Local Borel summability of Euclidean 311-1311-1311-1a simple proof via differential flow equations

It is shown how the differential flow equation (or, equivalently, the continous renormalization group) method can be employed to give an astonishingly easy proof of the local Borel summability of the renormalized perturbative Euclidean massive ₄ ⁴ .Supported by NSF grant # DMS-9100383     

Structural phase transitions in ‘hcp’ C70 single-crystals

The thermal expansion of vapor-grownC ₇₀ single crystals ahs been investigated using high-resolution capacitance dilatometry from 5–380 K. Measurements were made both parallel and perpendicular to the hexagonalc-axis. Three first-order phase transitions which we associate with the consecutive disordering of theC ₇₀ molecules are observed upon heating at 280 K (long-axis spinning), 300 K (long-axis precession) and 355 K (quasi-free rotation), respectively. The highest-temperature transition exhibits a very large (50 K) thermal hysteresis. Powder and single-crystal X-ray diffraction show that the crystals are predominantly hexagonal-close-packed (HCP) with an idealc/a1.63 above 360 K andc/a1.84 at 295 K.     

Two-photon spectroscopy of the low-lying singlet states of naphthalene and acenaphthene

Two-photon excitation spectra of naphthalene and acenaphthene have been measured up to 50000 cm^?1. In naphthalene. three two-photon allowed states are observed for which the symmetry assignment is confirmed by polarization. The corre- sponding transitions are also seen in acenaphthene. The experimental data are in excellent agreement with theoretical predictions.     

pH-Dependent force spectroscopy of tri(ethylene glycol)- and methyl-terminated self-assembled monolayers adsorbed on gold

Self-assembled monolayers (SAMs) of methoxy-tri(ethylene glycol)- (EG(3)-OMe) and methyl-terminated alkanethiols (C(16)) adsorbed on polycrystalline gold were investigated by chemical force spectroscopy. Measurements were performed in aqueous electrolyte solutions depending on ionic strength and pH value. Charged and hydrophobic tips were employed as probes to mimic local patches of proteins and to study the interaction at the organic/liquid interface in detail. Force-distance curves reveal information about the origin of the observed interaction and the underlying mechanisms. The measurements confirm an effective negative surface charge to be present at the oligo(ethylene glycol) (OEG) and the methyl interface and suggest that the charges are due to the adsorption of hydroxyl ions from aqueous solution. pH-dependent measurements further support the robustness of the established charge associated with the OEG films. Its sign does not change over the whole range of investigated values between pH approximately 3.5 and approximately 10. In contrast, the hydrophobic self-assembled hexadecanethiol films on gold show an isoelectric point (IEP) around pH 4. While the mechanism of charge establishment appears to be similar for both SA films, the strength of hydrogen bonding to interfacial water, which acts as a template for hydroxyl ion adsorption, is likely to be responsible for the observed difference.     

Koordinative Verankerung von Nickelkomplexen an Hectorit-Schichtsilicaten mit Hilfe langkettiger Diphenylphosphinogruppen

Coordinative Anchoring of Nickel Complexes on Hectorite-Layer Silicates through long-chain Diphenylphosphine Groups The treatment of sodium and calcium hectorites with 2-diphenylphosphinoethyltriethoxysilane leads, by condensation of free hydroxyl groups, to functionalized layer silicates with long-chain diphenylphosphine groups onto which nickel chloride can be coordinated. In these modified hectorites the fourth coordination site of the tetrahedrally coordinated nickel is occupied by a labile solvent molecule. On the other hand, the complex bis(2-diphenylphosphinoethyltriethoxysilane)nickel(II) chloride prepared beforehand also reacts with sodium hectorite under condensation; but the square-planar coordination of the four stable ligands (two chloride and two phosphor atoms) is maintained. This finds its expression in a significant activity decrease in catalytic reactions as compared to the aforementioned products.     

Polymeric Catalysts

The present-day position in the field of polymeric catalysts is outlined. The following selected groups of polymeric catalysts are discussed: synthetic hydrolases, immobilized enzymes, phase-transfer catalysts, nucleophilically active bases, polymers with conjugated π-systems, photosensitizers, polymers as carriers for catalytically active metals or ions, and immobilized homogeneous catalysts. Polymeric catalysts have the following valuable properties: insoluble polymeric catalysts are readily separable from reaction solutions and can often be re-used without loss of activity; a hydrophobic matrix protects the organometallic active center from deactivation by oxygen and water; by fixation of finely divided metals on an ion exchanger, multistage reactions may be effected successively in one reactor. Polymeric carriers may influence the catalytic properties; for example, in the case of immobilized enzymes on polyionic carriers the pH of the activity maximum may be shifted.     

An analogue to a conjecture of S. Chowla and H. Walum

It is proved that (for every ε > 0)

$\text{∑}\text{n?T}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{∑n<}\text{T}\text{n}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{n}{}^{\mathrm{a}}\text{m}{}^{\mathrm{b}}\text{B}{}_{\mathrm{k}}\text{({}\text{T}\text{nm}\text{}) = O(T}{}^{\mathrm{<mtext>(a+b+1)</mtext><mtext>3?</mtext>}}\text{)}$

(where {·} denotes the fractional part and B_k the Bernoulli polynomial of order k) under the suppositions that k ≥ 2 and 2a ? 1 ≥ b ≥ 1. If (1) were true for k = 1, a = b = 0, then Piltz' divisor problem (for n = 3) would be readily solved. This is an analog to a conjecture formulated by S. Chowla and H. Walum in 1963 and settled in the affirmative (under suitable suppositions) quite recently by S. Kanemitsu and R. Sita Rama Chandra Rao.     

Mass spectrometry of onium salts—I. Studies on anilinium oxides

The mass spectra of the three isomeric trimethylanilinium oxides and their methyl-d₃ analogues show that the m- and p- isomers undergo intermolecular trans-O-alkylation before evaporation. In the o-isomer, only 10% transalkylated product is observed and there is strong evidence that most of this isomer evaporates without undergoing structural changes. By indirect introduction, however, the o-isomer showed only transalkylated product. The most important fragmentation patterns on electron-impact are α-cleavage on the N-methyl carbon or expulsion of the O-substituent with formation of a quinoid structure. The latter dominates for the o- and p-methyl ethers while the former is the most important pathway for the m-isomer and for the corresponding phenols. Lower fragments are of modest intensity.     

Thermische Polymerisation von Acenaphthylen

Zusammenfassung Acenaphthylen wurde durch Anpolymerisation und zweifache Hochvakuumsublimation gereinigt. Die Reinigungsmethode wird ausführlich beschrieben.Bei verschiedenen Temperaturen wurde mit einer dilatometrischen Methode die thermische Bruttogeschwindigkeit gemessen. Zwischen 95 und 105 °C giltk _br=7,0₈·10¹⁰ exp (– 30,9 kcal/RT).Die beträchtliche Aktivierungsenergie der Bruttoreaktion ist sowohl auf eine große Aktivierungsenergie der thermischen Startreaktion als auch auf eine relativ hohe Wachstumsaktivierungsenergie zurückzuführen.Das Polymerisationsverhalten von Acenaphthylen kann vermutlich aufgrund seiner sterischen Eigenschaften erklärt werden.

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Summary Acenaphthylene was purified by partial polymerisation, followed by double stage high vacuum sublimation. The method of purification is described in detail.The thermal overall rate was measured at different temperatures by a dilatometric method. Between 95 and 105 °C the following relation holds:k _th=7,0₈ · 10¹⁰ exp (– 30,9 kcal/RT).The considerable energy of activation of the overall reaction depends on a relatively high energy of activation of both the thermal initiation and the propagation reaction.It is supposed, that the polymerisation behaviour of acenaphthylene depends mainly on its steric properties.