Convergence rate of solutions toward stationary solutions to the compressible Navier-Stokes equation in a half line

We study a large time behavior of a solution to the initial boundary value problem for an isentropic and compressible viscous fluid in a one-dimensional half space. The unique existence and the asymptotic stability of a stationary solution are proved by S. Kawashima, S. Nishibata and P. Zhu for an outflow problem where the fluid blows out through the boundary. The main concern of the present paper is to investigate a convergence rate of a solution toward the stationary solution. For the supersonic flow at spatial infinity, we obtain an algebraic or an exponential decay rate. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in the spatial asymptotic point, the solution converges to the corresponding stationary solution with the same rate in time as time tends to infinity. An algebraic convergence rate is also obtained for the transonic flow. These results are proved by the weighted energy method.     

Magnetic Alignment in Solid State and Temperature Hysteresis in Aqueous Tetrahydrofuran Solution for Tetrathiafulvaleno[18]annulenes

Tris(tetrathiafulvaleno)dodecadehydro[18]annulene‐hexaesters have a multi‐functionality that is very sensitive to small differences in the ester side‐chain. Self‐aggregation of the [18]annulenes in amphiphilic media such as THF–H₂O (v/v, 1:1) either produce a fibrous structure or result in temperature hysteresis of the color and ¹H NMR signals. This temperature hysteresis in solution is due to both strong self‐aggregation behavior and unique cluster formation in a binary solution of THF and water.     

Logarithmically improved regularity criteria for Navier–Stokes and related equations

We use an interpolation inequality on Besov spaces to show some logarithmically improved regularity criteria for Navier–Stokes equations, the harmonic heat flow, the Landau–Lifshitz equations, and the Landau–Lifshitz–Maxwell system. Copyright © 2009 John Wiley & Sons, Ltd.     

Modification of Tencel with Treatment of Ferric Sodium Tartrate Complex Solution I. Effect of Treatment Condition

Partial dissolution of cellulose by ferric sodium tartrate complex (FeTNa) solution was examined as refining treatment of the organic-solvent spun cellulose fiber (Tencel). The treatment conditions were discussed in terms of solvent strength, temperature, duration of the treatment, and free NaOH concentration by measuring the weight loss, crystallinity, and tenacity of the resultant yarns. For improving fibrillation resistance, the optimized solution of the FeTNa complex was composed of 1–1.5M FeCl₃ with 20% excess sodium tartrate and 1 N free NaOH, and the duration of the treatment was 60 min at 20°C. The loss in weight and tenacity could be maintained as low as 5% and 30–40%, respectively, by the optimized conditions. The resulting yarn showed significantly improved fibrillation resistance.     

Field Enhanced Sample Injection for the CE Determination of Arsenic Compounds Using Successive Multiple Ionic Polymer Layer Coated Capillaries

A capillary electrophoresis method using indirect UV detection has been applied to the determination of arsenate [As(V)], arsenite [As(III)], monomethylarsonic acid and dimethylarsinic acid. The arsenic species were successfully separated in a successive multiple ionic polymer layer coated capillary. On-line sample preconcentration of arsenic compounds were performed by employing field enhanced sample injection. A baseline separation was achieved in a basic background solution of 10 mM 2,6-pyridinedicarboxylic acid at pH 10.3. The precision of migration time was 1.2–2.4% RSD and peak height was 8.1–12.9% RSD. The limits of detection at a S/N ratio of 3 for the four arsenic compounds were found to be 20–70 ppb, which are comparable to other on-line preconcentration techniques. The enhancement factor was improved by 230–1,500-fold.     

Brownian motion under a time-dependent periodic potential proportional to the square of the position of a particle and classical fluctuation squeezing

A general stationary case of a Brownian particle with a time-dependent periodic potential proportional to the square of the position of the particle is treated. Even though the vigorous change of the time-dependent proportionality coefficient is applied, there are cases where the fluctuation of the particle decreases in contrary to our intuition, which is called classical fluctuation squeezing. We obtain time-average variances analytically for general cases of an arbitrary change in the coefficient and find conditions favorable for classical fluctuation squeezing. We introduce an asymmetric function behaves like trigonometric cosine one and consider its behavior explicitly.     

Total synthesis of 4-epi-atpenin A5 as a potent nematode complex II inhibitor

It is clear that atpenins and their analogs are useful chemical tools for elucidation of complex II functionality and that they could act as lead compounds for the development of novel helminth complex II-specific inhibitors. Recently, we discovered 4-epi-atpenin A5 as a potent nematode complex II inhibitor during our SAR studies of atpenin A5. This result led us to embark on a concise total synthesis of 4-epi-atpenin A5. In this study, we describe the total synthesis of 4-epi-atpenin A5. Importantly, this was more concise and practical synthesis than our previous total synthesis of atpenin A5.     

Analysis of amino acids and proteins using a poly(methyl methacrylate) microfluidic system

Plastic microchips are very promising analytical devices for the high-speed analysis of biological compounds. However, due to its hydrophobicity, their surface strongly interacts with nonpolar analytes or species containing hydrophobic domains, resulting in a significant uncontrolled adsorption on the channel walls. This paper describes the migration of fluorescence-labeled amino acids and proteins using the poly(methyl methacrylate) microchip. A cationic starch derivative significantly decreases the adsorption of analytes on the channel walls. The migration time of the analytes was related to their molecular weight and net charge or pI of the analytes. FITC-BSA migrated within 2 min, and the theoretical plate number of the peak reached 480,000 plates/m. Furthermore, proteins with a wide range of pI values and molecular weights migrated within 1 min using the microchip.