Oleophilic ion-exchange resins. IV. Swelling of quaternary ammonium polymers in mixed solvents

The swelling characteristics of an oleophilic anion-exchange resin in methanol–benzene and ethanol–chloroform mixed solvent systems were compared with those of a conventional anion-exchange resin. The oleophilic resin was prepared by amination of chloromethylated polystyrene 1% DVB with N,N-dimethyldodecylamine. It showed a large shift of the swelling peak from polar to less polar solution compositions in both methanol–benzene and ethanol–chloroform systems as compared with the swelling of conventional resins. Total solvent uptake and solvent distribution between resin and solvent phases were also determined. The less polar solvent (benzene or chloroform) was sorbed preferentially by the oleophilic resin over a wide range of composition, while preference for the more polar solvent (methanol or ethanol) by the conventional resin was shown over the entire composition of the mixed solvent systems. The Newman-Krigbaum treatment of mixed solvents was applied to swelling data on the ethanol–chloroform–oleophilic resin system, where the volume of the gel network plus the solvent imbibed was relatively constant over the entire range of composition. The result suggests a strong similarity of the liquid–liquid interaction terms in this gel phase compared with those in the pure binary liquid phase.     

Die mehrstellenformeln für den Laplaceoperator

Summary Difference methods for the numerical solution of linear partial differential equations may often be improved by using a weighted right hand side instead of the original right hand side of the differential equation. Difference formulas, for which that is possible, are called Mehrstellenformeln or Hermitian formulas. In this paper the Hermitian formulas for the approximation of Laplace's operator are characterized by a very simple condition. We prove, that in two-dimensional case for a Hermitian formula of ordern at leastn+3 discretization points are necessary. We give examples of such optimal formulas of arbitrary high-order.

     

Synthesis and Some Reactions of 2,4,6-Cycloheptatrienethione

The synthesis of 2,4,6-cycloheptatrienethione ( 1 ) was accomplished by reaction of tropone and phosphorus pentasulfide. Although 1 proved to be extremely unstable in concentrated solution, its UV. spectrum was measured, the ε-values being determined indirectly by hydrolysis to tropone. The proof of structure rests on analytical data, conversion to tropone oxime on reaction with hydroxylamine and reaction with the sodium salt of malonitrile to give 2-amino-3-cyano-3aH-cyclohepta[b]thiophene ( 4 ) which rearranged on chromatography to give what is probably the corresponding 8H-compound ( 5 ). On dissolving 1 in 95% sulfuric acid, a large hypsochromic shift in the UV. spectrum was observed, which may be due to the mercaptotropylium ion.     

Photochemistry of 5-phenyl-1-pentene in the gas phase

The photochemistry of the title compound has been studied in the gas phase using 254-nm irradiation. In addition to meta cycloadducts analogous to those observed in solution, population of S1(vib) in the gas phase gives several products, the relative amounts of which depend on quencher gas pressure but not on excitation wavelength. For example, in the absence of butane, the major photoproduct is compound 5. This product is formed by a [1,5] hydrogen shift in the primary photoproduct, compound 4. Compound 4 is an intramolecular meta cycloadduct that is generated in the gas phase with sufficient excess vibrational energy to undergo rearrangement unless quencher gas is present. Likewise, there is evidence that two other meta cycloadducts (2 and 3) are also formed with appreciable vibrational energy in the absence of a quencher gas. A unique intramolecular ortho cycloadduct is also formed from 1 but only within a narrow range of quencher gas pressures. This is a two-photon product, with the initial cycloadduct (11) ring opening to a cyclooctatriene (12) that photochemically closes to 6. The pressure dependence of this ortho cycloaddition may be due to a requirement for vibrational deactivation of 11 (Scheme 5) or a precursor species (Scheme 6). The overall chemistry is outlined in Scheme 7.     

On a question of H. Kraljević

In this paper, assuming a certain set-theoretic hypothesis, a positive answer is given to a question of H. Kraljevi, namely it is shown that there exists a Lebesgue measurable subsetA of the real line such that the set {c R: A + cA contains an interval} is nonmeasurable. Here the setA + cA = {a + ca: a, a A}. Two other results about sets of the formA + cA are presented.     

On Uniform Laws of Large Numbers for Ergodic Diffusions and Consistency of Estimators

Consider a regular diffusion process X with finite speed measure m. Denote the normalized speed measure by μ. We prove that the uniform law of large numbers holds if the class has an envelope function that is μ-integrable, or if is bounded in L _p(μ) for some p>1. In contrast with uniform laws of large numbers for i.i.d. random variables, we do not need conditions on the ‘size’ of the class in terms of bracketing or covering numbers. The result is a consequence of a number of asymptotic properties of diffusion local time that we derive. We apply our abstract results to improve consistency results for the local time estimator (LTE) and to prove consistency for a class of simple M-estimators. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Influence of Multi-Photon Absorption on Photon Statistics

A previous approximation scheme [6] which allowed to calculate, in a simple manner, the quantity Δn²/n (n mean value and Δn² variance of the photon number) in the course of a multi-photon absorption process, is extended to study the change of the shape of the photon distribution, too. It turns out that there is a tendency to symmetrize the distribution. Moreover, an approximative expression for the asymptotic distribution to which the distribution tends after a sufficiently strong absorption, irrespective of the initial distribution, is found in form of a Gaussian.     

The coherent radiation fraction of low‐emittance synchrotrons

In this work the coherence properties of the synchrotron radiation beam from an X‐ray undulator in a fourth‐generation storage ring are analyzed. A slightly focused X‐ray beam is simulated using a wavefront propagation through a non‐redundant array of slits and the mutual coherence function is directly obtained and compared with the Gaussian–Schell approximation. The numerical wave propagation and the approximate analytical approaches are shown to agree qualitatively, and it is also shown that, when the coherent fraction is selected by a finite aperture before the focusing element, even achromatic focusing systems like total reflection mirrors become slightly chromatic. This effect is also well accounted for in the Gaussian–Schell model. The wavefront propagation simulation through the non‐redundant array was repeated with an imperfect mirror demonstrating that, although the wavefront is distorted, its coherent length is practically unchanged.