An alternative theorem for set-valued maps via set relations and its application to robustness of feasible sets

Abstract

This paper contains a generalized Gordan-type alternative theorem for set-valued maps which characterizes set relations without any convexity assumptions using certain evaluation functions. As a direct consequence and as a good example, we discuss robustness (or stability) of linear programming problems for modelling error. Moreover, this theorem can be utilized for that of general vector optimization problems in special cases due to reformation of the evaluation functions.     

Two convergent routes to the left-wing fragment of ciguatoxin CTX3C using O,S-acetals as key intermediates

Ciguatoxins, principal causative toxins of ciguatera seafood poisoning, are large ladderlike polycyclic ethers. Here, we report two convergent routes to synthesis of the multiolefinic left half of ciguatoxins based on a newly developed acyl radical strategy. Remarkably, only 13 steps from the monocyclic E-ring were required to construct the left wing. [reaction: see text]     

Microstructure of Milled Mesophase Pitch-Based Carbon Fibers as an Anode Material for Li-ion Batteries

Abstract

The microstructure of milled mesophase pitch-based carbon fibers (mMPCFs) that have been developed as an anode material for Li ion batteries have been studied as a function of heat treatment temperature (HTT), by SEM, X-ray diffraction, and Raman spectroscopy. And the results obtained are compared with those by X-ray diffraction (XRD) and SEM observations, for the characterization of specific structural features of mMPCFs as a promising anode material.     

Mechanistic study of photocatalytic CO2 reduction using a Ru(ii)–Re(i) supramolecular photocatalyst

Supramolecular photocatalysts comprising [Ru(diimine)₃]²⁺ photosensitiser and fac-[Re(diimine)(CO)₃{OC(O)OC₂H₄NR₂}] catalyst units can be used to reduce CO₂ to CO with high selectivity, durability and efficiency. In the presence of triethanolamine, the Re catalyst unit efficiently takes up CO₂ to form a carbonate ester complex, and then direct photocatalytic reduction of a low concentration of CO₂, e.g., 10% CO₂, can be achieved using this type of supramolecular photocatalyst. In this work, the mechanism of the photocatalytic reduction of CO₂ was investigated applying such a supramolecular photocatalyst, RuC2Re with a carbonate ester ligand, using time-resolved visible and infrared spectroscopies and electrochemical methods. Using time-resolved spectroscopic measurements, the kinetics of the photochemical formation processes of the one-electron-reduced species RuC2(Re)−, which is an essential intermediate in the photocatalytic reaction, were clarified in detail and its electronic structure was elucidated. These studies also showed that RuC2(Re)− is stable for 10 ms in the reaction solution. Cyclic voltammograms measured at various scan rates besides temperature and kinetic analyses of RuC2(Re)− produced by steady-state irradiation indicated that the subsequent reaction of RuC2(Re)− proceeds with an observed first-order rate constant of approximately 1.8 s⁻¹ at 298 K and is a unimolecular reaction, independent of the concentrations of both CO₂ and RuC2(Re)−.

Formation processes and reactivity of an important intermediate of photocatalytic CO₂ reduction, one-electron reduced species of a Ru(ii)–Re(i) supramolecular photocatalyst with a carbonate ester ligand, were investigated in detail.     

Hetero-phase fluctuations in the pre-melting region in ionic crystals

The theory of the pre-melting phenomena in ionic crystals on the basis of the concept of the hetero phase fluctuation has been applied to KCl and AgCl crystal. The large scale molecular dynamics simulations (MD) in KCl and AgCl crystals are also performed to examine the ionic configuration in premelting region in the vicinity of their melting points. The size of the liquid like clusters are estimated by the theory and MD. The structural features of liquid like clusters are discussed by MD results using the Lindemann instability condition. The ionic conductivities in the pre-melting region are also discussed on the same theoretical basis.     

Helicity Induction and Memory of the Macromolecular Helicity in a Polyacetylene Bearing a Biphenyl Pendant

A novel, cis‐transoidal poly‐(phenylacetylene) bearing a carboxybiphenyl group as the pendant (poly‐ 1 ) was prepared by polymerization of (4′‐ethoxycarbonyl‐4‐biphenylyl)acetylene with a rhodium catalyst followed by hydrolysis of the ester groups. Upon complexation with various chiral amines and amino alcohols in dimethyl sulfoxide (DMSO), the polymer exhibited characteristic induced circular dichroism (ICD) in the UV/Vis region due to the predominantly one‐handed helix formation of the polymer backbone as well as an excess of a single‐handed, axially twisted conformation of the pendant biphenyl group. Poly‐ 1 complexed with (R)‐2‐amino‐1‐propanol showed unique time‐dependent inversion of the macromolecular helicity. Furthermore, the preferred‐handed helical conformation of poly‐ 1 induced by a chiral amine was further “memorized” after the chiral amine was replaced with achiral 2‐aminoethanol or n‐butylamine in DMSO. In sharp contrast to the previously reported memory in poly((4‐carboxyphenyl)acetylene), the present helicity memory of poly‐ 1 was accompanied by memory of the twisted biphenyl chirality in the pendants. Unprecedentedly, the helicity memory of poly‐ 1 with achiral 2‐aminoethanol was found to occur simultaneously with inversion of the axial chirality of the biphenyl groups followed by memory of the inverted biphenyl chirality, thus showing a significant change in the CD spectral pattern.