On Calabi’s Strong Maximum Principle via Local Semi-Dirichlet Forms

We give a stochastic proof of an extension of E. Calabi??s strong maximum principle under some geometric conditions in the framework of strong Feller diffusion processes associated to local regular semi-Dirichlet forms with lower bounds. As a corollary, our notion of subharmonicity implies a notion of viscosity subsolution in a stochastic sense. We can apply our result to singular geometric object like Alexandrov space, limit space under spectral distance of Riemannian manifolds with uniform lower Ricci curvature bound and so on.     

Synthesis and nanoimprinting of high refractive index and highly transparent polythioethers based on thiol-ene click chemistry

This work demonstrates the UV nanoimprinting lithography (UV-NIL) of high refractive index and highly transparent polythioethers based on thiol-ene click chemistry. Herein, 9,9-bis(3-mercaptopropylphenylether)fluorene (BMPF) is designed as a new thiol monomer with a high refractive index, high transparency, and good processability for UV-NIL. Colorless polythioethers are synthesized from BMPF and ene monomers under mild thiol-ene click reaction conditions. Excellent transmittance (96%) of 400 nm light is observed in all the polymer films and high refractive index values of 1.5972–1.6382 are attained. UV-NIL using thiol-ene photopolymerization affords polymer nanoimprinting patterns with various features on the order of 100–500 nm without any fractures. To the best of our knowledge, this is the first report on UV-NIL of high refractive index and highly transparent polymers. Through proper monomer and polymer design, novel polythioethers with suitable glass transition temperature (T _g) values are developed with high refractive index, high transparency, and good UV-NIL processability. Furthermore, UV-NIL based on thiol-ene click chemistry is accomplished at the nanoscale. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2175–2182     

Cholesteric induction power of β-galactose derivatives

Galactose derivatives were explored as chiral dopants, effective for inducing chiral nematic liquid crystal (LC) phases. Galactose bearing O-isopropylidene substituents at the C3 and C4 and butoxybiphenyl substituents at the C2 and C6 positions exhibits a high helical twisting power (HTP) value of ?74.4 μm^?1. Such a high HTP value for the galactose derivative is attributed to (1) linkage of the C3 and C4 carbons with the O-isopropylidene substituent, which places the C2 and C6 substitutes in a skew arrangement at a large angle and (2) enhancement of the affinity with the host nematic LCs by incorporating aromatic substituents at the C2 and C6 positions that are similar to those in the host.     

Large electro‐optic activity and enhanced temporal stability of methacrylate‐based crosslinking hyperbranched nonlinear optical polymer

A methacrylate‐based crosslinking hyperbranced polymers have been synthesized through initiator‐fragment incorporation radical polymerization and used for the temperature stable electro‐optic (EO) polymer application. This polymer consists of methyl methacrylate, 2‐metacryloxyethyl isocyanate, and ethylene glycol dimethacrylate (EGDMA) monomers. The use of EGDMA as a bifunctional unit resulted in the solvent‐soluble crosslinking hyperbranched chain, so that the EO polymer enhanced glass transition temperatures. A phenyl vinylene thiophene vinylene bridge nonlinear optical chromophore was attached to the polymer backbone as the side‐chain by a post‐functionalization reaction. The loading concentration of the chromophore was varied between 30 and 50 wt % by simply changing the mixing ratio of the precursor polymer to the chromophore. The synthesized EO polymers produced optical quality films with a light propagation loss of 0.61 dB/cm in a slab waveguide at 1.31 μm. The electrically poled film had an EO coefficient (r₃₃) of 139 pm/V at 1.31 μm. The EO crosslinking hyperbranced polymer had a high‐glass transition temperature of 170 °C, and exhibited excellent temporal stability of the EO activity at 85 °C for 500 h. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Synthesis of fluorine‐containing star‐shaped poly(vinyl ether)s via arm‐linking reactions in living cationic polymerization

Various types of fluorine‐containing star‐shaped poly(vinyl ether)s were successfully synthesized by crosslinking reactions of living polymers based on living cationic polymerization. Star polymers with fluorinated arm chains were prepared by the reaction between a divinyl ether and living poly(vinyl ether)s with fluorine groups (C₄F₉, C₆F₁₃, and C₈F₁₇) at the side chain using cationogen/Et_1.5AlCl_1.5 in a fluorinated solvent (dichloropentafluoropropanes), giving star‐shaped fluorinated polymers in high yields with a relatively narrow molecular weight distribution. The concentration of living polymers for the crosslinking reaction and the molar feed ratio of a bifunctional vinyl ether to living polymers affected the yield and molecular weight of the star polymers. Star polymers with block arms were prepared by a linking reaction of living block copolymers of a fluorinated segment and a nonfluorinated segment. Heteroarm star‐shaped polymers containing two‐ or three‐arm species were synthesized using a mixture of different living polymer species for the reaction with a bifunctional vinyl ether. The obtained polymers underwent temperature‐induced solubility transitions in various organic solvents, and their concentrated solutions underwent sol–gel transitions, based on the solubility transition of a thermoresponsive fluorinated segment. Furthermore, a slight amount of fluorine groups were shown to be effective for physical gelation when those were located at the arm ends of a star polymer. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Analysis of a meshless solver for high Reynolds number flow

In this paper, the extension of an upwind least‐square based meshless solver to high Reynolds number flow is explored, and the properties of the meshless solver are analyzed both theoretically and numerically. Existing works have verified the meshless solver mostly with inviscid flows and low Reynolds number flows, and in this work, we are interested in the behavior of the meshless solver for high Reynolds number flow, especially in the near‐wall region. With both theoretical and numerical analysis, the effects of two parameters on the meshless solver are identified. The first one is the misalignment effect caused by the significantly skewed supporting points, and it is found that the meshless solver still yields accurate prediction. It is a very interesting property and is opposite to the median‐dual control volume based vertex‐centered finite volume method, which is known to give degraded result with stretched triangular/tetrahedral cells in the near‐wall region. The second parameter is the curvature, and according to theoretical analysis, it is found in the region with both large aspect ratio and curvature, and the streamwise residual is less affected; however, the wall‐normal counterpart suffers from accuracy degradation. In this paper, an improved method that uses a meshless solver for the streamwise residual and finite difference for wall‐normal residual is developed. This method is proved to be less sensitive to the curvature and provides improved accuracy. This work presents an understanding of the meshless solver for high Reynolds number flow computation, and the analysis in this paper is verified with a series of numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd.     

Intra-abdominal fat area is a predictor for new onset of individual components of metabolic syndrome: MEtabolic syndRome and abdominaL ObesiTy (MERLOT study)

Objective: To investigate the significance of intra-abdominal fat area (IAFA) on new onset of individual components of the metabolic syndrome: high blood pressure, dyslipidemia, or hyperglycemia. Methods: We conducted a longitudinal study using checkup data of a hospital from 1994 to 2010. Of 25,255 subjects, we examined 1,380 Japanese, who underwent computed tomography to measure IAFA and had no metabolic syndrome components at baseline. Results: During 3.6 years of the mean follow-up period, one of metabolic syndrome components occurred in 752 subjects. Of three components, high blood pressure was more prevalent. The multiple Cox regression analysis disclosed that IAFA is significantly associated with onset of metabolic syndrome components (HR: 1.05 per 10 cm², 95%CI: 1.03–1.07). This finding was independent of BMI, and significant even in non-obese individuals with body mass index <25 kg/m². Conclusions: MERLOT study demonstrates that IAFA is an independent predictor for new onset of individual components of the metabolic syndrome, even in non-obese healthy Japanese.     

Total synthesis of pleurolactone

The stereoselective total synthesis of pleurolactone has been accomplished in 7 steps. The key synthetic features were the construction of four contiguous stereocenters using an endo-selective Diels-Alder reaction and high diastereoselective dihydroxylation.     

Proton Order–Disorder Phenomena in a Hydrogen‐Bonded Rhodium–η5‐Semiquinone Complex: A Possible Dielectric Response Mechanism

A newly synthesized one‐dimensional (1D) hydrogen‐bonded (H‐bonded) rhodium(II)–η⁵‐semiquinone complex, [Cp*Rh(η⁵‐p‐HSQ‐Me₄)]PF₆ ([ 1 ]PF₆; Cp*=1,2,3,4,5‐pentamethylcyclopentadienyl; HSQ=semiquinone) exhibits a paraelectric–antiferroelectric second‐order phase transition at 237.1 K. Neutron and X‐ray crystal structure analyses reveal that the H‐bonded proton is disordered over two sites in the room‐temperature (RT) phase. The phase transition would arise from this proton disorder together with rotation or libration of the Cp* ring and PF₆^? ion. The relative permittivity ε_b′ along the H‐bonded chains reaches relatively high values (ca., 130) in the RT phase. The temperature dependence of ¹³C CP/MAS NMR spectra demonstrates that the proton is dynamically disordered in the RT phase and that the proton exchange has already occurred in the low‐temperature (LT) phase. Rate constants for the proton exchange are estimated to be 10^?4–10^?6 s in the temperature range of 240–270 K. DFT calculations predict that the protonation/deprotonation of [ 1 ]⁺ leads to interesting hapticity changes of the semiquinone ligand accompanied by reduction/oxidation by the π‐bonded rhodium fragment, producing the stable η⁶‐hydroquinone complex, [Cp*Rh³⁺(η⁶‐p‐H₂Q‐Me₄)]²⁺ ([ 2 ]²⁺), and η⁴‐benzoquinone complex, [Cp*Rh⁺(η⁴‐p‐BQ‐Me₄)] ([ 3 ]), respectively. Possible mechanisms leading to the dielectric response are discussed on the basis of the migration of the protonic solitons comprising of [ 2 ]²⁺ and [ 3 ], which would be generated in the H‐bonded chain.