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.     

Zur Literaturdokumentation in der Analytischen Chemie

Zusammenfassung Anhand von 298 Referaten aus Fresenius Z. Anal. Chem. werden systematisch geordnete Listen von Indexbegriffen für die Bereiche Methoden und Anwendungen erstellt und auf diese Referate angewendet. Diese vorläufige Systematik umfaßt 63 und 32 Hauptindexwörter. Den dokumentierten Referaten wurden 815 Schlüsselwörter (Hauptindexwörter) zugeordnet (116 Referate mit 2, 134 Referate mit 3 Hauptindexwörtern, Minimum: 1, Maximum: 5). Für zwei Indexabschnitte, Atomabsorptionsspektrometrie und Geologisches Material, wird die vorgeschlagene Indexierung vorgestellt und mit der bisherigen in Fresenius Z. Anal. Chem. verglichen. Die überschaubare Zahl von 95 Hauptindexwörtern, die erkennbare, einfache Systematik und die Wahlmöglichkeiten von zusätzlichen Nebenindexwörtern sollen zu einer benutzerfreundlichen Dokumentation beitragen, welche hiermit zur Diskussion gestellt wird.

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Literature documentation in analytical chemistryIV. Development of a systematic, easily usable index and documentation system

Summary By means of 298 abstracts from Fresenius Z. Anal. Chem. systematically arranged lists of index terms for the fields methods and applications were compiled and used for these abstracts. This preliminary system contains 63 and 32 first index terms. 815 Key words were allocated to the abstracts (= first index terms): 116 abstracts with 2, 134 abstracts with 3 first index terms, minimum: 1, maximum: 5. For two index sections, l.e. atomic absorption spectrometry and geological materials, the proposed indexing system is presented and compared with the system hitherto used in Fresenius Z. Anal. Chem.. The favourable number of 95 first index words, the obviously simple system and the possibility of selecting additional second index terms should contribute to an easily usable documentation, which is herewith presented for discussion.

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Teil III: Fresenius Z Anal Chem (1982) 312:448–454     

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     

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.     

Der o-Effekt in den Massenspektren aromatischer Verbindungen

Zusammenfassung Das Massenspektrum des O-Äthylsalicylsäureamides VII b ist von dem seiner m- und p-isomeren Verbindung völlig verschieden und zeigt einen typischen massenspektrometrischen o-Effekt.Die bisher aufgefundenen Verbindungen mit massenspektro-metrischem o-Effekt gehören einem relativ kleinen Kreis von Aromaten mit ganz bestimmten Strukturmerkmalen an. Die Bildung der für den o-Effekt charakteristischen Bruchstücke kann in allen diesen Fällen nach einem vonMcLafferty aufgestellten Mechanismus zwanglos erklärt werden. Verbindung VIIb hätte unter der Voraussetzung, daß eine Entstehung der für den o-Effekt typischen Fragmente nur nach diesem Mechanismus möglich ist, keinen o-Effekt zeigen dürfen.Das Auftreten des o-Effektes im Massenspektrum von VIIb läßt erkennen, daß die Bedingung zur Bildung der für den o-Effekt charakteristischen Bruchstücke lediglich in der Möglichkeit zur Ausbildung stabiler Spaltprodukte zu suchen ist, und daß daher weit mehr Verbindungen einen o-Effekt zeigen sollten als bisher anzunehmen war.Mit 1 Abbildung     

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.     

Chemical algebra. II: Discriminating pairing products

The algebra of stereogenic pairing equlibria is presented in a very general context. Starting from the notions of fuzzy subgroup and conjugacy link, chemical pairing constants between molecular speciesu andv having a skeletal symmetry groupG are formulated as pairing products on aG-Hilbert space. Discriminating pairing productsK are defined by the conditions: K 1 and K = 1 the representative vectors of the paired species areG-equivalent. WhenG has only two elements, the pairing product is always discriminating. For several skeletal symmetries, if the vectors are enantiomorphic (v = u, ² =e, G), thenK is greater than 1 and reaches 1 only ifu is achiral: chirality indexes and general permutational indexes are then defined fromK(u u). The general model is illustrated by some examples.     

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.     

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.     

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.     

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

     

On the recognition of structural features: Some general problems illustrated by hamiltonian paths in polyhexes

Human and machine recognition skills are discussed, though not comprehensively reviewed, and some of the difficulties are illustrated by algorithms written to search for Hamiltonian paths in polyhexes. The most successful strategy for this is based upon the branching graph, a recently introduced graph-theoretical device which can aid the recognition of edges that arenot part of a Hamiltonian path. Another, more widely applicable approach that is interesting, although in this preliminary form only a little better than random methods, uses the metaphor of biological evolution, and tries to breed and grow paths subjected to natural selection.     

Topological complexity of potential surfaces and application to C2H2 molecule

Summary In this work, we search for the simplest complete surfaces of systems with three and four atoms, i.e. the minimal sets of critical points with their index, which are topologically consistent in the whole configuration space. Then we show the smallest change in the A₂B₂ system by requiring at least one stable acetylene configuration and one stable vinylidene configuration, like on the C₂H₂ surface. Finally, we give complete sets of minima, saddle points and maxima obtained for C₂H₂ with analytical potentials proposed in the literature and with a semi-empirical method at the CAS-CI level.     

Effects of Feed Composition of Coke Oven Gas on a Layered Bed H2 PSA Process

The effects of feed composition on the adsorption dynamics and the optimal process design were studied from the experimental and simulated results in the H₂ layered bed PSA with activated carbon and zeolite 5A. The breakthrough results using the base composition (56.4 vol% H₂; 26.6 vol% CH₄; 8.4 vol% CO; 5.5 vol% N₂; and 3.1 vol% CO₂) in various layered beds were compared with those using the higher nitrogen composition and the no nitrogen composition. In the breakthrough dynamics, the propagation velocity of wave front of each component was closely related to the slope of isotherm estimated at its concentration in the feed. Breakthrough behavior at each layered bed in the higher nitrogen composition showed similar trends as that in the base composition. However, the no nitrogen composition showed different breakthrough behavior from the other groups. In this feed composition, it was observed that the order of CO and CH₄ breakthrough times was reversed with a change in the carbon-to-zeolite ratio. Based on the adsorption dynamics and breakthrough behavior of each feed composition group in various layered beds, the effect of feed composition on a seven-step two-bed PSA process for the H₂ recovery from coke oven gas was investigated numerically to develop a well-designed H₂ PSA process under various operating conditions. As expected from the breakthrough results, the trends of the PSA performance in the higher nitrogen composition were similar to those in the base composition except for the slight decrease in the optimal carbon-to-zeolite ratio. However, in case of the no nitrogen composition, high purity product was obtained from the activated carbon-rich layered bed PSA because the adsorption capacity of the activated carbon for impurities was superior to that of zeolite. As a result, the optimum carbon-to-zeolite ratio at each operating condition was slightly changed depending on the propagation velocity of each component on each layer.     

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.     

Determination of polychlorobiphenyls and polycyclic aromatic hydrocarbons in the atmospheric aerosol of the Venice Lagoon

An analytical method for simultaneous determination of particle-associated and gaseous-phase concentrations of polychlorinated biphenyls (PCB) and polycyclic aromatic hydrocarbons (PAH) in atmospheric aerosol samples obtained by high-volume samplers using polyurethane foam adsorbent (PUF) and quartz fibber filters (QFF) has been investigated. Quality control of the analytical procedure was carried out by blank control and by evaluating limits of detection, recoveries, accuracy, and repeatability. The proposed method was subsequently used to determine PAH and PCB in the gaseous and particulate phases of the aerosols that enter the Venice Lagoon atmosphere. The highest concentrations of PCB and PAH were predominantly in the gaseous phase. In both particulate and gaseous phases the penta-CB congeners dominated total PCB concentrations whereas phenanthrene, fluoranthene, and pyrene dominated the PAH concentrations. Total (gaseous plus particulate) PCB and PAH concentrations were higher at the site directly influenced by the industrial plants but the concentrations in marine aerosol samples were lower by a factor four only and must be taken into consideration when studying the chemical contamination of the Venice Lagoon.     

Influence de divers paramètres de constitution et de composition sur la configuration du domaine d'existence et certaines propriétés de microemulsions quaternaires monophasiques

Macroscopically homogeneous, stable, fluid, generally optically transparent and isotropic media (currently called microemulsions) may be formed by adequately mixing together water, a hydrophobic hydrocarbon, (oil), and suitable amphiphilic substances. The microemulsion domains of numerous systems incorporating water, sodium dodecylsulfate, various straight or branched alkanols and various aliphatic or aromatic hydrocarbons were delineated at T=25 °C. It has thus been possible to bring out the influence of several composition factors upon microemulsion domain configuration, i. e. straight alkanol number of carbon atoms, alkanol isomery, normal aliphatic hydrocarbon number of carbon atoms, aliphatic hydrocarbon-aromatic hydrocarbon substitution. The existence of two main kinds of water/ionic surfactant/alkanol/hydrocarbon systems, according as the microemulsion realm-of-existence in the phase tetrahedron consists of two disjoined volumes, (long alkanols), or forms an all-in-one block volume, (short alkanols), can well be correlated with the existence of striking dissimilarities in certain transport properties of microemulsions, such as electrical conductivity or viscosity. For some short alkanols, (e. g. 1-pentanol or 2-pentanol), the microemulsion domains exhibits strange configuration irregularities. Results gained from studies of microemulsion electroconductive and viscous behavior and of cyclohexene-2-one-1 photodimerization in microemulsions tend to indicate that these configuration irregularities define certain ranges of system composition that correspond to microemulsions possessing an exotic structure.

     

X-ray structural analysis of tetrahydrofurofuran lignans

The crystal structures of two diastereomeric tetrahydrofurofuran lignans, diasesartemin (1) and episesartemin-B (2), were determined. The former one is of the classical axial-axial substitution type (the two aryl moieties of the 1,4-diaryl-tetrahydro-1H,3H-furo[3,4-c]furan in ax-ax position), the latter one belongs to the axial-equatorial type. Analysis of the X-ray results revealed that in both cases the substituents are attached in pseudo-equatorial positions due to a flip of the (slightly twisted) envelope conformation of the oxolane five-rings. In1 the oxygen atoms of the two five rings point against each other (overall boat conformation of the tetrahydrofurofuran system orendo-endo topology), in2 one ring is folded towards and the other one is folded away from the second ring (overall boat-chair conformation of the tetrahydrofurofuran system orendo-exo topology): as a consequence,all aryl substituents adopt a pseudo-equatorial position. The terms ax-ax, ax-eq, and eq-eq used throughout in the literature are therefore misleading as far as the true conformations are concerned. Analysis of the aromatic short wavelength CD couplet of1 by means of the coupled oscillator model shows that the X-ray derived geometry is compatible with the CD data in solution.

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Röntgenstrukturanalyse von Tetrahydrofurofuran-Lignanen

Zusammenfassung Es wurde die Kristallstruktur von zwei diastereomeren Tetrahydrofurofuran-Lignanen, Diasesartemin (1) und Episesartemin-B (2), bestimmt. Ersteres gehört dem klassischen axial-axial-substituierten Typ an (dabei sind die zwei Arylsubstituenten des 1,4-Diaryl-tetrahydro-1H,3H-furo[3,4-c]furans in ax-ax-Position), das zweite gehört zum axial-equatorial-Typ. Die Röntgenstrukturanalyse zeigte, daß die Aryl-Substituenten immer in pseudo-equatorialen Positionen stehen, da die Oxolan-Fünfringe eine entsprechende (leicht getwistete) Briefumschlag-Konformation einnehmen. In1 zeigen die Sauerstoffatome der beiden Ringe zueinander (insgesamt eine Boot-Konformation des Tetrahydrofurofuransystems bzw.endo-endo-Topologie), in2 ist ein Ring in Richtung zum, der andere Ring jedoch weg vom jeweils zweiten gegenüberliegenden gefaltet (insgesamt eine Boot-Sessel-Anordnung in der Tetrahydrofurofuran-Einheit bzw.endo-exo-Topologie): Eine Folge davon ist, daß alle Arylsubstituenten eine pseudo-equatoriale Position einnehmen. Die in der Literatur durchgehend verwendete Bezeichnung ax-ax, ax-eq oder eq-eq ist daher bezüglich der tatsächlichen Konformation mißverständlich. Die Analyse der kurzwelligen aromatischen CD-Banden von1 mittels des Modells der gekoppelten Oszillatoren zeigte, daß die Konformation aus der Röntgenstrukturanalyse mit den CD-Daten in Lösung in Übereinstimmung ist.

     

Dynamic surface elasticity of polymer solutions

The surfaces of surfactant solutions exhibit viscoelastic dilational behavior which may be investigated by modern optical and mechanical methods. The present study focuses on the dynamic dilational properties of the polymer solution — gas interface. Linear flexible polymer chains at the surface are considered as consisting of trains, lying on the surface, and loops and tails that protrude into the liquid. The Rouse model is used to describe the inner dynamics of the trains, whereas their motion relative to their neighbors on the surface can be described with the help of the reptation conception. An expression for the complex dynamic dilational surface elasticity has been derived. Although, in general, the relaxation of the surface tension is characterized by an infinite series of relaxation times, it is shown that for many systems the dynamics of the surface layer can be described approximately by only two main relaxation times. The dispersion equation, which was obtained earlier for solutions of conventional surfactants, is shown to be fulfilled for polymer solutions also.     

Theoretical am1 studies of inclusion complexes of α- and β-cyclodextrins with methylated benzoic acids and phenol,and γ-cyclodextrin with buckminsterfullerene

Semiempirical AM1 calculations have been performed on the inclusion complexes of - and -cyclodextrin with benzoic acid and phenol and -cyclodextrin with methylated benzoic acids in the head first and tail first positions. The results show that -cyclodextrin complexes with phenol and benzoic acid guests in the head first position are more stable than in the tail first position, while -cyclodextrin complexes with the same guests prefer the tail first position. The preferred orientation for -cyclodextrin with methylated benzoic acids is determined by the position of the methyl substituent(s). In general, para-methyl benzoic acid derivatives prefer the tail first position. -cyclodextrin forms a slightly unstable 1:1 complex with C₆₀ (3.4 kcal/mol), but two -cyclodextrins provide enough stabilization by about 10 kcal/mol to cage-in the C₆₀.