quality: A Case Study

The present paper deals with the application of several chemometrical methods (cluster and principal components analysis, source apportioning on absolute principal components scores) to an aerosol data collection from Unterloibach, Austria. It is shown that seven latent factors explaining almost 80% of the total variance are responsible for the data structure and are conditionally identified as secondary aerosol, mineral dust, oil burning, lead smelter, coal burning, salt and fertilizer emission sources. Furthermore, the contribution of each identified source to the formation of the particle total mass and chemical compounds total concentration is calculated. Thus, a reliable assessment of the air quality in the region is performed. The requirements of the sustainability concept for ecological indicators in this case is easily transformed into a multivariate statistical problem taking into account not separate indicators but the specific multivariate nature of aerosol pollution.     

Determination of molecular properties by the method of moments

Some precautions needed in the choice of weight functions when calculating wave functions by the method of moments are analysed. It appears that an important criterion for good weight functions is that the difference between the total and the truncated overlaps (both defined in the paper) be high.The method of moments is applied to wave functions involving Hylleraas-type correlation factors using weight functions made up of products of single-particle orbitals. The aim of the calculations is partly to test the criteria for good weight functions, partly a preparation of more extended calculations of a similar type.The new name of the institute is: Computer Application Research and Development Center of the Chemical Industries.     

Natural flavours of wine: correlation between instrumental analysis and sensory perception

Summary The aroma of wine consists of 600 to 800 aroma compounds from which especially those, typical for the variety, are already present in the grapes. The aroma extracts — received by extraction with trichlorofluoromethane — are separated by gas chromatography. There are significant varietal differences between the aromagrams (fingerprint pattern). Thus the amount of some flavour compounds (key substances) shows typical dependence on the variety. Especially monoterpene compounds play an important role in the differentiation of wine varieties.The German white wines can be differentiated into three groups only by quantitative determination of 12 monoterpenes (terpene profile). These groups are: Riesling type, Muscat type and Silvaner-Weißburgunder type. Such terpene profiles are also useful for the separation of real Riesling wines from others called Riesling (e.g. Welschriesling, Kap Riesling, Emerald Riesling) but not produced from grapes of the variety Riesling. Including further components and by means of statistical methods as for example linear discriminant analysis even the different varieties within the mentioned groups (for instance the Riesling-group: Riesling, Kerner, Ehrenfelser, Bacchus, Müller-Thurgau) can be separated from each other.To identify compounds causing off-flavours the sniffing technique is the method of choice. The off-flavour is pinpointed during gas chromatography separation of the complex aroma mixture by effluent sniffing. Once allocated, the chemical nature of the off-flavours is elucidated by spectroscopic methods. Substances contributing to the green pepper taint, the strawberry note, mousiness, corkiness etc. in wine could be found in this way.     

A canonical ordering of polybenzenes and polymantanes using a prime number factorization technique

The correlation described over twenty years ago by Matula between the prime factorization of integers and the class of alkanes is re-examined with a view to explaining the probable reason why there have, to date, been no major extensions of this idea. By considering the class of alkanes as a one-dimensional one-parameter system, a new perspective on the method is gained that is amenable to extension, but in a different direction than originally anticipated. With this new perspective, the classes of polybenzenes and polymantanes are seen to be the representatives of two- and three-dimensional one-parameter systems, respectively. A nomenclature, comparable to one that Matula used for alkanes, is created that gives a unique canonical name to all possible combinations of either polybenzene or polymantane modules. Such a nomenclature contains a built-in means of positioning the molecule in the field of interest in accordance with arbitrary pre-selected criteria, such as Patterson's rules, and also coding that indicates symmetries inherent in the structure of this molecule.     

Meeting future needs for metrological traceability—a physicist’s view

Abstract Metrological traceability of measurement results provides the comparability needed for reliable measurement in almost every aspect of our daily life, ranging from fundamental science, through health and safety to global trade. From the authors (a physicist) perspective and understanding of recent literature, measurements in chemistry compare the amount of analyte, are often made indirectly, are sometimes not fully traceable to the SI, and metrological traceability is perhaps not always the major concern of the practising analytical chemist. The present article examines which of these views are typically chemical, and which are common to both the physicist and the chemist. Much can be gained by formulating a common understanding of basic concepts of traceability of measurement results in meeting ever-increasing demands for comparability of measurement results in both traditional as well as new areas of technology and societal concern.Based on a lecture given by the author at a mini-symposium Emerging issues in metrology in chemistry organised by the IUPAC Analytical Chemistry Division and IUPAC Working Party for Harmonisation of Quality Assurance at IAEA Headquarters, Vienna, 17th February 2004.     

New algorithm for nonorthogonal ab initio valence bond calculations II: Subgraph-driven method

The permanent method for nonorthogonal VB calculations is extensively developed, and the so-called subgraph-driven procedure is proposed. To achieve high efficiency, the summation of a huge number of permanents is treated as a whole system, and the intermediate quantities, the contracted-cofactors of various orders, are introduced for the systematic summation. These intermediate quantities can be characterized by pairing graphs of 2n elements (n = 1, 2, ... 1/2N – 2). Some test calculations for systems of up to 20 electrons are performed. The practice shows that this method is highly efficient, and the CPU time increases in a quite moderate way with the increasing number of electrons.On leave from Chemistry Department, Xiamen University, 361005 Xiamen, PR China.     

Interplay of Thermochemistry and Structural Chemistry,the Journal (Volume 13, 2002) and the Discipline

As practiced disciplines, structural chemistry and thermochemistry need not be related. In the current study they are: the contents of the journal Structural Chemistry (Vol. 13) for the year 2002 have been reviewed and then most articles that appeared therein were given a thermochemical commentary, spin or slant.