Oxidation of sec‐alcohols with Ru(II)‐bearing microgel star polymer catalysts via hydrogen transfer reaction: Unique microgel‐core catalysis

Oxidation of sec‐alcohols was investigated with ruthenium‐bearing microgel core star polymer catalysts [Ru(II)‐Star]. The star polymer catalysts were directly prepared via RuCl₂(PPh₃)₃‐catalyzed living radical polymerization of methyl methacrylate (MMA), followed by the arm‐linking reaction with ethylene glycol dimethacrylate ( 1 ) in the presence of diphenylphosphinostyrene ( 2 ). The Ru(II)‐Star efficiently and homogeneously catalyzed the oxidation of 1‐phenylethanol ( S1 ) to give a corresponding ketone (acetophenone) in higher yield (92%) than the analogs of polymer‐supported ruthenium complexes. Importantly, the star catalyst afforded high recycling efficiency in the oxidation. They held catalytic activity against three times catalysis even though they were recovered under air‐exposure, whereas the conventional RuCl₂(PPh₃)₃ lost the activity for same recycling procedure due to the deactivation by oxygen. The stability of the star catalysts during the recycle experiment was confirmed by detailed spectroscopic characterization. The star polymers also catalyzed oxidation for a wide range of sec‐alcohols with aromatic and aliphatic groups. The substrate affinity was different from that with RuCl₂(PPh₃)₃, suggesting the unique selectivity caused by the specific structure. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011.     

Power operations in elliptic cohomology and representations of loop groups

Part I of this paper describes power operations in elliptic cohomology in terms of isogenies of the underlying elliptic curve. Part II discusses a relationship between equivariant elliptic cohomology and representations of loop groups. Part III investigates the representation of theoretic considerations which give rise to the power operations discussed in Part I.

     

Reproduction of distance matrices and original time series from recurrence plots and their applications

We propose a method to reproduce distance matrices and original time series from recurrence plots. The procedure is to (i)convert a recurrence plot to a weighted graph and (ii)calculate a distance between each pair of nodes on this weighted graph. We demonstrate this method by reproducing the topological shape of original time series. We also propose two applications. The first application is to obtain the maximal Lyapunov exponent from a recurrence plot without reproducing the shapes of original time series. The second application is to reconstruct a common deterministic driving force from observations of forced systems. Thus, the method opens new fields in data analysis.     

Highly refractive polymer resin derived from sulfur‐containing aromatic acrylate

New sulfur‐containing polymers with high‐refractive indices and low birefringences have been developed as UV‐curable high‐refractive polymer resins. The polymers derived from 2,7‐bis[(2‐acryloylethyl)sulfanyl]thianthrene (2,7‐BAST) and 4,4′‐bis[(acryloyloxyethylthio)diphenylsulfide (4,4′‐BADS) were prepared by photopolymerization under UV irradiation. Transparent UV‐cured films were obtained in both cases. Both polymers showed good thermal stability, such as a 5% weight‐loss temperature at 355 °C under nitrogen and glass transition temperatures (T_g) in the range of 94–143 °C. They also showed high‐refractive indices of 1.6531 and 1.6645 at 632.8 nm and low birefringences of 0.0039 and 0.0069 in addition to high transparency in the visible region. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2604–2609, 2010     

A local structure theorem on 5‐connected graphs

An edge of a 5‐connected graph is said to be contractible if the contraction of the edge results in a 5‐connected graph. Let x be a vertex of a 5‐connected graph. We prove that if there are no contractible edges whose distance from x is two or less, then either there are two triangles with x in common each of which has a distinct degree five vertex other than x, or there is a specified structure called a K₄^?‐configuration with center x. As a corollary, we show that if a 5‐connected graph on n vertices has no contractible edges, then it has 2n/5 vertices of degree 5. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 99–129, 2009     

Classification Performance of a Low Pressure Differential Mobility Analyzer for Nanometer-sized Particles

Size distribution measurements and classification tests by a low pressure differential mobility analyzer (LPDMA) for nanometer-sized silver particles and cesium iodide particles under low pressure conditions (123–300 Torr) were performed using a transmission electron microscope (TEM) and the tandem DMA technique. When the ratio of the sheath gas flow rate and the aerosol gas flow rate was set at 5 : 1, the targeted sizes calculated from the classification voltage applied to the LPDMA at 160 Torr are found to be in good correlation with the count mean Feret diameter obtained from the TEM observation of the particles collected after a classification ranging from 6 to 25 nm, although the targeted sizes set by the LPDMA were approximately 15% greater than the count mean Feret diameter measured by the TEM after classification. The geometric standard deviations of DMA-classified particles measured by TEM and those obtained from the tandem DMA method ranged from 1.08 to 1.17 and from 1.05 to 1.13, respectively. They were slightly greater than the ideal geometric standard deviations (1.05) of the particles classified with the LPDMA, which was calculated by neglecting the broadening effects due to Brownian diffusion. We experimentally demonstrated the validity of our LPDMA system for size measurements and classification of the nanometer-sized particles under low pressure conditions.