One-pot synthesis of optically active allyl esters via lipase-vanadium combo catalysis

The combination of vanadium-oxo compounds (3 or 4) with a lipase produced the regio- and enantioconvergent transformation of racemic allyl alcohols (1 or 2) into optically active allyl esters. In this system, the vanadium compounds catalyzed the continuous racemization of the alcohols along with the transposition of the hydroxyl group, while the lipase effected the chemo- and enantioselective esterification to achieve the dynamic kinetic resolution.     

Fresnel filtering of Gaussian beams in microcavities

We study the output from the modes described by the superposition of Gaussian beams confined in the quasi-stadium microcavities. We experimentally observe the deviation from Snell's law in the output when the incident angle of the Gaussian beam at the cavity interface is near the critical angle for total internal reflection, providing direct experimental evidence on the Fresnel filtering. The theory of the Fresnel filtering for a planar interface qualitatively reproduces experimental data, and a discussion is given on small deviation between the measured data and the theory.     

On the computation of all eigenvalues for the eigenvalue complementarity problem

In this paper, a parametric algorithm is introduced for computing all eigenvalues for two Eigenvalue Complementarity Problems discussed in the literature. The algorithm searches a finite number of nested intervals \([\bar{l}, \bar{u}]\) in such a way that, in each iteration, either an eigenvalue is computed in \([\bar{l}, \bar{u}]\) or a certificate of nonexistence of an eigenvalue in \([\bar{l}, \bar{u}]\) is provided. A hybrid method that combines an enumerative method [1] and a semi-smooth algorithm [2] is discussed for dealing with the Eigenvalue Complementarity Problem over an interval \([\bar{l}, \bar{u}]\) . Computational experience is presented to illustrate the efficacy and efficiency of the proposed techniques.     

Fast computation of incomplete elliptic integral of first kind by half argument transformation

We developed a new method to calculate the incomplete elliptic integral of the first kind, F(j|m){F(varphi|m)} , by using the half argument formulas of Jacobian elliptic functions. The method reduces the magnitude of j{varphi} by repeated usage of the formulas while fixing m. The method is sufficiently precise in the sense that the maximum relative error is 3–5 machine epsilons at most. Thanks to the simplicity of the half argument formulas, the new procedure is significantly faster than the existing procedures. For example, it runs 20–60% faster than Bulirsch’ function, el1, and 1.9–2.2 times faster than the method using Carlson’s function, R _F .     

Restricted generalized Nash equilibria and controlled penalty algorithm

The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem, in which each player’s strategy set may depend on the rival players’ strategies. The GNEP has recently drawn much attention because of its capability of modeling a number of interesting conflict situations in, for example, an electricity market and an international pollution control. However, a GNEP usually has multiple or even infinitely many solutions, and it is not a trivial matter to choose a meaningful solution from those equilibria. The purpose of this paper is two-fold. First we present an incremental penalty method for the broad class of GNEPs and show that it can find a GNE under suitable conditions. Next, we formally define the restricted GNE for the GNEPs with shared constraints and propose a controlled penalty method, which includes the incremental penalty method as a subprocedure, to compute a restricted GNE. Numerical examples are provided to illustrate the proposed approach.     

Synthesis of 2-alkylidenetetrahydrofurans by Ru-catalyzed regio- and stereoselective codimerization of dihydrofurans with alpha,beta-unsaturated esters

2-(1-Alkoxycarbonyl)alkylidenetetrahydrofurans were readily synthesized by the codimerization of 2,3- or 2,5-dihydrofurans with alpha,beta-unsaturated esters using a zerovalent Ru catalyst, Ru(cod)(cot), with high regio- and stereoselectivity.     

Intramolecular iodoetherification of ene or diene ketals: facile synthesis of spiroketals

A novel and rapid approach to chiral mono- or di-substituted spiroketals based on remote asymmetric induction by intramolecular iodoetherification of ene or diene ketals has been developed. This strategy concisely offers 5,5- and 5,6-spiroketals including the natural insect pheromone of the wasp.     

Anionic ring-opening polymerization behavior of trans-cyclohexene carbonate using metal tert-butoxides: Construction of living anionic ring-opening polymerization by lithium tert-butoxide

Anionic ring-opening polymerization (ROP) behavior of trans-cyclohexene carbonate (CHC) using metal alkoxides as initiators was investigated. As a result, lithium tert-butoxide-initiated ROP of CHC with a high-monomer concentration (10 M) at low temperature (−15 to −10°C) proceeded to afford a poly(trans-cyclohexene carbonate) (PCHC) without undesired side reactions such as mainly backbiting. The suppression of side reactions enables the control of the molecular weight (M_n = 2400–6100) of PCHC with low molar-mass dispersity values (M_w/M_n = 1.16–1.22). Furthermore, by increasing the feed ratio of the monomer to the initiator, the molecular weight increases proportionally, indicating a controllable polymerization. The results of a matrix-assisted laser desorption/ionization time-of-flight mass spectrometry analysis, a kinetic study, and a chain extension experiment suggested a living nature of this ROP using lithium tert-butoxide.     

Significant Effect of the Flexibility of Bridging Alkyl Chains on the Proximity of Stacked Porphyrin and Phthalocyanine Conjugated with a Fourfold Rotaxane Linkage

Spatial distance is an important factor in controlling the functional interactions between molecular units in a conjugate; therefore, the bridging unit has been closely examined. Here, we examined the effect of the flexibility of bridging alkyl chains on the proximity of stacked porphyrin and phthalocyanine conjugated with a fourfold rotaxane linkage. We found that closely stacking two π systems requires bridging alkyl chains above a certain length, and the shorter bridges hinder stacking because of their lower flexibility. The stacking distance between porphyrin and phthalocyanine in the conjugate with decyl (C₁₀) chains was estimated to be 4.03 Å and showed a unique physical character arising from short-distance interactions. The longer alkyl chains minimized steric restriction inside the fourfold rotaxane and allowed efficient communication between the porphyrin and phthalocyanine units. This is due to the flexibility of the side chains.