An -module structure of the cokernel of the second Johnson homomorphism

The Johnson homomorphisms τ_k (k1) give Abelian quotients of a series of certain subgroups of the mapping class group of a surface. Morita determined the rational image of the second Johnson homomorphism τ₂. In this paper, we study the structure of the torsion part of the cokernel of τ₂. First, we determine the rank of the cokernel over . Although we do it first by computing explicitly, later we improve the proof, using the Birman–Craggs homomorphism, obtained by the classical Rohlin invariant of homology 3-spheres. Since τ₂ is equivariant with respect to the action of the mapping class group, Im τ₂ is -invariant and hence acts on the cokernel. Moreover, computing this action explicitly, we show that the action reduces to that of the finite symplectic group .     

A ladder polysilane wrapped with amylose

A mixture of tricyclic ladder polysilane 1 and amylose, upon pH adjustment of aqueous media from very basic to neutral, affords a supramolecular complex in which a preferential twisted (helical) conformation is induced on the ladder polysilane to display optical activity. Under the experimental conditions used, 1 assumes a left-handed twisted structure in the left-handed helical channel of amylose.     

Spatiotemporal sub-cellular biopatterning using an AFM-assisted electrochemical system

The integration of electrochemical-based biolithography (ECBL) with an ordinary atomic force microscope (AFM) enables in situ lithography adjacent to a single, cultured cell, consequently allowing the morphological shape of the cell to be manipulated. The tip of a commercially available AFM cantilever was modified to serve as an electrode that could generate the oxidant HBrO for local, controlled etching of a cytophobic material (heparin or albumin) previously layered adjacent to a living cell. A NIH-3T3 fibroblast, initially confined to a patterned area, extended along a bioadhesive surface that had been newly exposed using the ECBL-AFM system.     

Electrochemical Condensation of Methylviologen on Specifically‐adsorbed Anion Layers

The adsorption of methylviologen dications (MV²⁺) on single‐crystalline Au electrodes in both H₂SO₄ and HClO₄ was examined. MV²⁺ strongly interacted with sulfate and bisulfate anions adsorbed on the Au(111) electrode surface in 0.05 M H₂SO₄ under a controlled potential of 1.25 V vs. the reversible hydrogen electrode (RHE). A characteristic non‐Faradaic current was observed at 1.10 V vs. RHE. When adsorption of MV²⁺ was carried out in 0.1 M HClO₄, the electrochemical response of MV²⁺ was less than that obtained in H₂SO₄. The results show that the formation of a highly ordered sulfate/bisulfate adlayer plays an important role in the formation of condensed MV²⁺ layers. Examination of polycrystalline Au and Au(100) electrodes revealed a poor electrochemical response due to the surface roughness of the Au substrate, but the electrochemical detection was applicable to polycrystalline Au electrodes. A systematic investigation of the structural dependency of viologen derivatives showed that molecular size is important for electrostatic interactions with a highly ordered sulfate/bisulfate adlayer. The findings of the present study demonstrate successful detection of MV²⁺ at a concentration of ≤1 pM with a non‐Faradaic current.     

Carbohydrate recognition of C3-symmetrical tripodal receptor-type 2,4,6-trisubstituted 1,3,5-triazine derivatives with antiviral activities

Journal of Thermal Analysis and Calorimetry - In our search for new bioactive compounds that interfere with the sugar recognition process, we have designed and synthesized C3- and Cs-symmetrical...     

An Infinite Family of Non-Invertible Surfaces in 4-Space

A proof is given that for each non-negative integer g, thereis an infinite family of knotted surfaces of genus g, none ofwhich is ambient isotopic to itself with the orientation reversed.2000 Mathematics Subject Classification 57Q45, 57R42.     

Synthesis and characterization of phthalocyanines with direct Si-Si linkages

Several cofacial phthalocyanines (Pcs) with an Si-Si linkage were obtained by one-step condensation of 1H-isoindole-1,3(2H)-diimine with hexachlorodisilane as template in quinoline. They were characterized by gel-permeation chromatography, IR, NMR spectroscopy, and mass spectrometry, and cyclic voltammetry. The results strongly suggest that we indeed obtained Pc dimers directly linked by an Si-Si bond using this novel concept of utilizing a compound/salt with an element-element bond as a template. The cofacial dimer structures are reasonably supported by X-ray absorption near-edge structure (XANES), electronic absorption and magnetic circular dichroism (MCD) spectra, and molecular orbital (MO) calculations. Interestingly, they show an electronic absorption spectrum very similar to that of silicon tetrabenztriazacorrole (SiTBC).     

Diazadibora[1.1.1.1]m,p,m,p‐cyclophanes: Ambipolar Conjugated Macrocycles with Different B–π–N Embedded Patterns

Are different B(boron)–π–N(nitrogen) embedded patterns to bring about significant different (opto)electronic properties for the same macrocyclic molecular backbone? A series of B–π–N‐embedded alternate‐meta‐para‐linked cyclophanes 1 – 3 have been prepared and characterized as a new class of ambipolar π‐conjugated B–π–N macrocycles. The answer to the opening question is yes. These macrocycles revealed the intramolecular charge transfer in the oxidized states and the intriguing photophysical proprerties in accordance with the embedded patterns, suggesting the electronic structures are tunable by introducing multiple B–π–N moieties.