The sigma function for trigonal cyclic curves

Letters in Mathematical Physics - A recent generalization of the “Kleinian sigma function” involves the choice of a point P of a Riemann surface X, namely a “pointed curve”...     

Comments on the height reducing property

A complex number α is said to satisfy the height reducing property if there is a finite subset, say F, of the ring ? of the rational integers such that ?[α] = F[α]. This property has been considered by several authors, especially in contexts related to self affine tilings and expansions of real numbers in non-integer bases. We prove that a number satisfying the height reducing property, is an algebraic number whose conjugates, over the field of the rationals, are all of modulus one, or all of modulus greater than one. Expecting the converse of the last statement is true, we show some theoretical and experimental results, which support this conjecture.     

The Spermine–Bisaryl Conjugate as a Potent Inducer of B‐ to Z‐DNA Transition

DNA containing alternating purine and pyrimidine repeats has the potential to adopt the Z‐DNA structure, one of the well‐studied structures besides A‐ and B‐DNA. Despite a number of molecular models that have been proposed to explain the mechanism for B→Z transition, there is continued discussion on the mechanism and physiological role of this transition. In this study, we have found that the bis(2‐naphthyl)‐maleimide–spermine conjugate ( 3 c ) exhibits a remarkable ability to cause the B→Z transition of d(CGCGCG)₂ at low salt concentrations. Using isothermal titration calorimetry (ITC) we show that the B→Z transition induced by 3 c is both enthalpically and entropically favorable. The ligand might effect the dehydration of B‐DNA, which leads to the B→Z transition. Interestingly, an intermediate CD between the B and Z forms was observed in the pH‐dependent transition in the presence of the ligand. The unique structure and characteristics of the ligand designed in this investigation will be useful for the study of Z‐DNA.     

A Stable Homodinuclear Biscobalt(III)–Schiff Base Complex for Catalytic Asymmetric 1,4‐Addition Reactions of β‐Keto Esters to Alkynones

Two metal cooperation : A homodinuclear Co₂–Schiff base complex Co₂(OAc)₂– 1 promoted the asymmetric 1,4‐addition of β‐keto esters to alkynones under solvent‐free conditions in air (see scheme). The reactions proceeded without air or moisture sensitivity in high yields and with high enantioselectivities (99–91 % ee) at room temperature under highly concentrated conditions (neat–20 M ) with 0.1–2.5 mol % catalyst loading.

     

Supramolecular nanostructured assemblies of different types of porphyrins with fullerene using TiO2 nanoparticles for light energy conversion

TiO₂ nanoparticles were modified with porphyrin derivatives, 5-[4-benzoic acid]-10,15,20-tris[3,5-di-tert-butylphenyl]-21H,23H-porphyrin (Ar-H₂P-COOH), 5-[4-benzoic acid]-10,20-tris[3,5-di-tert-butylphenyl]-21H,23H-porphyrin (H-H₂P-COOH), and 5,10,15,20-tetra[4-benzoic acid]-21H,23H-porphyrin (H₂P-4COOH). The porphyrin-modified TiO₂ nanoparticles were deposited on nanostructured OTE/SnO₂ electrode together with nanoclusters of fullerene (C₆₀) in acetonitrile-toluene (3/1, v/v) using an electrophoretic deposition technique to afford the porphyrin-modified TiO₂ composite electrode denoted as OTE/SnO₂/(porphyrin-modified TiO₂ nanoparticle+C₆₀)_n. The porphyrin-modified TiO₂ composite electrodes have efficient light absorbing properties in the visible region, exhibiting the photoactive response under visible light excitation using redox couple. The incident photon-to-photocurrent efficiency (IPCE) values of supramolecular nanostructured electrodes of porphyrin-modified TiO₂ nanoparticles with fullerene [OTE/SnO₂/(Ar-H₂P-COO-TiO₂+C₆₀)_n, OTE/SnO₂/(H-H₂P-COO-TiO₂+C₆₀)_n, and OTE/SnO₂/(H₂P-4COO-TiO₂+C₆₀)_n] are much larger than those of the reference systems of porphyrin-modified TiO₂ nanoparticles without C₆₀ [OTE/SnO₂/(Ar-H₂P-COO-TiO₂)_n, OTE/SnO₂/(H-H₂P-COO-TiO₂)_n, and OTE/SnO₂/(H₂P-4COO-TiO₂)_n]. In particular, the maximum IPCE value (41%) is obtained for OTE/SnO₂/(H-H₂P-COO-TiO₂+C₆₀)_n under the bias potential of 0.2 V versus SCE. This indicates that the formation of supramolecular complexes between porphyrins and fullerene on TiO₂ nanoparticles plays an important role in improvement of the light energy conversion properties.     

Design and application of linked-BINOL chiral ligands in bifunctional asymmetric catalysis

The design and application of linked-BINOLs investigated in our group are reviewed. Linked-BINOLs are a kind of semi-crown ether, thus they are flexible and applicable to metals having various ionic radii (Ga3+, Li+, Zn2+, In3+, La3+, and Y3+). The flexible linker segment, containing a coordinative heteroatom, has a crucial role in the construction of a unique and effective chiral environment that is not accessible from BINOL itself. Applications of linked-BINOLs to an epoxide opening reaction, Michael reactions, a direct aldol reaction, direct Michael reactions of a hydroxyketone, and direct Mannich-type reactions of hydroxyketones and N-acylpyrrole are described.     

Crystal structure of the pyrochlore oxide superconductor KOs2O6

We report the single-crystal X-ray analysis of the structure of the pyrochlore oxide superconductor KOs₂O₆. The structure was identified as the β-pyrochlore structure with space group and lattice constant at : the K atom is located at the 8b site, not at the 16d site as in conventional pyrochlore oxides. We found an anomalously large atomic displacement parameter at for the K cation, which suggests that the K cation weakly bound to an oversized Os₁₂O₁₈ cage exhibits intensive rattling, as recently observed for clathrate compounds. The rattling of A cations is a common feature in the series of β-pyrochlore oxide superconductors AOs₂O₆ (A=Cs, Rb and K), and is greatest for the smallest K cation.     

Switching catalytic reaction conducted in pore void of mesoporous material by redox gate control

A molecular gate attached on the pore outlet of a mesoporous material, which is opened and closed by redox system of thiol groups, effectively switched the progress of a catalytic reaction promoted by the acidic site in the pore void.