Regularized product expressions of higher Riemann zeta functions

As a generalization of recent work by Kurokawa, Matsuda, and Wakayama (2004) we introduce a higher Riemann zeta function for an abstract sequence. Then we explicitly determine its regularized product expression.

     

Solvent-dependent conformational switching of the aromatic N-methyl amides depending upon the acceptor properties of solvents

An aromatic N-methyl amide containing N-(2-pyridyl) and 2,6-pyridinedicarboxamide moieties switches its conformation from cis to trans depending upon the acceptor number of solvents.     

The Fixed Point of a Generalization of the Renormalization Group Maps for Self-Avoiding Paths on Gaskets

Let W(x,y) = ax ³+ bx ⁴+ f ₅ x ⁵+ f ₆ x ⁶+ (3 ax ²)² y+ g ₅ x ⁵ y + h ₃ x ³ y ² + h ₄ x ⁴ y ² + n ₃ x ³ y ³+a ₂₄ x ² y ⁴+a ₀₅ y ⁵+a ₁₅ xy ⁵+a ₀₆ y ⁶, and X = , , where the coefficients are non-negative constants, with a > 0, such that X ²(x,x ²)−Y(x,x ²) is a polynomial of x with non-negative coefficients. Examples of the 2 dimensional map Φ: (x,y)↦ (X(x,y),Y(x,y)) satisfying the conditions are the renormalization group (RG) maps (modulo change of variables) for the restricted self-avoiding paths on the 3 and 4 dimensional pre-gaskets. We prove that there exists a unique fixed point (x _f ,y _f ) of Φ in the invariant set . 2000 Mathematics Subject Classification Numbers: 82B28; 60G99; 81T17; 82C41.     

Copper‐Catalyzed Stereoselective Aminoboration of Bicyclic Alkenes

A copper‐catalyzed aminoboration of bicyclic alkenes, including oxa‐ and azabenzonorbornadienes, has been developed. With this method, amine and boron moieties are simultaneously introduced at an olefin with exo selectivity. Subsequent stereospecific transformations of the boryl group can provide oxygen‐ and nitrogen‐rich cyclic molecules with motifs that may be found in natural products or pharmaceutically active compounds. Moreover, a catalytic asymmetric variant of this transformation was realized by using a copper complex with a chiral bisphosphine ligand, namely (R,R)‐Ph‐BPE.     

Silver-catalyzed synthesis of disubstituted isoxazoles by cyclization of alkynyl oxime ethers

A facile and practical synthesis of 3,5-disubstituted isoxazoles via a silver-catalyzed cyclization and subsequent protonation of alkynyl oxime ethers has been developed. The methodology was successfully applied to the synthesis of a biologically active isoxazolecarboxylic acid.     

Photo-switchable spin-crossover iron(III) compound based on intermolecular interactions

Iron(III) spin-crossover compounds, [Fe(qnal)₂]CF₃SO₃·MeOH (1·MeOH) and [Fe(qnal)₂]CF₃SO₃·acetone (1·acetone) were prepared and their spin transition properties were characterized by magnetic susceptibility measurement, Mössbauer spectroscopy and single crystal analysis. Two iron(III) compounds exhibited abrupt spin transition with thermal hysteresis loop (T _1/2?? = 115 K and T _1/2?? = 104 K for 1·MeOH, and T _1/2?? = 133 K and T _1/2?? = 130 K for 1·acetone). Single crystal analysis revealed both of the structures in high-spin (HS) and low-spin (LS) states for 1·acetone. The difference of bond length between the HS and LS states for 1·acetone was ~0.10 Å, which was corresponding to that of typical iron(III) SCO compounds. Specially, it showed strong intermolecular interactions by ???C?? stacking formed between the neighbor complexes leading to 2-D sheet. Both 1·MeOH and 1·acetone exhibited LIESST effect when it was illuminated at 1000 nm. We also confirmed that the introduction of strong intermolecular interactions, such as ???C?? stacking, can play an important role in LIESST effect.     

Ordered nano-structure of a stamped self-organized protein layer on a HOPG surface using a HFB carrier

A groundbreaking method for ordered molecular layer preparation on a solid surface employing the drop-stamp method has been developed by us taking advantage of the characteristics of the HFB molecule as a self-organizer/adsorption carrier. It is a smart method which can be used to prepare a self-organized protein layer on a solid surface without unspecific adsorption or defects. In our previous report, we clarified the self-organizing nature of HFB-tagged protein molecules on a surface of a solution droplet. In this report, a protein layer was prepared on a HOPG surface by using the drop-stamp method with a maltose binding protein (MBP)-tagged HFBII molecule. The structure of the stamped protein layer was investigated using frequency modulation atomic force microscopy (FM-AFM) in a liquid condition. The FM-AFM images show that the drop-stamp method can prepare an ordered protein layer on a solid surface smartly. The drop-stamp method using a HFB carrier is a practical method which can be used to prepare an ordered protein layer on a solid substrate surface without unspecific adsorption defects.     

A remarkable effect of ionic liquids in transition-metal-free aerobic oxidation of benzylic alcohols

The transition-metal-free aerobic oxidation of benzylic alcohols is uniquely accelerated by a 1-butyl-3-methylimidazolium hexafluorophosphate (BMI-PF₆)/PhCF₃ biphasic system and Cs₂CO₃ to afford the corresponding ketones in good yields. The reaction system is also applicable to an oxidative cross-esterification of primary benzyl alcohols with a higher aliphatic alcohol.