The stability of generalized Volterra equations

In this paper, a particular type of a system of generalized Volterra equations [1], whose solutions are assured to be nonnegative for arbitrary nonnegative initial values, is considered. The extended stability theorem of LaSalle is used for deriving conditions for a nonnegative equilibrium point to be stable with respect to a certain subset of the Euclidean space. The obtained stability theorem has a close relation with Lyapunov's stability condition for linear systems with constant coefficients and is generally less restrictive than conditions known so far.     

Preparation of highly deuterated zeaxanthin, lycopene, and β-carotene from fully deuterated mevalonate using engineered Escherichia coli

Carotenoids are important natural pigments produced by various microorganisms and plants. Specific deuterium-labeling of these compounds is invaluable in biochemical and physiochemical research. In this paper, preparation of highly deuterated zeaxanthin, lycopene, and β-carotene using engineered Escherichia coli with fully deuterated mevalonate is described. Also described are physico-chemical properties of the obtained deuterated carotenoids.     

Asymmetric synthesis of optically pure (R)(−)-2-acetyl-5,8-dimethoxy-1,2,3,4-tetrahydro-2-naphthol,a key intermediate for optically active anthracyclinone synthesis

Asymmetric reduction of 2-acetyl-5,8-dimethoxy-3,4-dihydronaphthalene(3) with lithium aluminum hydride partially decomposed with (?)-N-methylephedrine and N-ethylaniline was found to give the optically active allylic alcohol((?)-4) in 92% optical yield. Optically pure (?)-4 obtained in 87% yield based on 3 by recrystallization, was elaborated to the title compound((R)(?)-1) according to the reaction scheme exploited in the preceding paper.     

Oligomeric polymer surfactant driven self-assembly of phenylene-bridged mesoporous materials and their physicochemical properties

The detailed synthesis of highly hydrophobic average pore benzene-bridged hybrid mesoporous silicas under an acidic medium is described. With the use of a 1,4-bis(triethoxysilane)benzene silsesquioxane precursor and biodegradable alkyl polyoxyethylene (Brij-56 or Brij-76) nonionic surfactant oligomers as supramolecular templates, no molecular scale periodicity was observed. The well-defined mesoporous materials could be synthesized with two-dimensional hexagonal (p6mm) symmetries. The textural and surface properties (adsorption isotherms of water and benzene vapors) were estimated and were compared to the analogous benzene-bridged mesoporous silica with molecular scale periodicity which was prepared using cationic surfactant under basic conditions. Different textural properties resulted for the two kinds of materials and revealed some important insights regarding the structure and nature of the materials.     

Cyclobutane ring formation by triflic imide catalyzed [2+2]-cycloaddition of allylsilanes

Cyclobutane forming [2+2]-cycloaddition reactions of allylsilane with electron-deficient olefin is promoted by triflic imide (Tf₂NH). Triflic imide is converted in situ to silyl triflic imide (R₃SiNTf₂), which serves as the actual catalyst for this process. When these reactions take place at higher than ambient temperatures, thermodynamically more stable anti-cyclobutanes are generated preferentially by equilibration of the initially formed adducts via retro [2+2]-cycloaddition.     

Synthesis of vicinal diols from various arenes with a heterocyclic, amino or carboxyl group by using recombinant Escherichia coli cells expressing evolved biphenyl dioxygenase and dihydrodiol dehydrogenase genes

Various aromatic molecules, in which heterocycles are linked with a phenyl or benzyl group, were converted to their respective 2,3-diols (catechols) in the benzene ring by growing cell reactions using recombinant Escherichia coli, which expressed the evolved biphenyl dioxygenase [bphA (2072)] genes and the subsequent bacterial dihydrodiol dehydrogenase (bphB) gene. These vicinal diol products showed strong in vitro inhibitory activity against the lipid peroxidation induced by free radicals and strong scavenging activity towards DPPH radicals. The vicinal diols were also synthesized from ionized monocyclic aromatics incorporating an amino or carboxyl group.     

Production of ultrafine particles of high-temperature tetragonal WO<Subscript>3</Subscript> by dc arc discharge in Ar–O<Subscript>2</Subscript> gases

Ultrafine particles of WO₃ are successfully produced by dc arc discharge in Ar-O₂ gases. Particle sizes are distributed from 10 nm to 1 m depending on production conditions: gas pressure, collection position and discharge current. Observations of the cooled particles by electron microscopy indicate that the WO₃ particles are tetragonal, a phase that is usually only stable above 725 °C. The octahedral crystals are bounded by eight {1 0 1} faces and occasionally truncated by {1 0 0} and/or {0 0 1} faces. This method of producing WO₃ by dc arc discharge therefore affords a high-temperature phase that is preserved upon cooling to room temperature.