Photocrosslinked poly(vinylbenzophenone)‐core micelles via mild Friedel–Crafts benzoylation of polystyrene amphiphiles

Photocrosslinkable poly(vinylbenzophenone)‐containing polymers were synthesized via a one‐step, Friedel–Crafts benzoylation of polystyrene‐containing starting materials [including polystyrene, polystyrene‐block‐poly(tert‐butyl acrylate), polystyrene‐block‐poly(ethylene oxide), polystyrene‐block‐poly(methyl methacrylate), and polystyrene‐block‐poly(n‐butyl acrylate)] with benzoyl trifluoromethanesulfonate as a benzoylation reagent. The use of this mild reagent (which required no added Lewis acid) permitted polymers with well‐defined compositions and narrow molecular weight distributions to be synthesized. Micelles formed from one of these benzoylated polymers, [polystyrene_0.25‐co‐poly(vinylbenzophenone)_0.75]₁₁₅‐block‐poly(acrylic acid)₁₄, were then fixed by the irradiation of the micelle cores with UV light. As the irradiation time was increased, the pendent benzophenone groups crosslinked with other chains in the glassy micelle cores. Dynamic light scattering, spectrofluorimetry, and Fourier transform infrared spectroscopy were all used to verify the progress of the crosslinking reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2604–2614, 2006     

SPAR: stochastic programming with adversarial recourse

We consider a general adversarial stochastic optimization model. Our model involves the design of a system that an adversary may subsequently attempt to destroy or degrade. We introduce SPAR, which utilizes mixed-integer programming for the design decision and a Markov decision process (MDP) for the modeling of our adversarial phase.     

Establishing vicinal proton-proton connectivities using two-dimensional proton zero quantum coherence NMR

Phenanthro[3,4:3′,4′]phenanthro[2,1-b]thiophene ( 1 ) served as the model system to evaluate two-dimensional proton zero quantum coherence nmr in order to establish the vicinal proton-proton connectivities. The utility of the two-dimensional proton zero quantum nmr experiment has been compared with the utility of the traditional autocorrelated proton-proton (COSY) experiment. In the case of a molecule such as 1 , where the proton chemical shifts are so highly congested, the zero quantum coherence experiment provides data not obtainable from the COSY experiment.     

Disturbing the Dyson conjecture, in a generally GOOD way

Dyson's celebrated constant term conjecture [F.J. Dyson, Statistical theory of the energy levels of complex systems I, J. Math. Phys. 3 (1962) 140-156] states that the constant term in the expansion of _∏1≦i≠j≦naj(1−xi/xj) is the multinomial coefficient (a₁+a₂+?+an)!/(a₁!a₂!?an!). The definitive proof was given by I.J. Good [I.J. Good, Short proof of a conjecture of Dyson, J. Math. Phys. 11 (1970) 1884]. Later, Andrews extended Dyson's conjecture to a q-analog [G.E. Andrews, Problems and prospects for basic hypergeometric functions, in: R. Askey (Ed.), The Theory and Application of Special Functions, Academic Press, New York, 1975, pp. 191-224]. In this paper, closed form expressions are given for the coefficients of several other terms in the Dyson product, and are proved using an extension of Good's idea. Also, conjectures for the corresponding q-analogs are supplied. Finally, perturbed versions of the q-Dixon summation formula are presented.     

Samuelson maps—recent results

Samuelson maps are maps whose Jacobian matrix has nowhere vanishing leading principal minors. This paper surveys some recent results on invertibility of Samuelson maps and their decomposition into maps that fix all but one coordinate. The most noteworthy result is that real, rational, everywhere defined Samuelson maps are invertible. Proofs are sketched or omitted entirely.     

On the physical interpretation of Heywood and Redhead's algebraic impossibility theorem

Heywood and Redhead's 1983 algebraic (Kochen-Specker type) impossibility proof, which establishes the inconsistency of a broad class of contextualized local realistic theories, assumes two locality conditions and two auxiliary assumptions. One of those auxiliary conditions, FUNC^*, has been called a physically unmotivated,ad hoc formal constraint.In this paper, we derive Heywood and Redhead's auxiliary conditions from physical assumptions. This allows us to analyze which classes of hidden-variables theories escape the Heywood-Redhead contradiction. By doing so, we hope to clarify the physical and philosophical ramifications of the Heywood-Redhead proof. Most current hidden-variables theories, it turns out, violate Heywood and Redhead's auxiliary conditions.1. See Redhead [1], pp. 133–136, for a complete discussion.2. Arthur Fine first pointed out the implicit reliance on FUNC^*, and proved FUNC^* to be both consistent with and independent of the Value Rule.3. LetA=_ia_i P _i andB=_jb_j P_j be spectral resolutions ofA andB. Then <A,B> is the observable associated with maximal operatorR=_ijf_ij P _iP_j, where f_ij=F(a_i,b_j), and where function F is 1:1.4. Heywood and Redhead's versions of these conditions employ equivalence-class notation to specify the ontological context. {<D,E>}={R} refers to the equivalence class of all possible <D,E> formed by using different F functions (cf. Footnote 3). Clearly, such notation assumes that ifR andR are two distinct commuting maximal operators formed as described in Fn. 3 fromD andE using two different F(d_i,e_j) functions, then [Q]^t _(R)(R)=[Q]^t _(R)(R), so that [Q]^t _{R}(R) is uniquely defined.Heywood and Redhead never rely upon this assumption in their proof, however. It is easily checked that a Heywood-Redhead contradiction follows from my non-equivalence class versions of OLOC, ELOC, VR, and FUNC^*. Therefore, I will not use equivalence class notation.5. Here I denote by µ_R the composite state of all the apparatuses needed to measure R. So µ_R may represent the state of more than one device.6 This is because in a hidden-variables framework, quantum mechanical probabilities are a weighted average of the underlying hidden-variables probabilities.7. This argument resembles a proof given by Fine [8].8. Recall from theorem 1 that ifQ=f(R), then for all quantum states , P_(t)(Qf(r), R=r)=0.     

N-α-Benzyloxyacetyl derivatives of (S)-4-benzyl-5,5-dimethyloxazolidin-2-one for the asymmetric synthesis of differentially protected α,β-dihydroxyaldehydes

α-Dibenzylamino- and α-benzyloxy- derivatives of N-acetyl-(S)-4-benzyl-5,5-dimethyloxazolidin-2-one readily undergo highly stereoselective boron mediated syn-aldol reactions with a range of aromatic and aliphatic aldehydes, generating the syn-aldol products in good to excellent yields as single diastereoisomers after purification. In the α-dibenzylamino series, deprotection of the functionalised aldol fragments to the corresponding α-amino-β-hydroxy methyl ester or α-amino-β-hydroxyaldehyde proved problematic, with a range of N- and O-protecting groups giving mixtures of products arising from endocyclic and exocyclic cleavage pathways. However, in the α-benzyloxy series, O-silyl protection of the aldol products, and subsequent DIBAL reduction gives stereoselectively the corresponding N-1′-hydroxyalkyloxazolidin-2-ones, which undergo base promoted fragmentation to the desired highly functionalised and differentially protected α,β-dihydroxyaldehydes in good yields and without loss of stereochemical integrity.     

Rhodathiaboranes with `anomalous' electron counts: synthesis, structure and reactivity

Analysis of the structures of 8,8-(PPh₃)₂-8,7-nido-RhSB₉H₁₀ and 9,9-(PPh₃)₂-9,7,8-nido-RhC₂B₈H₁₁ by RMS misfit calculations has confirmed that these rhodaheteroboranes possess nido 11-vertex cluster geometries in apparent contravention of Wade's rules. However, examination of the molecular structures of both species shows that the {RhP₂} planes are inclined by ca. 66° with respect to the metal-bonded SB₃ or CB₃ faces, and that two weak ortho-CHRh agostic interactions occupy the vacant co-ordination position thereby created. As a consequence of these agostic bonds the Rh atom, and hence the overall cluster, is provided with an additional electron pair, meaning that their nido structures are now fully consistent with Wade's rules. The chelated diphosphine compound 8,8-(dppe)-8,7-nido-RhSB₉H₁₀ is similar to the PPh₃ compound in showing the same agostic bonding. Attempts to prepare a bis-P(OMe)₃ analogue result in ligand scavenging and the formation of 8,8,8-{P(OMe)₃}₃-8,7-nido-RhSB₉H₁₀. Similarly, reaction between Cs[6-arachno-SB₉H₁₂] and RhCl(dmpe)CO does not result in CO loss but in formation of 8,8-(dmpe)-8-(CO)-8,7-nido-RhSB₉H₁₀, shown to exist as a mixture of two of three possible rotamers. Deprotonation of 8,8-(PPh₃)₂-8,7-nido-RhSB₉H₁₀ and 8,8-(dppe)-8,7-nido-RhSB₉H₁₀ with MeLi yields the anions [1,1-(PPh₃)₂-1,2-closo-RhSB₉H₉]⁻ and [1,1-dppe-1,2-closo-RhSB₉H₉]⁻, respectively, with octadecahedral cage structures. It is argued that anion formation causes the agostic bonding to be `switched-off' and results in the cluster adopting the closo architecture predicted by Wade's rules. This structural change is fully reversible on reprotonation, and if reprotonation of [1,1-(dppe)-1,2-closo-RhSB₉H₉]⁻ is carried out in MeCN, the product 8,8-(dppe)-8-(MeCN)-8,7-nido-RhSB₉H₁₀ forms. Interestingly, 8,8-(dppe)-8-(MeCN)-8,7-nido-RhSB₉H₁₀ reconverts to 8,8-(dppe)-8,7-nido-RhSB₉H₁₀ on standing in CDCl₃, suggesting that the agostic bonding is sufficiently strong to displace co-ordinated MeCN. All new compounds are fully characterised by multinuclear NMR spectroscopy and, in many cases, by single crystal X-ray diffraction.