On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities

Inspired by the symbol calculus of linear differential operators of infinite order applied to the Borel transformed WKB solutions of simple-pole type equation [Kamimoto et al. (RIMS Kôkyûroku Bessatsu B 52:127–146, 2014)], which is summarized in Section 1, we introduce in Section 2 the space of simple resurgent functions depending on a parameter with an infra-exponential type growth order, and then we define the assigning operator \({\mathscr{A}}\) which acts on the space and produces resurgent functions with essential singularities. In Section 3, we apply the operator \({\mathscr{A}}\) to the Borel transforms of the Voros coefficient and its exponentiation for the Whittaker equation with a large parameter so that we may find the Borel transforms of the Voros coefficient and its exponentiation for the boosted Whittaker equation with a large parameter. In Section 4, we use these results to find the explicit form of the alien derivatives of the Borel transformed WKB solutions of the boosted Whittaker equation with a large parameter. The results in this paper manifest the importance of resurgent functions with essential singularities in developing the exact WKB analysis, the WKB analysis based on the resurgent function theory. It is also worth emphasizing that the concrete form of essential singularities we encounter is expressed by the linear differential operators of infinite order.     

High‐Density Liquid‐Crystalline Polymer Brushes Formed by Surface Segregation and Self‐Assembly

High‐density polymer brushes on substrates exhibit unique properties and functions stemming from the extended conformations due to the surface constraint. To date, such chain organizations have been mostly attained by synthetic strategies of surface‐initiated living polymerization. We show herein a new method to prepare a high‐density polymer brush architecture using surface segregation and self‐assembly of diblock copolymers containing a side‐chain liquid‐crystalline polymer (SCLCP). The surface segregation is attained from a film of an amorphous base polymer (polystyrene, PS) containing a minor amount of a SCLCP‐PS diblock copolymer upon annealing above the glass‐transition temperature. The polystyrene portion of the diblock copolymer can work as a laterally mobile anchor for the favorable self‐assembly on the polystyrene base film.     

Total synthesis and evaluation of the actin-binding properties of microcarpalide and a focused library of analogues

A comparative investigation shows that hydroxylated 10-membered lactones modeled around the fungal metabolites microcarpalide (1) and pinolidoxin (2) are endowed with selective actin-binding properties. Although less potent than the marine natural product latrunculin A, which represents the standard in the field, nonenolides of this type are significantly less toxic and accommodate substantial structural editing. Most notable is the fact that even an intramolecular transesterification with formation of a hydroxylated butanolide skeleton does not annihilate their microfilament disrupting capacity. This finding calls for a reinvestigation of the biological profile of other fungal metabolites that embody a similar motif. Microcarpalide (1) serving as the calibration point for this comparative study was prepared by total synthesis based on ring-closing metathesis (RCM) as the key step. The chosen route favorably compares to previous approaches to this target and provides further support for the notion that the (E,Z)-configuration of a medium-sized cycloalkene can be controlled by proper choice of the catalyst as previously outlined by our group. 9-epi-Microcarpalide 26 and furanone 27 as representative examples of the "natural productlike" compounds investigated herein have been characterized by crystal structure analysis.     

Selective ultratrace detection of Al(III) and Ga(III) complexed with a calcein isomer by capillary zone electrophoresis with laser-induced fluorescence detection. Comparison of emissive polyaminocarboxylates as derivatizing ligands

A highly sensitive and selective capillary zone electrophoresis with laser-induced fluorescence detection (CZE-LIF) for Al(3+) and Ga(3+) was developed using a calcein 4',5'-isomer as a pre-capillary complexing agent. Direct fluorescent detection without an agent added to the carrier buffer provided the notable detection limits of 3.9x10(-10) and 4.6x10(-10)moldm(-3) for Al and Ga, respectively. By applying this system successfully to a river water sample, its potential for practical applications was ascertained. A comparison of three aromatic polyaminocarboxylate ligands related to the coordination structure and the distance between the fluorophore and the chelating moiety, revealed some interesting factors regarding their selectivity.     

Surface design for precise control of spatial growth of a mesostructured inorganic/organic film on a large-scale area

A microfabrication technique is presented to fabricate a mesostructured inorganic/organic composite film, i.e., silica/cetyltrimethylammonium chloride (CTAC) film, with near-perfect site-selectivity on a large surface area based on a spatially regulated growth method. To precisely regulate the site-selective growth of this mesocomposite film at the solid/liquid interface, we designed a novel microtemplate consisting of a "dual-component" self-assembled monolayer (SAM) with alternating hydrophobic trifluorocarbon (CF3) and cationic amino (NH2) groups. First, (heptadecafluoro-1,1,2,2-tetrahydrodecyl)trimethoxysilane (FAS)-SAM was formed onto Si substrate covered with native oxide (SiO2/Si) from vapor phase. The substrate was then photolithographically micropatterned using 172 nm vacuum UV light. Finally, the micropatterned FAS-SAM was immersed in a solution of 1 vol % (aminoethylaminomethyl)phenethyltrimethoxysilane (AEAMPS) in absolute toluene. Due to these treatments, a dual-SAM microtemplate with CF3- and NH2-terminated surfaces was fabricated, as evidenced by lateral force microscopy, ellipsometry, and X-ray photoelectron spectroscopy. Using this template, the microfabrication of a mesocomposite film was demonstrated. As a control, the micropatterned hydrophobic FAS-SAM template (composed of CF3- and OH-terminated surfaces) was also treated under the same conditions. Optical microscopy and atomic force microscopy confirmed that the formation of the continuous mesocomposite film proceeded only on the FAS-SAM-covered regions, while the AEAMPS-SAM-covered regions remained free of deposits. This shielding effect also remained constant regardless of the pattern's geometry, i.e., the interval distance between the FAS-SAM-covered areas in the pattern. Through this approach, we were able to obtain well-defined 5-, 10-, and 20-mum wide mesocomposite microlines over the entire 10 x 10 mm2 area with high area-selectivity. On the other hand, when the SiO2 regions were not terminated with the cationic NH2 groups, cluster formation proceeded not only on the hydrophobic CF3 regions but also on the SiO2 regions, particularly with an increase in the pattern interval distance, resulting in lower final pattern resolution.     

Unique molecular orientation in a smectic liquid crystalline polymer film attained by surface-initiated graft polymerization

Liquid crystalline (LC) polymer brushes containing a mesogenic azobenzene (Az) moiety are synthesized on a quartz or silicon substrate by surface-initiated atom transfer radical polymerization. The molecular orientation of the Az units and the LC properties in the grafted chains are evaluated by UV-vis spectroscopy, polarized optical microscopy, and grazing incidence X-ray diffraction measurements. The Az side chains of the grafted chains exhibited a smectic LC phase in which the smectic layers are oriented perpendicular to the substrate with a parallel orientation of the mesogens. In contrast, a spincast film of the identical LC polymer without grafting to the surface shows layer structures parallel to the substrate. A drastic effect of tethering one end to the substrate on the LC orientation is demonstrated.     

Direct conversion to 2-phenyl-4-quinolones via a 4-alkoxyflavylium salt from a naturally occurring flavanone

A flavanone, in which a hydroxyl group at the 5-position was protected with a methyl group, converted to the corresponding 5-methoxy-2-phenyl-4-quinolone via flavylium salt under mild conditions. Flavanone-O-rhamnoglucoside, naringin, was also converted to 5-methoxy-2-phenyl-4-quinolon-7-O-rhamnoglucoside in the same way in an overall 25% yield.     

Charge‐discharge properties of composites of polypyrrole and vanadium oxide powder

Composite of polypyrrole and crystalline V₂O₅ powder was prepared by chemical oxidation of pyrrole with use of V₂O₅ powder itself as an oxidizing agent. The V₂O₅ content was changed from 0 to 94 wt% by changing the amount of V₂O₅ dispersed in the preparation bath. The pellet electrodes could be prepared by pressing the composite powder alone even if amount of polypyrrole in the composite was only 6 wt%. The resulting pellet electrode exhibited good charge‐discharge performance as a positive electrode of Li rechargeable battery in an electrolyte solution as well as in a quasi‐solid cell fabricated by using a gel electrolyte sheet of poly(methyl methacrylate).