Mean dimension of $${\mathbb{Z}^k}$$-actions

Mean dimension is a topological invariant for dynamical systems that is meaningful for systems with infinite dimension and infinite entropy. Given a \({\mathbb{Z}^k}\)-action on a compact metric space X, we study the following three problems closely related to mean dimension.

1. (1)
   When is X isomorphic to the inverse limit of finite entropy systems?
    
2. (2)
   Suppose the topological entropy \({h_{\rm top}(X)}\) is infinite. How much topological entropy can be detected if one considers X only up to a given level of accuracy? How fast does this amount of entropy grow as the level of resolution becomes finer and finer?
    
3. (3)
   When can we embed X into the \({\mathbb{Z}^k}\)-shift on the infinite dimensional cube \({([0,1]^D)^{\mathbb{Z}^k}}\)?
    

These were investigated for \({\mathbb{Z}}\)-actions in Lindenstrauss (Inst Hautes Études Sci Publ Math 89:227–262, 1999), but the generalization to \({\mathbb{Z}^k}\) remained an open problem. When X has the marker property, in particular when X has a completely aperiodic minimal factor, we completely solve (1) and a natural interpretation of (2), and give a reasonably satisfactory answer to (3).A key ingredient is a new method to continuously partition every orbit into good pieces.     

Officinalioside,a new lignan glucoside from Borago officinalis L.

A new lignan glucoside, officinalioside (1), was isolated from n-BuOH fraction of the aerial parts of Borago officinalis L., together with four known compounds: actinidioionoside (2), roseoside (3), crotalionoside C (4) and kaempferol 3-O-β-D-galactopyranoside (5). The structure of the new compound was established by means of spectroscopic and chemical analyses. Compounds 1 and 2 showed a moderate DPPH radical scavenging activity (IC₅₀: 52.6 ± 1.70 and 41.3 ± 0.25 μM, respectively) comparable with that of the standard trolox (16.6 ± 2.2 μM) without any significant cytotoxicity towards human cell line A549 (IC₅₀ > 100 μM).     

Revised model core potentials of s-block elements

We developed new model core potentials (MCPs) for s-block elements from Na to Ra, in which the outer core (n-1)s and (n-1)p electrons are treated explicitly together with the ns electrons. By adding suitable correlating functions, we demonstrated that the present MCP basis sets show excellent performance in describing the electronic structures of atoms and molecules, bringing about accurate ionization potentials of atoms and very good spectroscopic constants of ionic and covalent molecules. The results obtained with the new MCPs are very close to the ones obtained using the all-electron correlation consistent basis sets of Dunning.     

Brønsted acid catalyzed formal insertion of isocyanides into a C-O bond of acetals

The Br?nsted acid catalyzed formal insertion of an isocyanide into a C-O bond of an acetal is described. A diverse array of acyclic and cyclic acetals can be applied to the catalytic insertion to form alpha-alkoxy imidates. Functional groups, such as nitro, cyano, halogen, ester, and alkoxy groups, are tolerant to the reaction conditions employed. The course of the reaction is highly dependent on the structure of the isocyanide. The use of an electron-deficient aryl isocyanide, such as 2c and 2d, is required to selectively obtain the monoinsertion product. When aryl isocyanides containing alkyl substituents, such as 2a and 2b, are employed, two molecules of the isocyanide are incorporated, and the double-insertion product is obtained. The reaction of tert-octyl isocyanide also induces a double incorporation, but the subsequent acid-mediated fragmentation leads to the 2-alkoxy imidoyl cyanide. The monoinsertion products, alpha-alkoxy imidates, can readily be hydrolyzed to alpha-alkoxy esters, realizing the formal carbonylation of an acetal.     

Cylindrospermopsin determination using 2-[4-(2-hydroxyethyl)-1-piperazinyl]ethanesulfonic acid (HEPES) as the internal standard

Cylindrospermopsin (CYN) was determined by liquid chromatography/electrospray ionization-mass spectrometry (LC/ESI-MS) using 2-[4-(2-hydroxyethyl)-1-piperazinyl]ethanesulfonic acid (HEPES) as the internal standard. In the selected ion monitoring of LC/ESI-MS, m/z 414 for CYN and 237 for HEPES were monitored using the negative mode; the retention times of CYN and HEPES were 12.41 and 14.21 min, respectively. CYN was determined from peak area ratios of m/z 414/237. By the treatment of an anion exchange cartridge using a buffer at pH 10.5, CYN was isolated and condensed. No interfering peak was observed. Linearity of this method was observed at the range of 0.10-31.12 ng. Total coefficients of variation were 5.1 and 2.9% at 104 and 1038 μg CYN L⁻¹. The quantitative limit at a signal-to-noise (S/N) ratio of 10 was 0.16 ng.CYN concentration in natural waters is low. CYN in waters should be condensed for determination. This method including the treatment for isolation and condensation of CYN is useful for determination of CYN in environmental and/or drinking waters.     

Comparative study of the water oxidizing reactions and the millisecond delayed chlorophyll fluorescence in photosystem II at different pH

Water splitting activity, the multiline EPR signal associated with S(2)-state of the CaMn(4)-cluster and the fast and slow phases of the induction curve of the millisecond delayed chlorophyll fluorescence from photosystem II (PSII) in the pH range of 4.5-8.5 were studied in the thylakoid membranes and purified PSII particles. It has been found that O(2) evolution and the multiline EPR signal were inhibited at acidic (pK approximately 5.3) and alkaline (pK approximately 8.1) pH values, and were maximal at pH 6.0-7.0. Our results indicate that the loss of O(2) evolution and the S(2)-state multiline EPR signal associated with the decrease of the millisecond delayed chlorophyll fluorescence only in alkaline region (pH 7.0-8.5). Possible correlations of the millisecond delayed chlorophyll fluorescence components with the donor side reactions in PSII are discussed.     

Medicinal flowers. XI. Structures of new dammarane-type triterpene diglycosides with hydroperoxide group from flower buds of Panax ginseng

Six new dammarane-type triterpene diglycosides with a hydroperoxide group, floralginsenosides A, B, C, D, E, and F, were isolated from ginseng flower, the flower buds of Panax ginseng C. A. MEYER, together with seven known dammarane-type triterpene oligoglycosides. The structures of new floralginsenosides were elucidated on the basis of chemical and physicochemical evidence.     

Metal patterning on silicon surface by site-selective electroless deposition through colloidal crystal templating

Site-selective Cu deposition on a Si substrate was achieved by a combination of colloidal crystal templating, hydrophobic treatment, and electroless plating. Uniformly sized nano/microstructures were produced on the substrate using a monolayer coating of colloidal spheres instead of a conventional resist. The Cu patterns obtained were of two different types: networklike honeycomb and isolated-island patterns with a minimum period of 200 nm. Each ordered pattern with the desired intervals was composed of clusters of Cu nanoparticles with a size range of 50-100 nm. By the present method, it is possible to control the periodicity of metal arrays by changing the diameter of the colloidal spheres used as an initial mask and to adjust the shape of the metal patterns by changing the mask structure for electroless plating.     

Unidirectional crystallization of charged colloidal silica due to the diffusion of a base

Dilute aqueous dispersions of charged colloidal silica (particle volume fraction = approximately 0.03-0.04, particle diameter = 110 nm) exhibit unidirectional crystal growth due to the diffusion of a weak base, pyridine (Py). Similar diffusion-crystallization is enabled by a salt of a weak acid and a strong base, sodium hydrogen carbonate (NaHCO3). The resulting crystals consist of columnar (or cubic) crystal grains with a maximum height of a few centimeters and a maximum width of 1 cm. The crystal growth process is attributed to a combination of (i) the diffusion of Py or NaHCO3 accompanied by a charging reaction of the silica particles and (ii) the charge-induced crystallization of the silica colloids. Theoretical growth curves based on the reaction-diffusion model for the case of Py were in good agreement with the observed curves. We also report the immobilization of the resulting large crystals by using a polymer hydrogel matrix.