Adiabatic compressibility of polymer solutions—III. Poly-2,6-dimethyl-1,4-phenyleneoxide in toluene and butanol-toluene mixtures

Adiabatic compressibility data for solutions of poly-2,6-dimethyl-1,4-phenyleneoxide in toluene and toluene-butanol mixtures are reported as a function of concentration. The differences between the observed and calculated values of the compressibility are attributed to polymer-solvent interactions. Comparison of the magnitude of the incremental compressibility and viscosity variation for the isomeric butanol-toluene-polymer solutions enabled investigation of the effects of steric interactions on the solvation process.     

The gas-phase pyrolysis of alkyl nitrites. IV. Ethyl nitrite

The rate of decomposition of methyl nitrite (MN) has been studied in the presence of isobutane-t-BuH-(167-200°C) and NO (170-200°C). In the presence of t-BuH (～0.9 atm), for low concentrations of MN (～10^?4M) and small extents of reaction (4-10%), the first-order homogeneous rates of methanol (MeOH) formation are a direct measure of reaction (1) since k₄(t-BuH) »k₂(NO): . The results indicate that the termination process involves only \documentclass{article}\pagestyle{empty}\begin{document}$ t - {\rm Bu\, and\, NO:\,\,}t - {\rm Bu} + {\rm NO\stackrel{e}{\longrightarrow}} $\end{document} products, such that k_e ～ 10¹⁰ M^?1 ～ sec^?1.Under these conditions small amounts of CH₂O are formed (3-8% of the MeOH). This is attributed to a molecular elimination of HNO from MN. The rate of MeOH formation shows a marked pressure dependence at low pressures of t-BuH. Addition of large amounts of NO completely suppresses MeOH formation. The rate constant for reaction (1) is given by k₁ = 10^{15.8°0.6-41.2°1}/· sec^?1. Since (E₁ + RT) and ΔH^Δ₁ are identical, within experimental error, both may be equated with D(MeO - NO) = 41.8 + 1 kcal/mole and E₂ = 0 ± 1 kcal/mol. From ΔS¹₁ and A₁, k₂ is calculated to be 10^10.1°0.6M^?1 · sec^?1, in good agreement with our values for other alkyl nitrites. These results reestablish NO as a good radical trap for the study of the reactions of alkoxyl radicals in particular. From an independent observation that k₆/k₂ = 0.17 independent of temperature, we conclude that \documentclass{article}\pagestyle{empty}\begin{document}$ E_6 = 0 \pm 1{\rm kcal}/{\rm mol\, and\,}\,k_6 = 10^{9.3} M^{- 1} \cdot {\rm sec}^{- 1} :{\rm MeO} + {\rm NO}\stackrel{6}{\longrightarrow}{\rm CH}_2 {\rm O} + {\rm HNO} $\end{document}. From the independent observations that k₂:k_2→: k_6→ was 1:0.37:0.04, we find that k_2→ = 10^9.7M^?1 ? sec^?1 and k_6→ = 10^8.7M^?1 ? sec^?1. In addition, the thermodynamics lead to the result In the presence of NO (～0.9 atm) the products are CH₂O and N₂O (and presumably H₂O) such that the ratio N₂O/CH₂O ～ 0.5. The rate of CH₂O formation was affected by the surface-to-volume ratio s/v for different reaction vessels, but it is concluded that, in a spherical reaction vessel, the CH₂O arises as the result of an essentially homogeneous first-order, fourcenter elimination of \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm HNO}:{\rm MN\stackrel{5}{\longrightarrow}CH}_{\rm 2} {\rm O} + {\rm HNO} $\end{document}. The rate of CH₂O formation is given by k₅ = 10^{13.6°0.6-38.5-1}/? sec^?1.     

Correction: Abelian Varieties defined over their Fields of Moduli, I

Bull London Math. Soc, 4 (1972), 370–372. The proof of the theorem contains an error. Before giving acorrect proof, we state two lemmas. LEMMA 1. Let K/k be a cyclic Galois extension of degree m, let generate Gal (K/k), and let (A, I, ) be defined over K. Supposethat there exists an isomorphism :(A,I,) (A, I, ) over K suchthat v^m–1 ... = 1, where v is the canonical isomorphism(A^m, I^m, ^m) (A, I, ). Then (A, I, ) has a model over k, whichbecomes isomorphic to (A, I, ) over K. Proof. This follows easily from [7], as is essentially explainedon p. 371. LEMMA 2. Let G be an abelian pro-finite group and let : G Q/Z be a continuous character of G whose image has order p.Then either: (a) there exist subgroups G' and H of G such that H is cyclicof order p^m for some m, (G') = 0, and G = G' x H, or (b) for any m > 0 there exists a continuous character m ofG such that p^m _m = . Proof. If (b) is false for a given m, then there exists an element G, of order p^r for some r m, such that () ¦ 0. (Considerthe sequence dual to 0 Ker (p^m) G ^pm G). There exists an opensubgroup G_o of G such that (G₀) = 0 and has order p^r in G/G₀.Choose H to be the subgroup of G generated by , and then aneasy application to G/G₀ of the theory of finite abelian groupsshows the existence of G' (note that () ¦ 0 implies that is not a p-th. power in G). We now prove the theorem. The proof is correct up to the statement(iv) (except that (i) should read: F' k₁ F'ab). To removea minor ambiguity in the proof of (iv), choose to be an elementof Gal (F'_ab/k₂) whose image $$\stackrel{\¯}{\sigma}$$ in Gal (k₁/k₂) generates this last group. The error occursin the statement that the canonical map v : A^P A acts on pointsby sending a^p a; it, of course, sends a a. The proof is correct, however, in the case that it is possibleto choose so that ^p = 1 (in Gal (F'/k₂)). By applying Lemma 2 to G = Gal (F'_ab/k₂) and the map G Gal(k₁/k₂) one sees that only the following two cases have to beconsidered. (a) It is possible to choose so that ^pm = 1, for some m, andG = G' x H where G' acts trivially on k₁ and H is generatedby . (b) For any m > 0 there exists a field K, F'ab K k₁ k₂is a cyclic Galois extension of degree p^m. In the first case, we let K F'_ab be the fixed field of G'.Then (A, I, ), regarded as being defined over K, has a modelover k₂. Indeed, if m = 1, then this was observed above, butwhen m > 1 the same argument applies. In the second case, let : (A, I, ) (A$$\stackrel{\¯}{\sigma}$$, I$$\stackrel{\¯}{\sigma }$$, $$\stackrel{\¯}{\sigma}$$) be an isomorphism defined over k₁ and let v ... ^p–1 = µ(R). If is replaced by for some Aut_k1((A, I, )) then is replacedby ^P. Thus, as µ(R) is finite, we may assume that ^pm–1= 1 for some m. Choose K, as in (b), to be of degree p^m overk₂. Let _m be a generator of Gal (K/k₂) whose restriction tok₁ is $$\stackrel{\¯}{\sigma }$$. Then : (A, I, ) (A^{$$\stackrel{\¯}{\sigma }$$}, I^{$$\stackrel{\¯}{\sigma}$$}, ^{$$\stackrel{\¯}{\sigma }$$} = (A^{$$\stackrel{\¯}{\sigma}$$m}, I^{$$\stackrel{\¯}{\sigma }$$m}, ^{$$\stackrel{\¯}{\sigma}$$m} is an isomorphism defined over K and v ^mpm–1, ... ^m =^pm–1 = 1, and so, by) Lemma 1, (A, I, ) has a model overk₂ which becomes isomorphic to (A, I, over K. The proof may now be completed as before. Addendum: Professor Shimura has pointed out to me that the claimon lines 25 and 26 of p. 371, viz that µ(R) is a puresubgroup of _R^*t, does not hold for all rings R. Thus this condition,which appears to be essential for the validity of the theorem,should be included in the hypotheses. It holds, for example,if µ(R) is a direct summand of µ(F).     

Schur functions,Good's identity,and hypergeometric series well poised in SU(n)

A simple direct proof is given of a fundamental identity involving Schur functions which contains as special cases the identity responsible for Good's proof of the Dyson conjecture and the summation theorem of Biedenharn and Louck that appears frequently in dealing with the explicit matrix elements which arise in the unitary groups. By using the Weyl character formula, a general identity is obtained which implies our result involving Schur functions when a root system of type A_{n ? 1} is considered. As a further application of our general identity, explicit analogs of Good's identity are given, corresponding to the root systems of types B_n, C_n, and D_n. In addition, methods to obtain q-analogs of all of these results are briefly described.     

Fractionation of polydisperse colloid with acousto-optically generated potential energy landscapes

The motion of colloidal particles on a periodic optical potential energy landscape in the presence of an external driving force may result in particle separation. In contrast to recent methods of holographic or interferometric generation of such landscapes, we use an acousto-optic deflector to create two-dimensional landscapes. We present what is believed to be the first experimental realization of fractionation with simultaneous sorting of four different sizes of colloidal microparticle into laterally separated parallel laminar streams.     

Oligomerization and cyclization of 1,2-ethanedithiol (EDT), HSCH2CH2SH,by selenium dioxide and iodine

The reaction of 1,2 ethanedithiol (EDT) with selenous acid in water or alcohol leads to selenopolysulfide chains or cycles, (C₂H₄SSeSC₂H₄SS)_n, with randomly distributed  SSeS and  SS moieties. The reaction in water produces incompletely reacted material, which on recrystallization, gives an oligomer corresponding to 5 EDT units (pentamer) as confirmed by molecular mass determination, Se analysis, ¹H- and ⁷⁷Se-NMR spectroscopy. In both the pentamer and cyclic forms the incidence of neighboring  SSeS moieties is higher than that expected statistically. The mechanism for the reaction of thiols with selenous acid provides some rationalization for this observation in as much as neighboring  SSeS groups, or groups that will lead rapidly to neighboring  SSeS groups are formed in general before  SS links can be formed. The Raman spectrum of these products show typical strong SS, SeS, and CS stretching bands at 510, 370, and 730 cm⁻¹. The high frequency of ν_CS is attributed to a preferred gauche conformation at the CS bonds. For comparison, polydisulfides were also prepared from EDT and iodine in methanol. These products consist of at least seven cyclic polymers ranging from the four-membered 1,2-dithietane to higher members. Heating above 100°C in chloroform for several hours gives a solution containing the four lowest molecular mass rings, which on standing for 24 h, precipitate highly insoluble material, which is probably chain or large-ring polymer. Molecular mass determination in camphor indicates that, like yellow sulphur, chain polymers are formed at the melting point of camphor (170°C). © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36 : 379–390, 1998     

Copper-catalyzed N-arylation of sulfonamides with aryl bromides under mild conditions

This Letter describes a copper catalyzed sulfonamide coupling reaction with aryl bromides to form N-aryl sulfonamides under mild conditions, including the first examples of Cu-catalyzed sulfonamide coupling at room temperature. The reaction protocol tolerates a broad range of substrates including a variety of primary and secondary sulfonamides and challenging heteroaryl bromides such as 2-bromothiazole.     

Synoxazolidinones A and B: novel bioactive alkaloids from the ascidian Synoicum pulmonaria

Bioassay-guided fractionation of the sub-Arctic ascidian Synoicum pulmonaria collected off the Norwegian coast led to the isolation of a novel family of brominated guanidinium oxazolidinones named synoxazolidinones A and B (1 and 2). The backbone of the compounds contains a 4-oxazolidinone ring rarely seen in natural products. The structure of the compounds was determined by spectroscopic methods. The synoxazolidinones exhibited antibacterial and antifungal activities.     

Optimized material requirements planning for semiconductor manufacturing

This paper describes a custom operational research algorithm, which is run nightly by IBM to create a material requirements plan for its semiconductor fabrication facility in Vermont, USA. To model alternative manufacturing processes and part substitutions, this application interweaves linear programming and heuristic methods to reap the benefits of each decision technology. At each level of the bills of materials supply chain with complex decision choices to be made, parallel linear programmes are invoked and their results are fed into a material requirements planning (MRP) heuristic, which processes parts through multiple iterations. The results from processing one level of the bills of materials supply chain are exploded to create demand for the next level and the interweaving of the two decision technologies continues. The algorithm creates recommended manufacturing releases and work-in-process priorities. These outputs point out opportunities for improvement in order to satisfy all demands on time. The output can be interpreted with well-known MRP assumptions.