Synthesis and Self‐Assembly of Cyclic 2,7‐Anthrylene Ethynylene 1,3‐Phenylene Ethynylene Trimer with a Planar Conformation

Cyclic arylene ethynylene hexamer 1 , composed of alternating 2,7‐anthrylene ethynylene units and meta‐phenylene ethynylene units, was synthesized. It shows C₃ symmetry and possesses a flat and rigid conformation with a large equilateral triangle‐like cavity. Macrocycle 1 self‐associates through π–π stacking interactions between the anthracene‐containing macrocyclic aromatic cores with indefinite‐association constant K_E=6980 m ^?1 in CDCl₃ at 303 K. Macrocycle 1 also self‐assembles into π‐stacked nanofibers in the drop‐cast film.     

Synthesis of thermoplastic curdlan alkyl carbamates having hydrogen bonding ability

Rigid and little moldable curdlan, a linear β-1,3-glucan having intra- and interchain hydrogen bonds, was reacted with several alkyl isocyanates, which gave thermoplastic curdlan alkyl carbamates (CrdC) with degree of substitution about 2. The alkyl carbamation at hydroxy groups in the glucan skeleton effectively broke the interchain hydrogen bonds of curdlan and increased flexibility of CrdC, while the newly formed carbamate moieties could moderately keep the hydrogen bonding ability in CrdC. Elongating the alkyl groups in the carbamate side chains increased solubility in organic solvents and thermoplasticity of CrdC, which enabled to make homogeneous and free-standing films by both methods of solution-casting and hot-pressing.     

Sharp Morawetz estimates

We prove sharp Morawetz estimates — global in time with a singular weight in the spatial variables — for the linear wave, Klein-Gordon, and Schrödinger equations, for which we can characterise the maximisers. We also prove refined inequalities with respect to the angular integrability.     

About the Connes embedding conjecture

In his celebrated paper in 1976, A. Connes casually remarked that any finite von Neumann algebra ought to be embedded into an ultraproduct of matrix algebras, which is now known as the Connes embedding conjecture or problem. This conjecture became one of the central open problems in the field of operator algebras since E. Kirchberg’s seminal work in 1993 that proves it is equivalent to a variety of other seemingly totally unrelated but important conjectures in the field. Since then, many more equivalents of the conjecture have been found, also in some other branches of mathematics such as noncommutative real algebraic geometry and quantum information theory. In this note, we present a survey of this conjecture with a focus on the algebraic aspects of it.     

Finite Time Extinction for Nonlinear Schrödinger Equation in 1D and 2D

We consider a nonlinear Schrödinger equation with power nonlinearity, either on a compact manifold without boundary, or on the whole space in the presence of harmonic confinement, in space dimension one and two. Up to introducing an extra superlinear damping to prevent finite time blow up, we show that the presence of a sublinear damping always leads to finite time extinction of the solution in 1D, and that the same phenomenon is present in the case of small mass initial data in 2D.     

Efficient transformation of 7,14-dihydroxy-ent-kaurenes to novel ent-abietanes having cis-fused α-methylene γ-lactones under Mitsunobu reaction conditions and their cytotoxicities

Transformation of plant-origin 7,14-dihydroxy-ent-kaurenes to ent-abietanes having a cis-fused α-methylene γ-lactones was accomplished efficiently under the Mitsunobu reaction conditions. The yields of the desired products were apparently influenced by the steric hindrance at C-1. The cytotoxic activity on P388 murine leukemia cells of the ent-abietanes having cis-fused α-methylene γ-lactones produced were assayed.     

Effect of temperature and concentration of solution in chemical treatment for MgB2 powder on the Jc–B property of ex situ processed MgB2 superconducting tapes

MgB₂ tapes were fabricated through an ex situ process in a powder-in-tube (PIT) technique using powders treated at elevated temperatures in benzene solutions of benzoic acid with various concentrations. The amount of carbon substitution in MgB₂ in heat-treated tapes with treatment at the boiling points (BPs) of the solutions is smaller than that at room temperature (RT). This carbon substitution improves the J_c property in the high-field region. For RT treatment, the J_c property is improved with increasing the solution concentration. In contrast, the J_c property is deteriorated with increasing the concentration for BP treatment. On the other hand, treatment with pure solvent does not bring about the J_c enhancement and carbon substitution at all at both RT and the BPs. This suggests that acidity essential for the dissolution of MgO layers attached to the surface of MgB₂ is required for carbon substitution. The BP treatment enhances the acting of the acidity and possibly inflicts damage on MgB₂ itself.