Post-lactonization of vinyl polymers containing pendent ester and hydroxymethyl groups

Copolymers of methyl methacrylate with methyl and ethyl α-hydroxymethylacrylate and with α-hydroxymethylstyrene have been prepared with free-radical initiators at temperatures below 80°C. At higher reaction temperatures or under extrusion conditions, alcohol was eliminated and the free hydroxyl content was greatly decreased. All evidence indicates the formation of six-membered lactone groups in this post-polymerization reaction: direct evidence for their formation is lacking, however, since neither infrared nor nuclear magnetic resonance spectra could be used to detect lactonization in this system. The loss of activity from ¹⁴C ester-labeled methyl methacrylate copolymer on heating could be correlated with the extent of lactonization. The degree of lactonization is relatively less with copolymers containing higher amounts of hydroxymethyl groups. The resulting polymers exhibit higher heat distortion temperatures and decreased impact resistance when compared to poly(methyl methacrylate). Attempts were made to incorporate similar lactone structures by cyclocopolymerization with methyl methacrylate of α-methacryloxymethylstyrene or ethyl α-methacryloxymethylacrylate, but only crosslinked polymers or polymers with pendent unsaturation were found.     

Quantum mechanics versus realism

Quantum theory accepts the point-like indivisible (classical) character of a particle as a mere product of a measuring process, or what has become known as a collapse. Following the notion of empty waves, which accepts the particle as a real existent entity without regard to the measurement process, we propose an experiment that may shed some light on the reality of the particle and the consequences of that reality.     

Oriented local entropies for expansive actions by commuting automorphisms

Given an expansive action α of ?² by automorphisms of a compact connected metrizable abelian groupX, we show how the entropy of the action may be decomposed into local contributions, 1 $$h(\alpha ) = \sum\limits_{p \leqslant \infty } {h_p^{(a,b)} } (\alpha )$$ in which the summandh _p ^(a,b) (α) represents thep-adic entropy due to arithmetic or geometric hyperbolicity in the direction (a, b). We recognize thep-adic contribution as an integral over thep-adic unit circle, in analogy with the global counterpart. As (a, b) changes, the decomposition (1) changes only when the line through (a, b) passes through one of a finite collection of critical directions, which are explicitly identified.     

Spectral-Null Codes and Null Spaces of Hadamard Submatrices

Codes of length 2 ^m over {1, -1} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of all have an rth order spectral null at zero frequency. Establishing the connection between and the parity-check matrix of Reed-Muller codes, the minimum distance of is obtained along with upper bounds on the redundancy of . An efficient algorithm is presented for encoding unconstrained binary sequences into .     

The formation of dimetallocycles from reactions of alkynes with (η-C5Me5)2Rh2(CO)2; X-ray structure of [(η-C5Me5)2Rh2(η-CO) {μ-η2,η2-C(O)C2-(CF3)2}]

The complexes (η-C₅Me₅)₂Rh₂(μ-CO) {μ-η²,η²-C(O)CRCR} are obtained from reactions between (η-C₅Me₅)₂Rh₂(CO)₂ and the alkynes RCCR (R  CF₃, CO₂Me, or Ph) at 25°C. The molecular geometry of the complex with R  CF₃ has been established by X-ray diffraction; the bridging 'ene-one' unit adopts a μ-η²,η² conformation. Other complexes isolated from these reactions include (η-C₅Me₅)Rh(C₆R₆) (R  CF₃, CO₂Me), (η-C₅Me)₂Rh₂(C₄R₄) (R  CO₂Me) and (η-C₅Me₅)₂Rh₂(CO₂C₂R₂) (R  Ph). The reaction between (η-C₅Me₅)₂Rh₂(CO)₂ and C₆F₅CCC₆F₅ gives (η-C₅Me₅)₂Rh₂(CO)₂(C₆F₅C₂C₆F₅). Mononuclear complexes such as (η-C₅Me₅)Co(C₄R₄CO) are the major products isolated from reactions between (η-C₅Me₅)₂CO₂(CO)₂ and alkynes at 25°C.     

Reactivity patterns of thermally stable, terminal, electrophilic phosphinidene complexes towards diazoalkanes: oxidation at the phosphorus centre and formation of P-bound eta1-phosphaazine, eta1-phosphaalkene and eta3-diazaphosphaallene complexes

The thermally stable, terminal phosphinidene complexes [CpM(CO)2(eta1-PNiPr2)]AlCl4(Cp= Cp, Cp*; M = Fe) and [Cp*M(CO)3(eta1-PNiPr2)]AlCl4 (M = Cr, Mo, W) react with Ph2C=N=N to form terminal P-coordinated eta1-phosphaazine and eta3-diazaphosphaallene ligands, respectively, whereas [CpFe(CO)2(eta1-PNiPr2)]AlCl4 reacts with Me3SiCHN2 affording a terminal phosphorus bound eta1-phosphaalkene complex.