Rotating Navier-Stokes Equations in $${\mathbb R}^{3}_{+}$$ with Initial Data Nondecreasing at Infinity: The Ekman Boundary Layer Problem

We prove time local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary solution called the Ekman spiral. We choose initial data in the vector-valued homogeneous Besov space for 2 <  p <  ∞. Here the L ^p -integrability is imposed in the normal direction, while we may have no decay in tangential components, since the Besov space contains nondecaying functions such as almost periodic functions. A crucial ingredient is theory for vector-valued homogeneous Besov spaces. For instance we provide and apply an operator-valued bounded H ^∞-calculus for the Laplacian in for a general Banach space .     

Spectrophotometric determination of titanium with o-carboxyphenylfluorone in cationic micellar media, and its equilibrium and kinetic studies

Spectrophotometric determination of titanium(IV) was accomplished with o-carboxyphenylfluorone (OCPF) in the presence of hexadecyltrimethyl ammonium chloride (HTAC) under strongly acidic media. In the determination of titanium(IV), Beer's law was obeyed in the range of 24-340 ng mL⁻¹ with an effective molar absorption coefficient (at 530 nm) and relative standard deviation of 2.24 × 10⁵ dm³ mol⁻¹ cm⁻¹ and 0.64% (n = 8), respectively. The severe interference of iron ions was easily eliminated by the addition of ethylenediaminetetraacetic acid (EDTA); the effects of other foreign substances were low. Equilibrium and kinetic studies under analytical conditions were investigated to quantitatively evaluate the reaction mechanism. The obtained orange complex is considered to be Ti(OCPF)₄. Its stability log K_f and rate constant K_obs are 16.88 and 1.65 × 10⁻² s⁻¹, respectively. It is suggested that the color of the complex is related to the species of OCPF in the solution.     

An LC method for quantifying bepridil in human plasma using 1-naphthol as the internal standard

A modified method for the quantitative determination of bepridil hydrochloride in human plasma is described. This method is unrelated to chemical methods currently in use. The mobile phase is 50 mM phosphate buffer (pH3.0)-methanol-acetonitrile-triethylamine (57:3:40:1, v/v), and the samples are fractionated on a C8-3 column (150 × 4.6 mm, 5 μm) using a flow rate of 0.9 mL/min. Bepridil was detected by UV spectroscopy at 254 nm. The retention times of bepridil and 1-naphthol were 12.6 min and 7.5 min, respectively; there was no interference originating from human plasma. We confirmed that the bepridil and 1-naphthol peaks were not influenced by the presence of 32 commercial medicines frequently co-administered with bepridil. Additionally, the concentration of bepridil in the plasma of five patients treated with bepridil for atrial fibrillation was measured. These samples were collected just before each dosage of bepridil. Their rhythm and rate control were well maintained. Trough concentrations ranged from 233.9 to 347.4 ng/mL, similar to previously reported values.     

Stereochemically controlled asymmetric 1,2-reduction of enones mediated by a chiral sulfoxide moiety and a lanthanum(III) ion

Enantiomerically pure (Z)-β-sulfinyl allylic alcohols of either handedness can be readily prepared from (Z)-β-sulfinyl enones using NaBH(4) or DIBAL reductants in the presence of LaCl(3) as a chelating agent. A chiral sulfoxide auxiliary induces the remote 1,2-asymmetric reduction (1,4-induction) to afford various chiral allylic alcohols in high yields with excellent stereoselectivities (up to 100% de).     

Evolving Graphs by Singular Weighted Curvature

A new notion of solutions is introduced to study degenerate nonlinear parabolic equations in one space dimension whose diffusion effect is so strong at particular slopes of the unknowns that the equation is no longer a partial differential equation. By extending the theory of viscosity solutions, a comparison principle is established. For periodic continuous initial data a unique global continuous solution (periodic in space) is constructed. The theory applies to motion of interfacial curves by crystalline energy or more generally by anisotropic interfacial energy with corners when the curves are the graphs of functions. Even if the driving force term (homogeneous in space) exists, the initial-value problem is solvable for general nonadmissible continuous (periodic) initial data. (Accepted July 5, 1996)     

Sliding acceleration of water droplets on a surface coated with fluoroalkylsilane and octadecyltrimethoxysilane

Both fluoroalkylsilane (FAS) and octadecyltrimethoxysilane (ODS) were coated on oxidized silicon wafers using soaking and CVD method. Smooth coatings with Ra values of less than 1 nm were attained. The slope of the sliding acceleration against the inverse of the droplet mass showed an inflection point. That point shifted to the direction of smaller droplets with decreasing FAS ratio to ODS. The water droplets’ length was increased when the sliding velocity was increased. Fluoroalkylsilane addition to ODS increases the interaction between water and the hydrophobic surface. Results showed that the sliding acceleration of a water droplet depends strongly on the surface ratio of these silanes.     

On a lower bound for the extinction time of surfaces moved by mean curvature

This paper considers a generalized evolution of a compact closed (hyper)-surface moved by its mean curvature. By a comparison of a shrinking ball the surface extincts in a finite time. An estimate of the extinction time from above is given by L. C. Evans and J. Spruck. In this paper we give an estimate from blow. In fact we proved that the extinction time is estimated from below by to times the square of the volume of a set enclosed by the initial surface over the initial area of the surface. The constant two is optimal.Partly supported by the Inamori Foundation     

Structure of thiotropocin,a new sulfur-containing 7-membered antibiotic

The structure of a new antibiotic thiotropocin is described.