Decay Structure for Symmetric Hyperbolic Systems with Non-Symmetric Relaxation and its Application

This paper is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation. When the relaxation matrix is symmetric, the dissipative structure of the systems is completely characterized by the Kawashima–Shizuta stability condition formulated in Umeda et al. (Jpn J Appl Math 1:435–457, 1984) and Shizuta and Kawashima (Hokkaido Math J 14:249–275, 1985) and we obtain the asymptotic stability result together with the explicit time-decay rate under that stability condition. However, some physical models which satisfy the stability condition have non-symmetric relaxation term (for example, the Timoshenko system and the Euler–Maxwell system). Moreover, it had been already known that the dissipative structure of such systems is weaker than the standard type and is of the regularity-loss type (see Duan in J Hyperbolic Differ Equ 8:375–413, 2011; Ide et al. in Math Models Meth Appl Sci 18:647–667, 2008; Ide and Kawashima in Math Models Meth Appl Sci 18:1001–1025, 2008; Ueda et al. in SIAM J Math Anal 2012; Ueda and Kawashima in Methods Appl Anal 2012). Therefore our purpose in this paper is to formulate a new structural condition which includes the Kawashima–Shizuta condition, and to analyze the weak dissipative structure for general systems with non-symmetric relaxation.     

An oxygen permeable membrane La0.8Sr0.2(Ga0.8Mg0.2)1 − xCrxO3 − δ for a reduced atmosphere

Mixed electron hole and oxide ion conducting perovskite-type oxides, La_0.8Sr_0.2(Ga_0.8Mg_0.2)_1 ? xCr_xO_3 ? δ (0 ≤ x ≤ 1.0)_, were prepared by solid state reaction. The phase stability and the oxygen permeation properties of the oxides were examined as a function of the content of Cr. La_0.8Sr_0.2(Ga_0.8Mg_0.2)_1 ? xCr_xO_3 ? δ has a perovskite related tetragonal phase with x = 0.1 to 0.8. The total electrical conductivity of La_0.8Sr_0.2(Ga_0.8Mg_0.2)_1 ? xCr_xO_3 ? δ increases with increasing x. The oxygen permeation flux across the La_0.8Sr_0.2(Ga_0.8Mg_0.2)_1 ? xCr_xO_3 ? δ membranes at higher temperatures increases with x up to x = 04. The maximum oxygen permeation flux of 1.6 × 10^? 7 mol^? 1 cm^? 2 at 1100 °C in a oxygen activity gradient of air/10^? 2 Pa is observed in La_0.8Sr_0.2(Ga_0.8Mg_0.2)_0.6Cr_0.4O_3 ? δ. This perovskite-type oxide is stable under an oxygen partial pressure of 7 × 10^? 10 Pa at 1000 °C.     

Crystal structures and magnetic properties of two-dimensional antiferromagnets Co1−xZnxTeMoO6

Crystal structures and magnetic properties of metal telluromolybdates Co_1−xZn_xTeMoO₆ (x=0.0, 0.1,…,0.9) are reported. All the compounds have an orthorhombic structure with space group P2₁2₁2 and a charge configuration of M²⁺Te⁴⁺Mo⁶⁺O₆. In this structure, M ions form a pseudo-two-dimensional lattice in the ab plane. Their magnetic susceptibility measurements have been performed in the temperature range between 1.8 and 300 K. The end member CoTeMoO₆ shows a magnetic transition at 24.4 K. The transition temperature for solid solutions rapidly decreases with increasing x and this transition disappears between x=0.4 and 0.5, which is corresponding to the percolation limit for the square-planer lattice. From the magnetization, specific heat, and powder neutron diffraction measurements, it is found that the magnetic transition observed in the CoTeMoO₆ is a canted antiferromagnetic ordering of Co²⁺ ions. The antiferromagnetic component of the ordered magnetic moment (3.12(3)μ_B at 10 K) is along the b-axis. In addition, there exists a small ferromagnetic component (0.28(3)μ_B) along the a-axis.     

A mild and expedient one-pot synthesis of substituted benzimidazoles in water using a phase-transfer catalyst

Abstract  1-Alkyl/phenyl-2-arylbenzimidazoles have been synthesized in very good to excellent yields by a one-pot condensation of N-alkyl/phenyl-o-phenylenediamines with aryl aldehydes in water at room temperature using cetylpyridinium bromide as a cheap and eco-friendly catalyst. Graphical abstract        

Determination of Bisphenol A in Water Using a Packed Needle Extraction Device

A fiber-packed needle extraction device was used as a novel method for the extraction of bisphenol A from water samples. A bundle of filaments having a coating of polydimethylsiloxane was packed longitudinally into the needle. Good extraction efficiency was obtained even for an extraction time of 10 min, when the water sample was pumped through the needle with a syringe pump. The needle could be used repeatedly. The preparation procedure, included a derivatization process. Under optimum conditions, use of the fiber-packed needle showed a higher extraction efficiency than conventional sample preparation methods such as liquid–liquid extraction and solid-phase extraction.     

A DFT Study on the Reaction Pathways for Carbon?Carbon Bond‐Forming Reactions between Propargylic Alcohols and Alkenes or Ketones Catalyzed by Thiolate‐Bridged Diruthenium Complexes

The reaction pathways of two types of the carbon? carbon bond‐forming reactions catalyzed by thiolate‐bridged diruthenium complexes have been investigated by density‐functional‐theory calculations. It is clarified that both carbon? carbon bond‐forming reactions proceed through a ruthenium–allenylidene complex as a common reactive intermediate. The attack of π electrons on propene or the vinyl alcohol on the ruthenium–allenylidene complex is the first step of the reaction pathways. The reaction pathways are different after the attack of nucleophiles on the ruthenium–alkynyl complex. In the reaction with propene, the carbon? carbon bond‐forming reaction proceeds through a stepwise process, whereas in the reaction with vinyl alcohol, it proceeds through a concerted process. The interactions between the ruthenium–allenylidene complex and propene or vinyl alcohol have been investigated by applying a simple way of looking at orbital interactions.     

On Lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres

The n-dimensional complex hyperquadric is a compact complex algebraic hypersurface defined by the quadratic equation in the (n+1)-dimensional complex projective space, which is isometric to the real Grassmann manifold of oriented 2-planes and is a compact Hermitian symmetric space of rank 2. In this paper, we study geometry of compact Lagrangian submanifolds in complex hyperquadrics from the viewpoint of the theory of isoparametric hypersurfaces in spheres. From this viewpoint we provide a classification theorem of compact homogeneous Lagrangian submanifolds in complex hyperquadrics by using the moment map technique. Moreover we determine the Hamiltonian stability of compact minimal Lagrangian submanifolds embedded in complex hyperquadrics which are obtained as Gauss images of isoparametric hypersurfaces in spheres with g(=  1, 2, 3) distinct principal curvatures. Dedicated to Professor Hajime Urakawa on his sixtieth birthday. H. Ma was partially supported by NSFC grant No. 10501028, SRF for ROCS, SEM and NKBRPC No. 2006CB805905. Y. Ohnita was partially supported by JSPS Grant-in-Aid for Scientific Research (A) No. 17204006.     

Wireless biosensor system for real-time cholesterol monitoring in fish “Nile tilapia”

The rapidly increasing demand for cultured fish as a food resource requires simple, effective methods for controlling fish health in culture conditions. Plasma total cholesterol levels are significantly related to fish mortality following bacterial challenge, and are thus a good indicator of the general health of fish. We developed a wireless biosensor system to continuously monitor the total cholesterol concentration in fish (Nile tilapia, Oreochromis niloticus). The biosensor was constructed with Pt-Ir wire (φ0.178 mm) as the working electrode and Ag/AgCl paste as the reference electrode. Cholesterol oxidase and cholesterol esterase were immobilized on the working electrode using glutaraldehyde. The sensor output was linear and strongly correlated with the cholesterol level (R = 0.9970) in the range of 2.65-403 mg dl⁻¹. This range covers the range of total cholesterol levels in fish. To avoid blood coagulation and proteins coalescing on the sensor, we implanted the sensor in the fluid under the scleral surface of the eyeball (EISF). The EISF is presumed to reflect the levels of most blood components and does not include the substances contained in blood that inhibit sensor measurement. Total cholesterol concentrations in blood and EISF were strongly correlated (R = 0.8818, n = 72) in the blood total cholesterol range of 74-480 mg dl⁻¹. Therefore, we used EISF as an alternative to blood and performed continuous in vivo-monitoring of the total cholesterol concentration in fish. We also investigated the application of the calibration method and wireless monitoring system. These applications enabled us to securely monitor total cholesterol levels in free-swimming fish in an aquarium for over 40 h. Thus, our newly developed sensor provided a rapid and convenient method for real-time monitoring of total cholesterol concentrations in free-swimming fish.     

Development of novel fiber-packed needle interface for off-line reversed-phase liquid chromatography–capillary gas chromatography

For two-dimensional reversed-phase liquid chromatography–gas chromatography (2D RPLC–GC), a specially-designed needle packed with a polymer-coated fibrous stationary phase was introduced as a novel interface. The bundle of synthetic fibers coated with polydimethylsiloxane (PDMS) was packed into the head section of the needle, and served as the extraction medium. Using the post-column dilution of the LC eluent by water and subsequent extraction with the needle interface, the analyte was successfully concentrated to the PDMS phase on the fibrous support in the needle. The concentrated analytes were directly injected to GC system by inserting the needle to a heated GC injector. 2D separations of aliphatic and aromatic hydrocarbons, and also kerosene-extract were performed with the off-line RPLC–GC system interfaced by the needle extractor. The results suggested that the fiber-packed needle interface could be one of the simple and effective approaches to develop an on-line coupled LC–GC system.