The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity

For nonlinear Schrödinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating procedure, the argument is simplified and some of technical assumption of the nonlinearity to derive the conservation law and time global solutions, is removed.     

Where is the Oxygen? Structural Analysis of α‐Humulene Oxidation Products by the Crystalline Sponge Method

Crystal structures of α‐humulene, a cyclic sesquiterpene, and its oxidized subproducts, were analyzed by the crystalline sponge method. Regio‐ and stereochemistry, including absolute configuration when a chiral oxidant was applied, and the stable conformations of all the scaffold‐related compounds were successfully determined for samples on a 5–50 μg scale.     

A Tray‐Shaped,PdII‐Clipped Au3 Complex as a Scaffold for the Modular Assembly of [3×n] Au Ion Clusters

A tray‐shaped Pd^II₃Au^I₃ complex ( 1 ) is prepared from 3,5‐bis(3‐pyridyl)pyrazole by means of tricyclization with Au^I followed by Pd^II clipping. Tray 1 is an efficient scaffold for the modular assembly of [3×n] Au^I clusters. Treatment of 1 with the Au^I₃ tricyclic guest 2 in H₂O/CH₃CN (7:3) or H₂O results in the selective formation of a [3×2] cluster ( 1 ⋅ 2 ) or a [3×3] cluster ( 1 ⋅ 2 ⋅ 1 ), respectively. Upon subsequent addition of Ag^I ions, these complexes are converted to an unprecedented Au₃–Au₃–Ag–Au₃–Au₃ metal ion cluster.     

Neomacrophorin I,II, and III,novel drimenyl cyclohexanes with hydroxylated butanoates from Trichoderma sp. 1212-03

Neomacrophorins I (1), II (2), and III (3) were isolated from the culture broth of Trichoderma sp. 1212-03, which was collected at Shirakami Mountainous area in Japan. Structural analyses disclosed that these resemble known macrophorins but possess axial-hydroxy group at C3 as well as different side chains at C7′. These are diastereomeric forms of macrophorins for 5′,6′-epoxide functionality. The NMR analyses suggested their relative configurational relationship between the C1–C15 drimene and C1′–C7′ epoxyquinone moieties. ECD spectral discussions verified them particularly for C5′,C6′-epoxyquinone (1), C5′,C6′-epoxysemiquinone (2 and 3), and 2″,3″-dihydroxybutanoate moiety in 1 and 2. The configuration of C3″-stereocenter of 3 was determined by chiral GC–MS after converting into methyl (S)-3″-hydroxybutanoate by basic of 3 methanolysis. Biological assays disclosed that 1 induces hyphal branching of Cochliobolus miyabeanus as well as cytotoxicity against human colorectal cancer COLO 201.     

Synthesis,Crystal Packing,and Ambipolar Carrier Transport Property of Twisted Dibenzo[g,p]chrysenes

A versatile method for the synthesis of dibenzo[g,p]chrysene (DBC) derivatives based on regio‐ and stereoselective stannyllithiation to diarylacetylenes is described. This method affords a variety of DBCs possessing both electron‐donating and electron‐withdrawing functional groups. These twisted molecules take brickwork packing structures in single crystals. Thus, ambipolar carrier transport properties with mobility values of up to 10^?3 cm² V^?1 s^?1 in the amorphous state were achieved. Functional groups on DBC frameworks are considered to increase carrier mobility through the enhancement of intermolecular interactions in the brickwork packing structures.     

Proton Conduction at High Temperature in High-Symmetry Hydrogen-Bonded Molecular Crystals of RuIII Complexes with Six Imidazole-Imidazolate Ligands

A new H-bonded crystal [Ru^III(Him)₃(Im)₃] with three imidazole (Him) and three imidazolate (Im⁻) groups was prepared to obtain a higher-temperature proton conductor than a Nafion membrane with water driving. The crystal is constructed by complementary N−H⋅⋅⋅N H-bonds between the Ru^III complexes and has a rare Icy-c* cubic network topology with a twofold interpenetration without crystal anisotropy. The crystals show a proton conductivity of 3.08×10⁻⁵ S cm⁻¹ at 450 K and a faster conductivity than those formed by only HIms. The high proton conductivity is attributed to not only molecular rotations and hopping motions of HIm frameworks that are activated at ∼113 K, but also isotropic whole-molecule rotation of [Ru^III(Him)₃(Im)₃] at temperatures greater than 420 K. The latter rotation was confirmed by solid-state ²H NMR spectroscopy; probable proton conduction routes were predicted and theoretically considered.     

Novel Method for the Fabrication of a Charge‐Transfer Complex Crystal by Photoirradiation

A novel method for the fabrication of a charge‐transfer complex crystal was developed. Photoirradiation of a solution of TPP[Co(tbp)(CN)₂] and TPP[Co(Pc)(CN)₂] (tbp=tetrabenzoporphyrin, Pc=phthalocyanine, TPP=tetraphenylphosphonium) gave a molecular conducting crystal of a charge‐transfer complex TPP[Co(tbp)(CN)₂]₂, which was produced by the process in which the photoexcited electron in tbp was transferred from the LUMO of tbp to that of Pc.     

Formation of One‐Dimensional Helical Columns and Excimerlike Excited States by Racemic Quinoxaline‐Fused [7]Carbohelicenes in the Crystal

A series of quinoxaline‐fused [7]carbohelicenes (HeQu derivatives) was designed and synthesized to evaluate their structural and photophysical properties in the crystal state. The quinoxaline units were expected to enhance the light‐emitting properties and to control the packing structures in the crystal. The electrochemical and spectroscopic properties and excited‐state dynamics of these compounds were investigated in detail. The first oxidation potentials of HeQu derivatives are approximately the same as that of unsubstituted reference [7]carbohelicene (Heli), whereas their first reduction potentials are shifted to the positive by about 0.7 V. The steady‐state absorption, fluorescence, and circular dichroism spectra also became redshifted compared to those of Heli. The molecular orbitals and energy levels of the HOMO and LUMO states, calculated by DFT methods, support these trends. Moreover, the absolute fluorescence quantum yields of HeQu derivatives are about four times larger than that of Heli. The structural properties of the aggregated states were analyzed by single‐crystal analysis. Introduction of appropriate substituents (i.e., 4‐methoxyphenyl) in the HeQu unit enabled the construction of one‐dimensional helical columns of racemic HeQu derivatives in the crystal state. Helix formation is based on intracolumn π‐stacking between two neighboring [7]carbohelicenes and intercolumn CH ??? N interaction between a nitrogen atom of a quinoxaline unit and a hydrogen atom of a helicene unit. The time‐resolved fluorescence spectra of single crystals clearly showed an excimerlike delocalized excited state owing to the short distance between neighboring [7]carbohelicene units.     

Assembly of Na3V2(PO4)3 Nanoparticles Confined in a One‐Dimensional Carbon Sheath for Enhanced Sodium‐Ion Cathode Properties

Structural and morphological control is an effective approach for improvement of electrochemical properties in rechargeable batteries. One‐dimensionally assembled structure composed of NASICON‐type Na₃V₂(PO₄)₃ nanoparticles were fabricated through an electrospinning method to meet the requirements for the development of efficient electrode materials in Na‐ion batteries. High‐temperature treatment of electrospun precursor fibers under an argon flow provides a nonwoven fabric of nanowires comprising crystallographically oriented nanoparticles of NASICON‐type Na₃V₂(PO₄)₃ within a carbon sheath. The mesostructure comprising NASICON‐type Na₃V₂(PO₄)₃ and carbon give a short sodium‐ion transport pass and an efficient electron conduction pass. Electrochemical properties of NASICON‐type Na₃V₂(PO₄)₃ are improved on the basis of one‐dimensional nanostructures designed in the present study.