Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems

This paper is concerned with Hamiltonian systems of linear differential equations with periodic coefficients under a small perturbation. It is well known that Krein's formula determines the behavior of definite multipliers on the unit circle and is quite useful in studying the (strong) stability of Hamiltonian system. Our aim is to give a simple formula that determines the behavior of indefinite multipliers with two multiplicity, which is generic case. The result does not require analyticity and is proved directly. Applying this formula, we obtain instability criteria for solutions with periodic structure in nonlinear dissipative systems such as the Swift-Hohenberg equation and reaction-diffusion systems of activator-inhibitor type.     

Aerobic Photooxidative Synthesis of β‐Alkoxy Monohydroperoxides Using an Organo Photoredox Catalyst Controlled by a Base

Transition‐metal‐free synthesis of β‐alkoxy monohydroperoxides via aerobic photooxidation using an acridinium photocatalyst was developed. This method enables the synthesis of some novel hydroperoxides. The peroxide source is molecular oxygen, which is cost‐effective and atomically efficient. Magnesium oxide plays an important role as a base in the catalytic system.     

Detection and amplification of chirality by helical polymers

A unique feature of synthetic helical polymers for the detection and amplification of chirality is briefly described in this article. In sharp contrast to host-guest and supramolecular systems that use small synthetic receptor molecules, chirality can be significantly amplified in a helical polymer, such as poly(phenylacetylene)s with functional pendants, which enable the detection of a tiny imbalance in biologically important chiral molecules through a noncovalent bonding interaction with high cooperativity. The rational design of polymeric receptors can be possible by using chromophoric helical polymers combined with functional groups as the pendants, which target particular chiral guest molecules for developing a highly efficient chirality-sensing system. The chirality sensing of other small molecular and supramolecular systems is also briefly described for comparison.     

Hydrothermal routes to prepare nanocrystalline mesoporous SnO2 having high thermal stability

We report simple hydrothermal routes to prepare thermally stable SnO2 particles having high specific surface areas and mesoporosity. The preparation method includes a new combination of synthetic processes: hydrolysis of tin(IV) chloride at 95 degrees C in the absence of alkaline solutions (aqueous NH3 or NaOH), formation of nanocrystalline SnO2, and subsequent hydrothermal treatments at temperatures between 100 and 200 degrees C. After annealing treatments of the hydrothermally treated SnO2 particles at 400 or 500 degrees C, their crystallite sizes remained smaller than 7.7 nm and their specific surface areas were still higher than 110 m2/g, indicative of the high thermal stability against particle growth and sintering. Furthermore, mesoporosity evolved with a relatively narrow pore size distribution typically in the range of 3.0-4.3 nm. The effects of the hydrothermal treatment were explained by uniformization of the particle size that was beneficial to the suppression of particle growth.     

A facile synthetic method of α-quaternary-β,γ-unsaturated aldehydes via the stereoselective 1,4-elimination and α-regioselective Ferrier reaction

The 1,4-elimination reaction of 2-substituted-(2Z)-4-methoxy-O-alkenyl acetals with n-butyllithium is shown to afford the 2-substituted-(1Z,3E)-O-1,3-dienyl acetals in high stereoselectivities. The Ferrier reaction of the O-1,3-dienyl acetals thus obtained provides the corresponding α-quaternary-β,γ-unsaturated aldehydes in excellent yields with high α-regioselectivities.     

Control of chemical reaction involving dissolved oxygen using magnetic field gradient

This study investigated the control of dissolved oxygen concentration using magnetic forces from gradient magnetic fields near a Nd–Fe–B permanent magnet. Maximum values of magnetic flux density and the product of the magnetic flux density and its gradient were 0.63 T and 44 T²/m, respectively. The magnet was placed under a Petri dish filled with 15 ml of 10% ammonia water. The Petri dish had a copper sheet in the center. Absorbance of tetraamminecopper(II) complex produced by the reaction in oxygen was measured using a spectrophotometer to observe oxygen concentration. Results showed that the magnetic field quantitatively enhanced tetraamminecopper(II) complex production. Moreover, remarkable enhancement of the copper complex production occurred in the magnetic field at less than 2 mm depth. The calculated magnetic force increase near the magnet surface supports this result. These results show that greater enhancement of the reaction rate occurs when the stronger magnetic force acts on oxygen molecules.     

Preconcentration technique for nonylphenol using cellulose cotton with homogenous liquid–liquid extraction for liquid chromatographic analysis

A powerful preconcentration method for nonylphenol (NP) has been developed for liquid-chromatography by combining the use of cellulose cotton (solid-phase extraction) with homogeneous liquid–liquid extraction. A 100 ml of sample solution was preconcentrated using cotton, and the eluate obtained (acetonitrile; 5 ml) was further preconcentrated to 50 l within 10 min using a homogeneous liquid–liquid extraction method (volume ratio, 2,000-fold; 100 ml 50 l). The sample concentration increases from preconcentration was 1,599-fold, and NP was extracted into the sedimented phase at 80%. The proposed method was applied to high performance liquid chromatography with fluorescence detection (FL/HPLC); the lowest determination limit obtained was 1.0×10^–9 mol l^–1.     

Novel reactions of 1-benzoyl-2-methyl-3,4-dihydro-2-thianaphthalene with compounds having an acidic hydrogen

Thermal reaction of 1-benzoyl-2-methyl-3,4-dihydro-2-thianaphthalene ($\text{1}$) with acids or thiols in benzene afforded ring-opened products cleaving C₁-S bond. On the other hand, ring-expanded product was produced by the reaction of $\text{1}$ with imides or phenols.     

Double-modification of lectin using two distinct chemistries for fluorescent ratiometric sensing and imaging saccharides in test tube or in cell

The site-selective incorporation of two different fluorophores into a naturally occurring protein (lectin, a sugar-binding protein) has been successfully carried out using two distinct orthogonal chemical methods. By post-photoaffinity labeling modification, Con A, a glucose- and mannose-selective lectin, was modified with fluorescein in the proximity of the sugar binding site (Tyr100 site), and the controlled acylation reaction provided the site-selective attachment of coumarin at Lys114. In this doubly modified Con A, the fluorescein emission changed upon the binding to the corresponding sugars, such as the glucose or mannose derivatives, whereas the coumarin emission was constant. Thus, the doubly modified Con A fluorescently sensed the glucose- and mannose-rich saccharides in a ratiometric manner while retaining the natural binding selectivity and affinity, regardless of the double modification. On the benefit of the ratiometric fluorescent analysis using two distinct probes, the sugar trimming process of a glycoprotein can be precisely monitored by the engineered Con A. Furthermore, the doubly modified Con A can be used not only for the convenient fluorescent imaging of saccharides localized on a cell surface, such as the MCF-7, a breast cancer cell having rich high-mannose branch, but also for the ratiometric fluorescent sensing of the glucose concentration inside HepG2 cells. These results demonstrated that the semisynthetic lectin modified doubly by two distinct chemistries is superior to the singly modified one in function, and thus, it may be potentially useful in cell, as well as in test tube.