Characterization of intermediate values of the triangle inequality II

In [Mineno K., Nakamura Y., Ohwada T., Characterization of the intermediate values of the triangle inequality, Math. Inequal. Appl., 2012, 15(4), 1019–1035] there was established a norm inequality which characterizes all intermediate values of the triangle inequality, i.e. C _n that satisfy 0 ≤ C _n ≤ Σ _j=1 ⁿ ‖x _j ‖ ? ‖Σ _j=1 ⁿ x _j ‖, x ₁,...,x _n ∈ X. Here we study when this norm inequality attains equality in strictly convex Banach spaces.     

Numerical analysis of thermal lens effect for sensitive detection on microchips

Thermal lens microscope (TLM) is a sensitive detection method for nonfluorescent molecules and widely applied to detection in a capillary or on a microchip. In this paper, we developed a flexible design tool for TLM systems to meet various applications utilizing a microspace. The TL effect was modeled, including signal processing, and calculated by combining fluidic dynamics and wave optics software. The coincidence of the calculations and experiments was investigated by measuring the effects of optical path length or focus positions of the excitation beams on TL signals which are quite difficult to calculate by a conventional method. Good agreement was shown and the applicability of the TLM design tool was verified.     

Circular dichroism thermal lens microscope in the UV wavelength region (UV-CD-TLM) for chiral analysis on a microchip

We have developed a circular-dichroism thermal lens microscope for UV wavelengths (UV-CD-TLM), for the first time, to realize sensitive chiral analysis on a microchip. Quasi-continuous-wave phase modulation of a pulsed UV laser was used to generate left-circularly polarized light and right-circularly polarized light and to detect the generated TL signal amplitude and phase with a lock-in amplifier. The amplitude and phase were used to determine the concentration and chirality, respectively, of a sample. The basic principle of UV-CD-TLM for chiral analysis on a microchip was verified by measuring aqueous solutions of optically active camphorsulfonic acids (CSA). Lower limits of detection (LOD) were calculated at S/N = 2 and were 8.7 × 10⁻⁴ mol L⁻¹ (ΔA = 5.2 × 10⁻⁶ Abs.) for (+)-CSA and 8.4 × 10⁻⁴ mol L⁻¹ (ΔA = 5.0 × 10⁻⁶ Abs.) for (−)-CSA. In terms of number of molecules, LODs for UV-CD-TLM were calculated to be 8.7 fmol and 8.4 fmol, respectively. This is at least three orders of magnitude lower than previously obtained. The applicability of UV-CD-TLM for chiral analysis on a microchip was verified. Figure Sensitive chiral analysis by thermal lens microscope (TLM)     

General entry to asymmetric one-pot [N + 2 + N] cyclization for the synthesis of three- to seven-membered azacycloalkanes

Enantio- and diastereoselective one-pot synthesis of three- to seven-membered cis-azaheterocycles was achieved using a triggered asymmetric conjugate addition reaction of lithium amide with an enoate, followed by alkylation of the resulting lithium enolate with α,ω-dihaloalkane and N-alkylation. Isomerization of cis-azaheterocycles with a base yielded the trans-product, constituting a one-pot synthesis of cis-azacycles and a two-step synthesis of trans-azacycles. The four-step asymmetric synthesis of nemonapride highlights the general utility of the method.     

Micropatterning of biomolecules on a glass substrate in fused silica microchannels by using photolabile linker-based surface activation

Platinum nanoparticles were electrodeposited onto a film of dihexadecyl hydrogen phosphate deposited on a glassy carbon electrode (GCE) and modified with dispersed acetylene black. Scanning electron microscopy and electrochemical impedance spectroscopy revealed that this nanocomposite has a uniform nanostructure and a large surface area that enables fast electron-transfer kinetics. The modified GCE showed high electrocatalytic activity for the oxidation of nitric oxide (NO). Under optimal conditions, the oxidation peak current of nitric oxide is linearly related to the concentration of NO in the concentration range between 0.18 and 120?μM, and the detection limit is as low as 50?nM (at an S/N of 3). The modified electrode was successfully applied to sensing of NO as released from rat liver.

Microchip-based cellular biochemical systems for practical applications and fundamental research: from microfluidics to nanofluidics

By combining cell technology and microchip technology, innovative cellular biochemical tools can be created from the microscale to the nanoscale for both practical applications and fundamental research. On the microscale level, novel practical applications taking advantage of the unique capabilities of microfluidics have been accelerated in clinical diagnosis, food safety, environmental monitoring, and drug discovery. On the other hand, one important trend of this field is further downscaling of feature size to the 10¹–10³ nm scale, which we call extended-nano space. Extended-nano space technology is leading to the creation of innovative nanofluidic cellular and biochemical tools for analysis of single cells at the single-molecule level. As a pioneering group in this field, we focus not only on the development of practical applications of cellular microchip devices but also on fundamental research to initiate new possibilities in the field. In this paper, we review our recent progress on tissue reconstruction, routine cell-based assays on microchip systems, and preliminary fundamental method for single-cell analysis at the single-molecule level with integration of the burgeoning technologies of extended-nano space.     

Determination of the absolute structure of (+)-akaterpin

We describe the total synthesis and structural determination of (+)-akaterpin (1), an inhibitor of phosphatidylinositol-specific phospholipase C (PI-PLC). The key features of the synthetic strategy include the resolution of β,γ-unsaturated ketone (±)-2a with chiral sulfoximine 6. The absolute stereochemistry was determined by comparison of the specific optical rotation data of (+)-1 and (-)-1 with that of natural akaterpin.     

Dual of two dimensional Lorentz sequence spaces

In [M. Kato and L. Maligranda, On James and Jordan–von Neumann constants of Lorentz sequence spaces, J. Math. Anal. Appl. 258 (2001) 457–465], it is an open problem to compute the James constant of the dual space of two dimensional Lorentz sequence space d⁽²⁾(w,q). In this paper, we shall determine the dual norm of d⁽²⁾(w,q) and completely compute the James constant of d⁽²⁾(w,q).     

A symmetric oxyselenenylation of simple olefins using optically active selenobinaphthyls

Asymmetric trans-addition reactions of simple olefins have been performed by using optically active 2-selenobinaphthyls 1 , 2a–g. Introduction of an amide group at the 2′-position in the binaphthyl skeleton enhances considerably the diastereomeric excess (de) of the asymmetric methoxyselenenylation. In the case of trans-olefins, introduction of another chiral center in the amide group further enhances the de due to double stereodifferentiation between the (R)-binaphthyl skeleton and the chiral amide group introduced at the 2′-position in the binaphthyl skeleton. The use of chiral nucleophiles is also effective to enhance the de for symmetrical cis-olefins.