Teiji Takagi, Founder of the Japanese School of Modern Mathematics

This article is a brief historical report on Teiji Takagi which was prepared at the commencement of ‘Takagi Lectures’ of The Mathematical Society of Japan. The first of its two purposes is to give some informations on the circumstances of education and research of mathematics in Japan surrounding Takagi who could finally established himself as the founder of the Japanese school of modern mathematics. The other is a brief overview on Takagi’s works of mathematics some of which are still attractive to and influential on especially ambitious students of mathematics. The author hopes that careful readers may find some hints for the questions how and why Takagi was able to establish his class field theory. At the end of this article the readers will find an English translation of the preface of his book Algebraic theory of numbers (in Japanese) which is the only thing that he left for us to see his total view over class field theory after the establishment of Artin’s reciprocity law.     

Occurrence of a rare 4(9).6(6) structural topology, chirality, and weak ferromagnetism in the [NH4][MII(HCOO)3] (M = Mn, Co, Ni) frameworks

We report the synthesis, crystal structures, thermal, IR, UV-vis, and magnetic properties of a series of divalent transition metal formates, [NH4][M(HCOO)3], where M = divalent Mn, Co, or Ni. They crystallize in the hexagonal chiral space group P6(3)22. The structure consists of octahedral metal centers connected by the anti-anti formate ligands, and the ammonium cations sit in the channels. The chiral structure is a framework with the rarely observed 49.66 topology, and the chirality is derived from the handedness imposed by the formate ligands around the metals and the presence of units with only one handedness. The thermal properties are characterized by a decomposition at ca. 200 degrees C. The three compounds exhibit an antiferromagnetic ground state at 8.4, 9.8, and 29.5 K for Mn, Co, and Ni, respectively. The last two display a weak spontaneous magnetization due to a small canting of the moments below the critical temperature, and the Co compound shows a further transition at lower temperatures. The isothermal magnetizations at 2 K show spin-flop fields of 600 Oe (Mn), 14 kOe (Co), and above 50 kOe (Ni) and a small hysteresis with a remnant magnetization of 25 cm3 G mol(-1) (Co) and 50 cm3 G mol(-1) (Ni) and coercive field of 400 Oe (Co) and 830 Oe (Ni).     

Metal-organic frameworks from copper dimers with cis- and trans-1,4-cyclohexanedicarboxylate and cis,cis-1,3,5-cyclohexanetricarboxylate

Single crystals of three coordination networks containing the Cu(2)(COO)(4) core bridged by cyclohexane have been hydrothermally prepared by the reaction of 1,4-cyclohexanedicarboxylic (1,4-H(2)chdc) or 1,3,5-cyclohexanetricarboxylic (1,3,5-H(3)chtc) acid and Cu(NO(3))(2) x 6H(2)O. We report their characterizations by single-crystal X-ray structure determinations, IR spectroscopy, thermal analyses, and their magnetic properties. [Cu(2)(trans-1,4-chdc)(2)] (1) consists of 4 x 4 grids with the dimeric nodes connected by the trans-1,4-chdc, and these grids are then connected to each other by Cu-O bonds, resulting in a porous network (void volume of 130 Angstrom(3) per cell or 25%) with no solvent in its cavities. [Cu(2)(cis-1,4-chdc)(2)(H(2)O)(2)] (2) consists of two-legged ladders where the dimer nodes are bridged by pairs of cis-1,4-chdc and the water molecules cap the ends of the Cu dimers. [Cu(2)(1,3,5-Hchtc)(2)] (3) displays 4 x 4 grids, but each dimeric node is connected to its neighbors within the same grid by Cu-O bonds to form a layered network which further makes hydrogen-bond interactions with its neighbors. 2 and 3 have compact structures without any space for solvents. IR and DT-TGA confirm the absence of water in the empty channels of 1, while IR shows the presence of both protonated and deprotonated carboxyl groups for 3. The magnetic properties of all three compounds are dominated by the strong Cu-Cu antiferromagnetic interaction resulting in singlet-triplet gaps of 450-500 K.     

Synthesis of phenyl furyl sulfides and phenyl furyl ethers by nucleophilic substitution of nitrofurans

Phenyl furyl sulfides ( 3a‐j ) and phenyl furyl ethers ( 3k‐n ), which are useful in synthesizing furocondensed 3‐ring compounds, can be synthesized by nucleophilic substitution of nitrofurans having electron withdrawal groups. In our experiments using 5‐nitrofurans having electron withdrawal groups ( 2a‐i ), nucleophilic substitution readily occurred with the benzenethiolate anion of thiosalicylic acid ( 1a ), the benzenethiolate anion of thiosalicylate ester ( 1b ), and the phenylate anions of salicylate esters ( 1c‐d ) to yield phenyl furyl sulfides ( 3a‐j ) and phenyl furyl ethers ( 3k‐n ).     

Effect of intervening structure between CuO2 sheets in heavily Fe-substituted high-Tc superconductor FeSr2YCu2O6+δ

Heavily Fe-substituted Ba₂YCu₃O_6+δ-type compound FeSr₂YCu₂O_6+δ exhibits superconductivity around 60 K, only when it is annealed in N₂ and subsequently in O₂. Cationic distribution in this compound is strongly dependent on ionic radius at the Y site, and its superconducting properties are affected by the cationic distribution. In contrast, although the compound with the substitution of fluorite-type unit for Y has cationic order, it does not exhibit superconductivity. We have analyzed the crystal structure of the compounds with the substitution of other lanthanoid elements for Y and with substitution of fluorite-type unit for Y.     

Magnetic and charge transport properties of the Na-based Os oxide pyrochlore

The Na-based osmium oxide pyrochlore was synthesized for the first time by an ion-exchange method using KOs₂O₆ as a host. The composition was identified as Na_1.4Os₂O₆·H₂O by electron probe micro-analysis, thermogravimetric analysis, and structural analysis using synchrotron X-ray diffraction. Na_1.4Os₂O₆·H₂O crystallizes in a regular pyrochlore structure with some defects (space group: Fd-3m, a=10.16851(1) Å). Electrical resistivity, heat capacity, and magnetization measurements clearly showed absence of superconductivity down to 2 K, being in large contrast to what was found for the β-type pyrochlore superconductor AOs₂O₆ (A=Cs, Rb, and K). The Sommerfeld coefficient is 22 mJ K⁻² mol⁻¹, being the smallest among AOs₂O₆. A magnetic anomaly at ∼57 K and associated magneto-resistance (+3.7% at 2 K in 70 kOe) were found.     

Tuning of Electronic Properties of Single‐Walled Carbon Nanotubes under Homogenous Conditions

Reversible and non‐bonding interaction between SWNTs and ODCB is observed from the analyses of visible near‐infrared absorption data and Raman spectroscopies (see spectra). The solvent effect on SWNTs effectively controls the electronic structure of SWNTs under homogeneous conditions.