A remark on normal forms and the “upside-down” I-method for periodic NLS: Growth of higher Sobolev norms

We study growth of higher Sobolev norms of solutions of the onedimensional periodic nonlinear Schr?dinger equation (NLS). By a combination of the normal form reduction and the upside-down I-method, we establish $${\left\| {u(t)} \right\|_{{H^s}}} \le {(1 + \left| t \right|)^{a(s - 1) + }}$$ with ?? = 1 for a general power nonlinearity. In the quintic case, we obtain the above estimate with ?? = 1/2 via the space-time estimate due to Bourgain [4, 5]. In the cubic case, we compute concretely the terms arising in the first few steps of the normal form reduction and prove the above estimate with ?? = 4/9. These results improve the previously known results (except for the quintic case). In the Appendix, we also show how Bourgain??s idea in [4] on the normal form reduction for the quintic nonlinearity can be applied to other powers.     

Effect of light/dark cycle on bacterial hydrogen production by Rhodobacter sphaeroides RV

Hydrogen production by photosynthetic bacteria provides an efficient energy conversion method under low light intensity. However, under strong illumination, such as midday sunlight, the efficiency drops. This prevents the method from being applied industrially. To overcome this problem, we examined a method to thin out the excessive illumination. Light was given intermittently to reduce the total energy flux. The on/off ratio was set at 1/1 throughout the study, so that the time average of the light energy flux became half the continuous illumination. By keeping the time-average light flux constant (0.6 kW·m⁻²), the effects of the cycle period were examined in the range of hours to seconds. The hydrogen production rate was greatly affected by the cycle period, but cell growth and substrate consumption rates remained almost constant. The 30-min light/dark cycle (30 min on and 30 min off) provided the highest rate of hydrogen production (22 L·m⁻²·24 h⁻¹). At the shorter cycles, the rate decreased except that there was a suboptimum at about 40 s. Under excessive light intensity (1.2 kW·m⁻²), the light-to-hydrogen conversion efficiency was greatly enhanced. The hydrogen production rate during the 30-min cycle was twice as high as during a 12-h cycle under the same conditions.     

Construction of Trinervitane and Kempane Skeletons Based on Biogenetical Routes

Based on the putative biogenesis of trinervitane‐ and kempane‐type diterpenes (Scheme 1), a biogenetic‐type transformation was simulated by cyclization of 7,16‐secotrinervita‐7,11,15‐triene‐2α,3α,17‐triol ( 23 ) and of its 17‐chloro derivative 30 . The requisite substrates were prepared from geranylgeranoic acid chloride 6 (Schemes 2, 4, and 5). Treatment of 30 with AgClO₄ at −20° provided the trinervitantrienediols 32 and 33 in 68 and 5% yields, while kempadienediol 35 was obtained in 50% yield by the same reagent at +20° (Scheme 7). The structures of the cyclization products were elaborated from detailed inspection of NMR spectra including H,H COSY, C,H COSY, and NOESY (Tables 1 and 2). The conformation of 30 and its plausible cyclization intermediate was discussed with the help of physical evidence, including X‐ray crystallographic analysis.     

Topological bonding formation between an ultra‐high molecular weight linear polymer and a prepolymer at an early stage of free‐radical crosslinking polymerization

The free‐radical crosslinking polymerization of diallyl adipate (DAA) was carried out in the presence of poly(benzyl methacrylate) (poly(BzMA)) as a chemically inactive polymer in order to clarify the topological bonding formation between linear polymer and prepolymer before gelation; we found by chance that even at an early stage of the polymerization, the topological bonding was formed between ultra‐high molecular weight poly(BzMA) and poly(DAA) prepolymer.     

Preparation of amphotropic liquid crystalline poly(alkoxycarbonylphenylene)s

Poly(alkoxycarbonylphenylene)s with long alkoxy groups were prepared by dehalogenative polycondensation of alkyl dichlorobenzoates with nickel bromide/zinc/triphenylphosphine catalyst. The poly(alkoxycarbonyl‐p‐phenylene)s and poly(alkyloxycarbonyl‐m‐phenylene)s are liquid crystalline, although the latter are composed wholly of kinked repeating units. While poly(hexyloxycarbonylphenylene)s exhibit only thermotropic liquid crystalline behavior, poly(dodecyloxycarbonylphenylene)s and poly(hexadecyloxycarbonylphenylene)s show amphotropism.     

Highly stereospecific protonation of stereoregular living PMMA anions with several alcohols

Living and highly isotactic poly(methyl methacrylate) (PMMA) anion (M̄n = 2.5 × 10³) prepared with t-C₄H₉MgBr as an initiator was protonated with phenol in toluene at −78°C. The reaction was stereospecific toward meso addition, and the meso/racemo ratio at the chain-end of the resultant polymer was 89/11. Addition of 1,4-dioxane to the living isotactic PMMA anion in toluene at −78°C remarkably reduced the viscosity of the system, and protonation of the PMMA anion with phenol in the presence of 1,4-dioxane enhanced the meso-specificity to 94%. On the other hand, the protonation reaction of the living syndiotactic PMMA anion (M̄n = 2.5 × 10³), which was generated by t-C₄H₉Li/(n-C₄H₉)₃Al in toluene at −93°C, with t-butanol was found to be 97% racemo-specific. These highly stereospecific protonation reactions of the stereoregular PMMA anions were in contrast to the protonation of the anions with methanol or benzyl alcohol which was almost non-stereospecific.     

Supported Noble Metal Catalysts and Adsorbents with Soft Lewis Acid Functions

Heterogeneous noble metal catalysts exhibit various functions. Although their redox functions have been extensively studied, we focused on their soft Lewis acid functions. Supported Au, Pt, and Pd catalysts electrophilically attack the π-electrons of soft bases such as alkynes, alkenes, and aromatic compounds to perform addition and substitution reactions. Hydroamination, intramolecular cyclization of alkynyl carboxylic acids, isomerization of allylic esters, vinyl exchange reactions, Wacker oxidation, and oxidative homocoupling of aromatics are introduced based on a discussion of the active species and reaction mechanisms. Furthermore, the adsorption of sulfur compounds, which are soft bases, onto the supported AuNPs is discussed. The adsorption and removal of 1,3-dimethyltrisulfane (DMTS), which is the compound responsible for the stale odor of “hine-ka” in alcoholic beverages, particularly Japanese sake, is described.