A rigid graph for every set

A graph G is called rigid if the identical mapping V(G)→V(G) is the only homomorphism G→G. In this note we give a simple construction of a rigid oriented graph on every set. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 108–110, 2002     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH₂)₂C₆H₃OH (LH) revealed compounds L₃Al ( 1 ) and L₂AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe₂ ( 3 ), rather 2 together with Me₃Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, ¹H and ¹³C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph₃SnOH, giving LSnPh₃ ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy and ¹H, ¹¹⁹Sn HMBC experiments. The system 2 and B(C₆F₅)₃ in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

SPECTROSCOPIC STUDIES OF PURINES—I. FACTORS AFFECTING THE FIRST EXCITED LEVELS OF PURINE*

Abstract— Studies of purine absorption and emission in seven solvents differing greatly in dielectric constant and hydrogen bonding potential, reveal a variety of solvent effects. For example, the resolution of structure in the absorption spectrum, the position and/or intensity of the X₂ absorption band, the intensity of fluorescence, the magnitude of the long wave-lenth tail, and the position of the X₁ absorption band are differentially affected—in the order listed—by the solvents tested. Even though it is possible to correlate the extent of decrease in the n-π* tail with increasing solvent dielectric constant, probably alterations in all of these spectroscopic parameters depend most critically upon the ability of the various solvents to form hydrogen bonds with the hydrogen on N9 and/for with the non-bonding electrons on the purine nitrogens: it is tentatively concluded that the probability of hydrogen bonding is directly correlated with the electronegativity of the aza nitrogens (N7 > N3 > N1). In solvents like isopropanol not all of the non-bonding electrons must be solvated maximally in most purine molecules since there is appreciable fluorescence under conditions where a long wavelength tail is readily observed in the absorption spectrum (alternatively some noa-bonding electrons may not te relevant to fluorescence quenching.) Decreases in fluorescence yield are associated with red shifts in the fluorescence maximum, and in the solvents of highest polarity the fluorescence yield is again small indicating that glycerol and water can enhance radiationless tunneling—presumably by altering Franck-Condon configurations and/or improving electronic-vibrational coupling between solute and solvent. The quantum yield is uniform throughout the atsorption band for a given solvent, but studies in aqueous buffers varying from pH 1 to 11 show that the fluorescence yield is greater for charged than for neutral molecules. Further, the fluorescence excitation peak is red shifted in powders. Since phosphorescence is the predominant emission at 777deg;K and increases in fluorescence can be correlated with the presumed solvation of non-bonding electrons, the singlet excited state of lowest energy in ‘unperturbed’ purine must be n-π* in nature. The shape of the phosphorescence band and the decay lifetime of ? 1 sec at 77°K lead to the conclusion that the emitting triplet is a π-π* state. The eight vibrational structures in phosphorescence emission can be readily grouped into two progressions: there is an average separation of about 1300 cm^-1 between peaks within a given progression, and the two sets are mutually displaced by about 500 cm-^l. Individual vibrational peaks are favoured in different solvents and the whole band may be shifted up to 500 cm^-l. Even larger shifts are observed in charged purine molecules and in powders (up to 3000 cm^-l) and the presumed 0–0 band is not observed.     

On distribution of molecular weight in anionic polymerizates of caprolactam

Measurement has been made of the dependence of the molecular weight distribution on the ratio of the catalytic system components and on the polymerization time for polycaprolactam obtained by anionic polymerization. A bimodal character of the curves was observed for products made using molar ratios of activator (N-benzoylcaprolactam) to initiator (sodium dihydro-bis(methoxyethoxy)aluminate) of 1:1 and 1:3, when the polymerization times were less than 1 hr. This course is explained by the influence of fast side-reactions, mainly condensations. For a ratio of 3:1 of the components of the catalytic system, smooth integral distribution curves are obtained, accounting for a very fast decrease in the strong base concentration in the initial stages of the polymerization.     

Towards rod-shaped molecules based on the twelve-vertex ferratricarbollides

The compounds with a single and double -CH₂C₆H₄CH₂- spacer, [CpFeC₃B₈H₁₀-NH-CH₂C₆H₄CH₂-NH-C₃B₈H₁₀FeCp] and [CpFeC₃B₈H₁₀-N-(CH₂C₆H₄CH₂)₂-N-C₃B₈H₁₀FeCp], represent the first example of designed shaping by extremely stable cyclopentadienyl-ferratricarbollide (CpFeTCB) cages into rigid molecular constructions approaching linear arrangement.     

Aproximate pairing properties of SCF solutions in highly symmetric heteroatomic systems

Approximate pairing properties are proved for the Hartree-Fock solutions for highly symmetric heteroatomic molecules. These molecules have an alternant topology and are built from two kinds of atoms in such a way that by an operation the atoms of one kind go over into the atoms of the second kind and vice versa.

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Zusammenfassung Es werden genäherte alternierende Eigenschaften für Hartree-Fock-Lösungen hochsymmetrischer heterocyclischer Moleküle abgeleitet. Diese Moleküle haben eine alternierende Topologie, sie sind aus zwei Sorten von Atomen in solcher Weise aufgebaut, daß die Atome der ersten Sorte in die Atome der zweiten Sorte — und umgekehrt — transformiert werden können.

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Résumé Des propriétés d'accouplement orbital approché sont prouvées pour les solutions de type Hartree-Fock des molécules hétéroatomiques hautement symétriques. Ces molécules ont une topologie alternante et sont formées de deux classes d'atomes de telle sorte qu'il existe une opération interchangeant les atomes des deux classes.

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Supported in part by a grant to The Johns Hopkins University from the Petroleum Research Fund of the American Chemical Society.     

The additivity principle in pyrolysis—gas chromatography of brown coal

Pyrolysis—gas chromatography of brown coal exhibits additive properties and it is therefore possible to construct the pyrogram of the original coal from the individual pyrograms of the bitumen, humic acids, lignin and humin fractions. The contents of phenols in the pyrograms are typical for all of the above classes except bitumen and are in agreement with the contents of the individual groups in the original coal. The results suggest that the separation does not bring about significant chemical changes in individual brown coal fractions.     

Determination of imazalil by on-line coupled capillary isotachophoresis with capillary zone electrophoresis

A simple, rapid and reproducible capillary isotachophoretic on-line coupled with capillary zone electrophoresis (CITP-CZE) method for the determination of IMz in food packaging extracts and its residues in apples is described. A good separation of the IMZ from other sample constituents was achieved within 15 minutes without any sample clean up. Method characteristics (linearity, accuracy, intra-assay and detection limit) were determined. Less amount of time involved, sufficient sensitivity and low running cost are the important attributes of CITP-CZE method.     

Polyaniline-coated silica gel

Silica gel microspheres 7 and 15 μm in diameter were coated with an overlayer of polyaniline camphorsulfonate or hydrochloride during the oxidative polymerization of aniline. Coated silica gel and polyaniline precipitate were separated using a difference in sedimentation rate. In an alternative approach, the microspheres were modified with polyaniline in the presence of 35 nm colloidal silica. This technique prevented the macroscopic precipitation of polyaniline. Coatings of neat, 3-aminopropyl- and octadecyl-modified silica gel with polyaniline hydrochloride were compared. The surface composition of coated microspheres was characterized by X-ray photoelectron spectroscopy. Potential applications of particles in electrorheology, organic catalysis, and in modeling of conductivity behavior in composites are demonstrated.