Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point,II — Its relevance to the Mathieu equation and the Legendre equation

We develop the exact WKB analysis of an M2P1T (merging two simple poles and one simple turning point) Schrödinger equation. In Part II, using a WKB-theoretic transformation to the algebraic Mathieu equation constructed in Part I, we calculate the alien derivative of its Borel transformed WKB solutions at each fixed singular point relevant to the simple poles through the analysis of Borel transformed WKB solutions of the Legendre equations. In the course of the calculation of the alien derivative we make full use of microdifferential operators whose symbols are given by the infinite series that appear in the coefficients of the algebraic Mathieu equation and the Legendre equation.     

Palladium‐Catalyzed Domino CH/NH Functionalization: An Efficient Approach to Nitrogen‐Bridged Heteroacenes

Palladium‐catalyzed domino C?H/N?H functionalization for the synthesis of novel nitrogen‐bridged thienoacenes and 10H‐benzo[4,5]thieno[3,2‐b]indole derivatives from dihaloarene is reported. This domino sequence consists of initial C?H functionalization of the benzo[b]thiophene moiety, followed by Buchwald–Hartwig coupling. This transformation is also useful for the synthesis of highly π‐extended compounds.     

Anionic polymerization of N,N‐dialkyl‐2‐methylenebut‐3‐enamide: Effect of alkyl substituents on polymerization behavior

Anionic polymerizations of three 1,3‐butadiene derivatives containing different N,N‐dialkyl amide functions, N,N‐diisopropylamide (DiPA), piperidineamide (PiA), and cis‐2,6‐dimethylpiperidineamide (DMPA) were performed under various conditions, and their polymerization behavior was compared with that of N,N‐diethylamide analogue (DEA), which was previously reported. When polymerization of DiPA was performed at ?78 °C with potassium counter ion, only trace amounts of oligomers were formed, whereas polymers with a narrow molecular weight distribution were obtained in moderate yield when DiPA was polymerized at 0 °C in the presence of LiCl. Decrease in molecular weight and broadening of molecular weight distribution were observed when polymerization was performed at a higher temperature of 20 °C, presumably because of the effect of ceiling temperature. In the case of DMPA, no polymer was formed at 0 °C and polymers with relatively broad molecular weight distributions (M_w/M_n = 1.2) were obtained at 20 °C. The polymerization rate of PiA was much faster than that of the other monomers, and poly(PiA) was obtained in high yield even at ?78 °C in 24 h. The microstructure of the resulting polymers were exclusively 1,4‐ for poly(DMPA), whereas 20–30% of the 1,2‐structure was contained in poly(DiPA) and poly(PiA). © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3714–3721, 2010     

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.     

Electrical resistivity and thermal conductivity of UP1−xSx

UP, US, and their solid solutions of several compositions were prepared, and the electrical resistivities of these samples were measured from liquid nitrogen temperature to 1000 K and the thermal diffusivities from 300 to 1000 K. It was shown that the resistivity of UP_1?xS_x at the paramagnetic region arose mainly from the scattering of conduction electrons by disordered spins localized at uranium ion sites. The resistivity of UP_0.4S_0.6 showed another anomaly below the transition temperature. A gentle hump of the thermal diffusivity of UP was observed at about 650 K. This was concluded to be due to the anomalous negative temperature coefficient of electrical resistivity observed above the Néel temperature up to about 550 K. The composition dependence of thermal conductivity of UP_1?xS_x was compared with that of UC_1?xN_x by separating the total conductivity into electronic and phonon contributions.     

Novel ring transformation of quinolines to indole derivatives in two steps via 1,4-dihydroquinoline derivatives

Diphenyl 1-phenoxycarbonyl-1,4-dihydroquinoline-4-phosphonates 5c-g, obtained from the reaction of corresponding quinoline derivatives 1 with phenyl chloroformate and triphenyl phosphite in one step, were ozonized in CHCl₃ and CH₃COOH. Treatment of the resulting mixture with NaHCO₃ produced the 3-formyl-1-phenoxycarbonylindole derivatives 8a-e in high yields. The ring transformation of quinolines 1 to indoles 8 proceeds under mild conditions.     

Behavior of the Bergman kernel at infinity

We give a precise decay rate of the Bergman kernel and metric at infinity on model domains, characterized in terms of certain convex polyhedron.Supported by JSPS.     

The effect of bath pH on electrodeposition and corrosion properties of ternary Fe-W-Zn alloy platings

Journal of Solid State Electrochemistry - As a new trial to improve the corrosion resistance of the Fe-W alloy platings, Fe-W alloys incorporating a small amount of Zn, namely novel ternary Fe-W-Zn...     

On the multiplicities of the zeros of Laguerre-Pólya functions

We show that all the zeros of the Fourier transforms of the functions , , are real and simple. Then, using this result, we show that there are infinitely many polynomials such that for each the translates of the function

generate . Finally, we discuss the problem of finding the minimum number of monomials , , which have the property that the translates of the functions , , generate , for a given .