On the Cauchy problem for non-effectively hyperbolic operators,the Gevrey 5 well-posedness

In this paper, we prove that for non-effectively hyperbolic operators with smooth double characteristics exhibiting a Jordan block of size 4 on the double manifold, the Cauchy problem is well-posed in the Gevrey 5 class, beyond the generic Gevrey class 2 (see, e.g., [5]). Moreover, we show that this value is optimal, due to certain geometric constraints on the Hamiltonian flow of the principal symbol. These results, together with results already proved, give a complete picture of the well-posedness of the Cauchy problem around hyperbolic double characteristics.     

Synthesis and spectroscopic investigation of π‐conjugated (E)‐enyne polycarbazole with different organo‐metallic catalysts from 3,6‐diethynyl‐9‐(2‐ethylhexyl)carbazole

In the present study, a new (E)‐rich‐enyne π‐conjugated polymer containing a carbazole was designed and synthesized. Two different synthesis methods of poly[N‐(2‐ethylhexyl)‐3,6‐carbazolyleneethynylene‐(E)‐vinylene] (PCZEV) have been prepared from 3,6‐diethynyl‐9(2‐ethylhexyl)carbazole by using the palladium‐carbene‐catalyzed reaction and/or by using the organolanthanide‐catalyzed reaction leading to well‐defined polymer, and their general properties were studied. Compared to poly[N‐(2‐ethylhexyl)‐3,6‐carbazolyleneethynylene] (PCE), the UV‐vis absorption and photoluminescence of the PCZEV was red‐shifted, which indicates the extension of conjugation length. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2434–2442, 2009     

Hydrogen bond network-stabilisation of blue phases by addition of a chiral N-(10-hydroxydecyl)succinimide derivative and alkane diols

Blue phases (BPs) obtained by doping a commercially available liquid crystalline compound (4-butyl-N-(4-ethoxybenzylidene)aniline (EBBA)) with (2R,3R)-2,3-bis(4-octyloxyphenylbenzoyloxy)-N-(hydroxydecyl)succinimide (1) were highly stabilised by the addition of a small amount of alkane diols. Especially, addition of only 0.5 mol% of octane-1,8-diol increased the BP–Iso transition temperature by 10 K and widened the BP temperature range up to 35 K. A model stabilisation mechanism based on the construction of a hydrogen bond network in each disclination zone in BPs was proposed.     

3D atomic imaging by internal-detector electron holography

A method of internal-detector electron holography is the time-reversed version of photoelectron holography. Using an energy-dispersive x-ray detector, an electron gun, and a computer-controllable sample stage, we measured a multiple-energy hologram of the atomic arrangement around the Ti atom in SrTiO3 by recording the characteristic Ti Kα x-ray spectra for different electron beam angles and wavelengths. A real-space image was obtained by using a fitting-based reconstruction algorithm. 3D atomic images of the elements Sr, Ti, and O in SrTiO3 were clearly visualized. The present work reveals that internal-detector electron holography has great potential for reproducing 3D atomic arrangements, even for light elements.     

On almost holomorphic Lagrangian fibrations

We prove that the pull back of an ample line bundle by an almost holomorphic Lagrangian fibration is nef. As an application, we show birational semi rigidity of Lagrangian fibrations.     

Precise synthesis of a series of poly(4‐n‐alkylstyrene)s and their glass transition temperatures

Poly(4‐n‐alkylstyrene)s with six kinds of n‐alkyl groups such as methyl, ethyl, propyl, butyl, hexyl, and octyl groups covering wide molecular weight range from around 5 k to over 100 k were precisely synthesized by living anionic polymerizations. It was confirmed that all the polymers obtained have narrow molecular weight distribution, that is, M_w/M_n is all less than 1.1, by SEC. T_gs of all the polymers were estimated by DSC measurements and it turned out to be clear that their molecular weight dependence was well described by the Fox–Flory equations. Furthermore, it is evident that T_g monotonically decreases as a number of carbon atoms of n‐alkyl group is increased, though T_g values are all 20 K or more higher than those reported previously for the same polymer series. This is because backbone mobility increases by introducing longer n‐alkyl side groups with high mobility, while T_g difference in between this work and the previous one may due to the experimental conditions and also to the molecular weight range adopted. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 757–763     

Alkyl side chain length dependent compatibility of poly(4‐n‐alkylstyrene)s and 1,4‐rich polyisoprene blends

We investigated the compatibility of blends of 1,4‐rich polyisoprene (1,4‐PI) and poly(4‐n‐alkylstyrene)s with six kinds of n‐alkyl side groups, that is, methyl, ethyl, propyl, butyl, hexyl, and octyl focusing on carbon number of alkyl groups. Poly(4‐methylstyrene)/1,4‐PI blend was turned out to be immiscible at all temperature range adopted in this work and poly(4‐ethylstyrene)/1,4‐PI blend revealed UCST type phase behavior, while the others were found to be compatible. The phase diagrams of poly(4‐ethylstyrene)/1,4‐PI blends were obtained by optical microscopy, and the temperature dependence of the Flory‐Huggins interaction parameter χ has been estimated to be χ = ?0.036 + 24/T by applying lattice theory, where T is the absolute temperature. From this relationship χ value at room temperature (298 K) was calculated to be 0.045, the value is reasonably low for miscible polymers system. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55 , 1791–1797     

General Information to Obtain Spherical Particles with Ordered Mesoporous Structures

Conditions for the synthesis of aluminum organophosphonate (AOP) and aluminophosphate (AlPO) spheres containing periodic mesopores were optimized and demonstrated to be general morphological controls for the surfactant‐assisted synthesis of mesoporous materials. High‐quality AOP and AlPO spheres with uniform mesopores were obtained at low and high temperatures, respectively. The aerosol‐assisted synthesis of materials with uniform mesopores was categorized by using the difference in relative density of soluble AOP and AlPO oligomers that interact with ethylene oxide (EO) units in EO_nPO_mEO_n triblock copolymer (PO=propylene oxide). Then, ordered mesoporous structures are constructed with the adequate amount of species in resultant frameworks, and the number of interactive points in soluble species determines the resultant density of the frameworks after self‐assembly. Consequently, temperature‐dependent synthesis, which allows controlled infiltration of soluble species to match the density of resultant frameworks, is required for the formation of ordered mesoporous structures under morphological control.