The type of group measure space von Neumann algebras

LetG be a countable discrete group acting by measure-preserving automorphisms of a finite measure space (M, ) and let (G,M) be the corresponding group measure space von Neumann algebra, which will be a finite von Neumann algebra. Necessary and sufficient conditions are given for (G,M) to have a non-zero type I part, and the projection on the type I part is explicitly described.This research was supported in part by National Science Foundation Grant MCS 74-19876.     

Preparation of Neutral Ionophores for Alkali and Alkaline Earth Metal Cations and their application in ion selective membrane electrodes

The preparation of a series of non-cyclic, uncharged ligands able to selectively complex alkali and alkaline earth metal cations is described. These molecules are designed to be used as carriers for cations through membranes. Some of the compounds show high Ca²⁺ and Na⁺ selectivity, respectively, in liquid membrane electrodes.     

Enzymatic desymmetrization of a meso polyol corresponding to the C(19)-C(27) segment of rifamycin S

The stereoselective acylation of meso polyol 2 by vinyl acetate (solvent and acyl donor) in the presence of porcine pancreas lipase gave the corresponding monoester 5 in good yield (76%) and high enantiomeric purity (ee > 98%). The enzymatic reaction was also highly regioselective for a primary alcohol end group, and the two unprotected secondary alcohols were not involved. Compound 5 corresponds to the C(19)-C(27) fragment of rifamycin S.     

A theorem on products of matrices

A new result on products of matrices is proved in the following theorem: let M_i (i=1,2,…) be a bounded sequence of square matrices, and K be the l.u.b. of the spectral radii ρ(M_i). Then for any positive number ε there is a constant A and an ordering p(j) (j = 1,2,…) of the matrices such that

$\text{∏}\text{j=1}\text{n}\text{M}{}_{\mathrm{p(j)}}\text{?A·(K+ε)}{}^{\mathrm{n}}\text{(n = 1,2,…)}$

. The ordering is well defined by p(j), a one-to-one mapping on the set of positive integers. In general the inequality does not hold for any ordering p(j) (a counterexample is provided); however, some sufficient conditions are given for the result to remain true irrespective of the order of the matrices.     

An improved synthesis of cyclopropanes from stabilized phosphonates and 1,2-dioxines

Addition of stabilized Horner-Wadsworth-Emmons (HWE) phosphonates to substituted 1,2-dioxines leads to diastereomerically pure di- and trisubstituted cyclopropanes in high yields and represents a viable alternative to ylides in the cyclopropanation reaction involving 1,2-dioxines. While yields are comparable, reaction times with these stabilized phosphonates were accelerated and the diastereoselectivity for this cyclopropanation reaction was significantly greater than for the previously reported examples employing ylides.     

Interactions magnétiques dans des groupements binucléaires du Ruthénium +V

The cationic ordering in the $\text{Ba}\text{M}{}_{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{Ru}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{O}{}_3\text{(M =}\text{Mg, Ca, Cd, Sr}\text{)}$ oxides which crystallize with the 6H structure gives rise to Ru⁵⁺Ru⁵⁺ pairs in (Ru₂O₉) clusters. The magnetic properties have been analyzed on the basis of the Heisenberg-Dirac-Van Vleck model: The d electrons are localized on each Ru⁵⁺ ion and interact strongly through antiferromagnetic exchange. The susceptibility curves agree with the H.D.V.V. model. The values of the exchange integrals have been determined by fitting the experimental values.     

Amine-terminated dendrimers as biomimetic templates for silica nanosphere formation

In diatoms, silica synthesis occurs by use of complex posttranslationally modified peptides, termed silaffins, and highly complex biological polyamine structures. Silaffin peptides have lysine residues that are modified to long-chain polyamine moieties of N-methyl derivatives of polypropylenimine to drive silica synthesis at slightly acidic pH conditions. Using polypropylenimine (PPI) and PAMAM amine-terminated dendrimers as a biomimetic analogue of the polyamine modifications of silaffins, we have demonstrated the condensation of silica nanospheres. We have shown that the dendrimers react in an amine concentration-dependent fashion yielding silica nanospheres with a distinct size distribution reminiscent of the structures produced from both the modified and nonmodified peptides extracted from diatoms. Additionally, the templates were encapsulated by the growing nanospheres and precipitated from solution in a manner similar to that previously described for the bioactive peptides and polyamines.     

Flash photolysis studies of the reaction of NH2 radicals with NO

The kinetics of the reaction NH₂ + NO → N₂ + H₂O were studied, using a conventional flash photolysis system. A value of k₁ = (1.1 ± 0.2) × 10¹⁰ & mole^?1 s^?1 was obtained at room temperature and in the pressure range 2–700 torr in the presence of nitrogen. A slight negative temperature coefficient was observed between 300 and 500 K, equivalent to a negative activation energy of 1.05 ± 0.2 kcal mole^?1.     

The Yellow Polymorphs of Mercuric Iodide (HgI2)

HgI₂ crystallizes under ambient conditions from various solvents and by sublimation into three concomitant polymorphs whose colors are red, orange, and yellow. The orange and yellow phases are metastable and transform into the red phase when touched. A phase transition from red to yellow occurs at 400 K. The reverse transition from yellow to red shows a huge hysteresis. We established that the structures of the metastable yellow^M phase (determined by single‐crystal X‐ray diffraction) and the high‐temperature yellow^HT phase (determined by powder synchrotron X‐ray diffraction and second‐harmonic generation) are different, albeit closely related. Both show analogous packings of I? Hg? I molecules, which are straight in the first and bent with an angle of ca. 160° in the second. The red and orange phases are tetrahedral semiconductor structures that sublime even at room temperature. The growth of the yellow^M phase from 2‐chloroethanol and the kinetics of the reconstructive phase transition red to yellow^HT and back were studied by optical microscopy, Raman spectroscopy in solution, luminescence, and powder synchrotron X‐ray diffraction as a function of time at various temperatures. Both yellow phases grow by accretion of HgI₂ molecules, present in the solution or liberated from the red crystals, on the surface of the crystal. In contrast, the reverse transformation from yellow to red occurs in the bulk of the crystal, presumably by migration of Hg in the packing of I and subsequent rearrangement of I. The displacement parameters of Hg in both structures are considerably larger than those of I and apparently not dominated by disorder effects.     

Absolute line intensity measurements of hot bands for carbonyl sulfide at 12 microm

Using diode-laser spectroscopy, the intensities of 58 lines of the v(1) + v(1/2) - v(1/2) band and 36 lines of the 2v(1) - v(1) band of OCS have been measured. The corresponding band strengths S(0)(v) and the vibrational transition dipoles micro(v) have been derived through least squares fitting of these individual intensities. The band strengths values have been determined with a precision better than 2.5%.