The determinant expressions of some theta constant identities

In this paper, we derive two interesting theta constant identities by considering determinant structures. One of the two identities which we obtained is given by the Pfaffian, and the other is expressed by the resultant.     

Variable Lebesgue norm estimates for BMO functions. II

The paper concerns characterization of BMO in terms of Banach function spaces. In particular, we are interested in characterizing BMO by using the variable Lebesgue norm.     

Synthesis of All Stereoisomers of Monomeric Spectomycin A1/A2 and Evaluation of Their Protein SUMOylation-Inhibitory Activity

A synthetic methodology to access all possible stereoisomers of spectomycin A1 (SMA1) and A2 (SMA2) has been established through late-stage diversification. The key reaction for the construction of all four diastereomers is an intramolecular cyclization based on the umpolung of π-allyl palladium species with bis(pinacolato)diborane (B₂(pin)₂). Silyl group assisted direct benzylic oxidation of each isomer enabled construction of the fragile β-hydroxytetralone skeleton to provide the SMAs. The relative and absolute stereochemistry of SMA2 was also determined, and the absolute stereochemistry of SMA1 was extrapolated based on the optical rotation of SMA2. The axial chirality of SMAs is discussed based on circular dichroism spectra and DFT calculations, and it is concluded that the M isomer is predominant in solution. Biochemical assessment of all isomers in vitro revealed that the C9 hydroxyl group and dimeric structure were both important for protein SUMOylation-inhibitory activity.     

Skeletal Transformation Triggered by C−F Bond Activation after Photochemical Rearrangement of Fluorinated [7]Helicenes

Tri- and tetra-fluorinated [7]helicenes are photolabile and undergo a double fluorine atom transfer. Herein, we show that the transferred product further undergoes a skeletal transformation on silica gel. The transformation begins with activation of the allylic C−F bond on the silanol surface. Then, the resulting carbocation readily undergoes a regioselective nucleophilic aromatic substitution with water, depending on the position of the fluorine substituents. Hexafluoro-2-propanol also activated the allylic C−F bond and acted as a nucleophile. These findings support the generation of a highly reactive cationic electrophilic intermediate in the successive transformations involving fluorine atoms.     

Arylpyrrolyldiketone Boron Complexes Exhibiting Various Anion‐Binding Modes Based on Dynamic Conformation Changes

Arylpyrrolyldiketone boron complexes as anion‐responsive π‐electronic molecules were synthesized by Claisen condensations of acetylpyrrole and corresponding aryl esters. The synthesized π‐electronic molecules exhibited anion‐binding behavior with various binding modes including pyrrole‐inverted and non‐inverted [1+1]‐type anion complexes as well as [2+1]‐type complexes owing to the presence of only a single pyrrole ring. Furthermore, solid‐state ion‐pairing assemblies, comprising receptor–anion complexes and countercations, were constructed based on fairly planar [2+1]‐type complexes.     

Catalytic C−H/C−F Coupling of Azoles and Acyl Fluorides

A method for the palladium/copper-catalyzed direct acylation of azoles with acyl fluorides is described. This study reports the first examples of acyl fluorides being used as acylation reagents in transition-metal-catalyzed aromatic C−H bond functionalization reactions. Depending on the reaction temperature, decarbonylative coupling may also occur. Mechanistic studies suggest that the cleavage of the aromatic C−H bond, promoted by a copper-phosphine species, is not the rate-limiting step of this acylation.     

Evolution of long-period stacking order (LPSO) in Mg97Zn1Gd2 cast alloys viewed by HAADF-STEM multi-scale electron tomography

We have studied three-dimensional (3D) structures and growth processes of 14H-type long-period stacking order (LPSO) formed in Mg₉₇Zn₁Gd₂ cast alloys by single tilt-axis electron tomography (ET) using high-angle annular dark-field scanning transmission electron microscopy. Evolution of the solute-enriched stacking faults (SFs) and the 14H LPSO by ageing were visualised in 3D with a high spatial resolution in multi-scale fields of views from a few nanometres to ~10 μm. Lateral growth of the solute-enriched SFs and the LPSO in the (0?0?0?1)_Mg plane is notable compared to the out-of-plane growth in the [0?0?0?1]_Mg direction. The 14H LPSO grows at the cost of decomposition of the (Mg, Zn)₃Gd-type precipitates, and accompany a change of in-plane edge angles from 30 to 60°. We have updated the Time–Temperature–Transformation diagram for precipitation in Mg₉₇Zn₁Gd₂ alloys: starting temperatures of both solute-enriched SFs and LPSO formation shifted to a shorter time side than those in the previous diagram.     

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.