Independence number,connectivity, and r-factors

We show that if r ? 1 is an odd integer and G is a graph with |V(G)| even such that k(G) ? (r + 1)²/2 and (r + 1)²α(G) ? 4rk(G), then G has an r-factor; if r ? 2 is even and G is a graph with k(G) ? r(r + 2)/2 and (r + 2)α(G) ? 4k(G), then G has an r-factor (where k(G) and α(G) denote the connectivity and the independence number of G, respectively).     

Synthesis of 2-azabicyclo[2.1.0]pentanes by the intramolecular nucleophilic substitution of cyclopropylmagnesium carbenoids with magnesium anilide

A variety of 2-azabicyclo[2.1.0]pentanes were synthesized by the intramolecular nucleophilic substitution of cyclopropylmagnesium carbenoids with magnesium anilide. The 1-chlorocyclopropyl p-tolyl sulfoxides possessing an N-aryl-substituted aminomethyl group were prepared from dichloromethyl p-tolyl sulfoxide, α,β-unsaturated carboxylic acid esters, and anilines in four steps. The deprotonation of the amine with t-BuMgCl followed by sulfoxide/magnesium exchange of the sulfoxides with i-PrMgCl led to the generation of the cyclopropylmagnesium carbenoids possessing a magnesium anilide moiety. Subsequent intramolecular nucleophilic substitution of the cyclopropylmagnesium carbenoids occurred in a 4-exo-tet manner to give the 2-azabicyclo[2.1.0]pentanes. The optically active 2-azabicyclo[2.1.0]pentane was synthesized using a p-tolylsulfinyl group as a chiral auxiliary.     

Morphological change of crystalline polymer films by annealing: substrate‐ and heating/cooling‐rate‐dependent surface roughness

We study the morphological change of crystalline polymer films by annealing using atomic force microscope, X‐ray diffraction, and Fourier transform infrared spectroscopy techniques. As typical samples, we employ high‐density and low‐density polyethylene films prepared by the cast method. After annealing at 135 °C for 4 h, the surface roughness of polyethylene films by the atomic force microscope significantly increases, and the crystallite size by the X‐ray diffraction also shows some increase, while the Fourier transform infrared spectroscopy spectrum hardly exhibits any change. This can be well explained as a result of the growth of crystal structure by recrystallization during annealing. More interestingly, we find that the choice of the substrate and also the heating/cooling rates for annealing significantly influences the surface roughness of the films. Copyright © 2017 John Wiley & Sons, Ltd.     

Preparation of Enzymatically Recyclable Hydrogels Through the Formation of Inclusion Complexes of Amylose in a Vine‐Twining Polymerization

In this paper, we describe the preparation of hydrogels through the formation of an inclusion complex of amylose in a vine‐twining polymerization. This is achieved by the phosphorylase‐catalyzed polymerization of α‐D ‐glucose 1‐phosphate from maltoheptaose primer, in the presence of a water‐soluble copolymer having hydrophobic graft‐chains (poly(acrylic acid sodium salt‐graft‐δ‐valerolactone)). The mixture turns into a gel during the polymerization process. Evaluation of the hydrogels is conducted by shear‐viscosity measurements of the products. For the hydrogels with relatively high viscosities, fast relaxation modes of the cooperative diffusions are observed by scanning microscopic light scattering measurements, which indicate the nanometer‐size network structures of the hydrogels. In addition, we found that the enzymatic disruption and reproduction of the hydrogels are achieved by the combination of the amylase‐catalyzed hydrolysis of the amylose component and the formation of amylose by the phosphorylase‐catalyzed polymerization.     

Automata in Groups and Dynamics and Induced Systems of PDE in Tropical Geometry

In this paper we develop a dynamical scaling limit from rational dynamics to automata in tropical geometry. We compare these dynamics and induce uniform estimates of their orbits. We apply these estimates to introduce a comparison analysis of theory of automata groups in geometric group theory with analysis of rational dynamics and some hyperbolic PDE systems. Frameworks of characteristic properties of automata groups are inherited to the corresponding rational or PDE dynamics. As an application we study the Burnside problem in group theory and translate the property as the infinite quasi-recursiveness in rational dynamics.     

Synthesis of carbazole‐based light‐emitting polymers incorporating 2,5‐bis(phenylethenyl)‐4‐decyloxyanisole as collateral fluorophore

The Suzuki coupling polymerization between bis(carbazole) monomer ( CzDB ) and 9,9‐dihexylfluorene‐2,7‐diboronic acid was carried out to obtain PFCz‐PEDA0 having the number‐averaged molecular weight of 7000. The absorption and emission maximum wavelengths were observed at 344 and 408 nm, respectively. The quantum yield (QY) was relatively low (0.12) because of the photo‐induced electron transfer. Subsequently, CzPEDA ‐bearing 2,5‐bis(phenylethenyl)‐4‐decyloxyanisole (PEDA) segment sandwiched with 3‐bromocarbazole units was copolymerized to give PFCz‐PEDAn (n = 05, 10, 20, 35, and 50). The content of PEDA segment in polymer could be controlled by the monomer feed ratio. In CHCl₃ solution, the absorbance at around 400 nm became larger with one isosbestic point at 370 nm, and the emission peak at 448 nm became prominent with increasing the PEDA content. The QY of polymer was increased as the PEDA content, which was a consequence of the fluorescence resonance energy transfer from carbazole‐containing chromophore (energy donor) to PEDA fluorophore (energy acceptor). In spin‐coated film, the maximum QY was obtained in PFCz‐PEDA05 having the most appropriate molar balance of energy donor and acceptor units. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 8141–8148, 2008     

Synthesis of β-hydroxyphosphonates by iron-catalyzed oxidative addition of phosphonyl radicals to alkenes

Phosphorohydrazidates have been shown to work as radical precursors by iron-catalyzed aerobic oxidation to generate corresponding phosphonyl radicals. Generated radicals cause intermolecular addition to various alkenes in the presence of molecular oxygen to give β-hydroxyphosphonate compounds in good yield.