A variant of Shelah's characterization of Strong Chang's Conjecture

Shelah considered a certain version of Strong Chang's Conjecture which we denote , and proved that it is equivalent to several statements, including the assertion that Namba forcing is semiproper. We introduce an apparently weaker version, denoted , and prove an analogous characterization of it. In particular, is equivalent to the assertion that the the Friedman‐Krueger poset is semiproper. This strengthens and sharpens results by Cox and sheds some light on problems posed by Usuba, Torres‐Perez and Wu.     

A Theoretical study on the charge and discharge states of Na-ion battery cathode material,Na1+xFePO4F

Na₂FePO₄F is a promising cathode material for a Na-ion battery because of its high electronic capacity and good cycle performance. In this work, first principle calculations combined with cluster expansion and the Monte Carlo method have been applied to analyze the charge and discharge processes of Na₂FePO₄F by examining the voltage curve and the phase diagram. As a result of the density functional theory calculation and experimental verification with structural analysis, we found that the most stable structure of Na_1.5FePO₄F has the P2₁/b11 space group, which has not been reported to date. The estimated voltage curve has two clear plateaus caused by the two-phase structure composed of P2₁/b11 Na_1.5FePO₄F and Pbcn Na₂FePO₄F or Na₁FePO₄F and separated along the c-axis direction. The phase diagram shows the stability of the phase-separated structure. Considering that Na₂FePO₄F has diffusion paths in the a- and c-axis directions, Na₂FePO₄F has both innerphase and interphase diffusion paths. We suggest that the stable two-phase structure and the diffusion paths to both the innerphase and interphases are a key for the very clear plateau. We challenge to simulate a nonequilibrium state at high rate discharge with high temperature by introducing a coordinate-dependent chemical potential. The simulation shows agreement with the experimental discharge curve on the disappearance of the two plateaus. © 2018 Wiley Periodicals, Inc.     

A cost-scaling algorithm for minimum-cost node-capacitated multiflow problem

Mathematical Programming - Many practical integer programming problems involve variables with one or two-sided bounds. Dunkel and Schulz (A refined Gomory–Chvátal closure for polytopes...     

On the electronic structure and hydrogen evolution reaction activity of platinum group metal-based high-entropy-alloy nanoparticles

We report the synthesis of high-entropy-alloy (HEA) nanoparticles (NPs) consisting of five platinum group metals (Ru, Rh, Pd, Ir and Pt) through a facile one-pot polyol process. We investigated the electronic structure of HEA NPs using hard X-ray photoelectron spectroscopy, which is the first direct observation of the electronic structure of HEA NPs. Significantly, the HEA NPs possessed a broad valence band spectrum without any obvious peaks. This implies that the HEA NPs have random atomic configurations leading to a variety of local electronic structures. We examined the hydrogen evolution reaction (HER) and observed a remarkably high HER activity on HEA NPs. At an overpotential of 25 mV, the turnover frequencies of HEA NPs were 9.5 and 7.8 times higher than those of a commercial Pt catalyst in 0.05 M H₂SO₄ and 1.0 M KOH electrolytes, respectively. Moreover, the HEA NPs showed almost no loss during a cycling test and were much more stable than the commercial Pt catalyst. Our findings on HEA NPs may provide a new paradigm for the design of catalysts.

RuRhPdIrPt high-entropy-alloy nanoparticles with a broad and featureless valence band spectrum show high hydrogen evolution reaction activity.     

Decacyclene Radical Anions Showing Strong Low‐energy Intramolecular Absorption and Magnetic Coupling of Spins in a Hexagonal Network

Two salts of the aromatic hydrocarbon decacyclene, {cryptand[2.2.2](Cs⁺)} (decacyclene^.?) ( 1 ) and {Bu₃MeP⁺}(decacyclene^.?) ( 2 ), were obtained. In both salts, decacyclene^.? radical anions formed channels occupied by cations. However, corrugated hexagonal decacyclene^.? layers could be outlined in the crystal structure of 1 with several side‐by‐side C???C approaches. The decacyclene^.? radical anions showed strong distortion in both salts, deviating from the C₃ symmetry owing to the repulsion of closely arranged hydrogen atoms and the Jahn‐Teller effect. Radical anions showed intense unusually low energy absorption in the IR‐range, with maxima at 4800 and 6000 cm^?1. According to the carculations, these bands can originate from the SOMO‐LUMO+1 and SOMO‐LUMO+2 transitions, respectively. Radical anions exhibited a S=1/2 spin state, with an effective magnetic moment of 1.72 μ_B at 300 K. The decacyclene^.? spin antiferromagnetically coupled with a Weiss temperature of ?11 K. Spin ordering was not observed down to 1.9 K owing to spin frustration in the hexagonal decacyclene^.? layers.     

A 116-Nuclear Metallosupramolecular Cage-of-Cage Showing Multistep Single-Crystal-to-Single-Crystal Transformation

Here a unique single-crystal-to-single-crystal (SCSC) transformation of a 116-nuclear Au^I₇₂Cd^II₄₀Na^I₄ cage-of-cage ( 2 _CdNa) is reported, which was created from a trigold(I) metalloligand with d -penicillamine by way of a 9-nuclear Au^I₆Cd^II₃ cage ( 1 ). Cage-of-cage 2 _CdNa is composed of 12 cages of 1 that are linked by 4 Cd²⁺ and 4 Na⁺ ions, with its surface being covered by 12 NO₃⁻ ions to form a discrete, spherical molecule with a diameter ca. 4.7 nm. In crystal 2 _CdNa, the cage-of-cage molecules are packed in a cubic lattice with a huge cell volume of ca. 4.5×10⁵ ų_, so as to have large interstices with diameters of more than 3 nm. Upon soaking crystals 2 _CdNa in aqueous Cu(NO₃)₂, all Cd²⁺ and Na⁺ were quickly exchanged by Cu²⁺ to produce an analogous Au^I₇₂Cu^II₄₄ cage-of-cage ( 2 _Cu) in a SCSC manner. Prolonged soaking led to the SCSC transformation to another supramolecular structure ( 2′ _Cu) consisting of 152-nuclear Au^I₇₂Cu^II₈₀ cage-of-cages that are alternately H-bonded with the Au^I₇₂Cu^II₄₄ cage-of-cages. 2′ _Cu showed the accommodation of MoO₄²⁻ and the conversion of MoO₄²⁻ to β-Mo₈O₂₆⁴⁻ in the crystal, with retention of single-crystallinity.     

Alkane Shape- and Size-Recognized Selective Vapor Sorption in “Channel-Like” Crystals Based on Thiacalixarene Assemblies

Alkanes composed of C−C and C−H show a low electric polarization, and therefore, there is only very weak interaction between alkanes and adsorbents. Thus, it is difficult to separate a specific alkane from a mixture of alkanes by adsorption. Here, two activated “channel-like” crystals generated from brominated thiacalix[4]arene propyl ethers, which adopt 1,3-alternate and partial cone conformations, recognize specific alkane vapors depending on alkane-shape and -size, sorting in three-type alkane guests such as linear, branched, and cyclic alkanes. Two activated crystals, which are prepared by removal of solvent upon heating under reduced pressure, incorporate branched and/or cyclic alkane vapors by a unique “gate-opening” mechanism via a crystal transformation in the process. Linear alkane vapors do not trigger gate opening and are not taken up by the activated crystals. The shape and size molecular-recognition properties of the activated crystals promises considerable usefulness for the separation of linear, branched, and cyclic alkanes.     

Cyclization from Higher Excited States of Diarylethenes Having a Substituted Azulene Ring

The cyclization reaction of diarylethenes having an azulene ring occurs only via higher excited states. Novel diarylethenes having an azulene ring with a strong donor or acceptor were synthesized and examined in these reactions. A derivative having an electron-donating 1,3-benzodithiol-2-ylidenemethyl group at the 1-position of the azulene ring showed photochromism, whereas neither a derivative having a π-conjugated electron-donating group at the 3-position of the azulene ring nor derivatives having a π-conjugated electron-withdrawing group at the 1- or 3-position of the azulene ring showed any photochromism. The photoreactivities of these compounds were explained by calculating forces and bond orders on the excited states using density functional theory (DFT) and time-dependent (TD)-DFT.     

meso-Diazacorrphycenes: Neighboring Effect of Two Nitrogen Atoms

The neighboring effect of two adjacent heteroatoms influences the structures and properties of heterocyclic compounds. Herein, we demonstrated that the introduction of two adjacent sp² nitrogen atoms into a porphyrinic skeleton significantly enhanced its Brønsted basicity due to the repulsive interaction between two lone pairs on the nitrogen atoms. Palladium- and copper-templated ring closure of dichlorobis(dipyrrin) with hydrazine hydrate provided meso-diazacorrphycene palladium and copper complexes in good yields. The structural, magnetic, and electrochemical properties of the diazacorrphycene complexes were investigated experimentally and theoretically to elucidate the effect of the meso-nitrogen atoms.