Chiral Interlocked Corrole Dimers Directly Linked at Inner Carbon Atoms of Confused Pyrrole Rings

A facile synthetic strategy towards conformationally stable chiral chromophores based on dimeric porphyrinoids has been established. A peculiar class of face-to-face intramolecularly interlocked corrole dimers were formed by the oxidative C−C coupling linked at the inner carbon sites upon simple treatment of copper(II) ions. Their intrinsic electronic structures were modulated by the peripheral corrole ring annulations, which lead to distinct optical properties and redox profiles. The stereogenic carbon centers implemented in the confused corrole skeleton provided a rationale for designing novel chiral materials.     

Analysis method of the angiotensin-I converting enzyme inhibitory activity based on micellar electrokinetic chromatography.

A micellar electrokinetic chromatography (MEKC) method was developed for estimating the angiotensin-I converting enzyme (ACE) inhibitory activity by separating the hippuric acid liberated in the ACE reaction mixture in the presence of an inhibitor, captopril. The hippuric acid was successfully separated and detected by MEKC with a 25 mM sodium dodecyl sulfate solution in a 25 mM phosphate-50 mM borate buffer at pH 7.0; the total analysis took about 5 min. A good linear relationship was observed between the inhibitor and the peak area of hippuric acid release. No significant difference in the ACE inhibitory activity (IC50) of captopril (an antihypertensive medicine) or autolyzed-mushrooms (functional foods) was observed between the conventional method and the MEKC method. The MEKC method was found to be a useful technique for a rapid assay of the ACE inhibitory activity.     

On the Lp–Lq maximal regularity for Stokes equations with Robin boundary condition in a bounded domain

We obtain the L_p–L_q maximal regularity of the Stokes equations with Robin boundary condition in a bounded domain in ?ⁿ (n?2). The Robin condition consists of two conditions: v ? u=0 and αu+β(T(u, p)v – 〈T(u, p)v, v〉v)=h on the boundary of the domain with α, β?0 and α+β=1, where u and p denote a velocity vector and a pressure, T(u, p) the stress tensor for the Stokes flow and v the unit outer normal to the boundary of the domain. It presents the slip condition when β=1 and non‐slip one when α=1, respectively. The slip condition is appropriate for problems that involve free boundaries. Copyright © 2006 John Wiley & Sons, Ltd.     

Effect of annealing on structure and permeability of poly [(l-trimethylsilyl)-l-propyne]

The permeability of annealed poly (l-(trimethylsilyl)-l-propyne) was studied from the viewpoint of structural information obtained from x-ray diffraction and density. The sample cast from benzene solution had low density (0.82 g/cm³) and high permeability, whereas the annealed sample had a higher density (0.88 g/cm³) and permeability lower by two orders of magnitude. The smaller-angle x-ray diffraction peak for each sample, which was likely to reflect the distance between intermolecular chains, increased in intensity and shifted toward higher angle, corresponding to the change of the density with annealing. The logarithmic oxygen permeability was proportional to the density, namely the free volume fraction correlated with the diffusion coefficient and controlled by annealing and swelling by alcohols.     

Group symmetry in tensor categories and duality for orbifolds

A duality for orbifolds is presented as an application of group extensions in tensor categories.     

Uptake and excretion of total inorganic arsenic by the freshwater alga Chlorella vulgaris

Arsenic-tolerant freshwater alga Chlorella vulgaris which had been collected from an arsenicpolluted environment were tested for uptake and excretion of inorganic arsenic. Approximately half the quantity of arsenic taken up by C. vulgaris was estimated to be adhered to the extraneous coat (10 wt %) of the cell. The remainder was bioaccumulated by the cell. Both adhered and accumulated arsenic concentrations increased with an increase in arsenic(V) concentration of the aqueous phase. Arsenic(V) accumulation was affected by the growth phse: arsenic was most actively accumulated when the cell was exposed to arsenic during the early exponential phase and then accumulation decreased with an increase in culture time exposed to arsenic. The alga grew well in the modified Detmer (MD) medium containing 1 mg As(III) dm^?3 and the growth curve was approximated by a ‘logistic equation’. Arsenic(III) was accumulated up to the second day of the culture time and arsenic(III) accumulation decreased with an increase in the culture time after that. Arsenic accumulation was also largely affected by various nutrients, especially by managanese, iron and phosphorus compounds. A modified MD medium with the three nutrients was proposed for the purpose of effective removal of arsenic from the aqueous phase. Using radioactive arsenate (Na₂H⁷⁴AsO₄), the arsenic accumulated was found to be readily excreted under conditions which were unfavourable for the multiplication of C. vulgaris.     

Micro-phase sorbent extraction for trace analysis via in situ sorbent formation: application to the spectrophotometric determination of nitrite in environmental waters.

A micro-phase sorbent in situ formation from an aqueous solution was proposed for the sensitive spectrophotometric determination of nitrite in environmental waters. Nitrite in a 10 mL sample solution was converted into a cationic azo dye by the reaction with 4-trifluoromethylanilinium ion and N-1-naphthylethylenediammonium ion in an acidic medium. Addition of dodecylbenzenesulfonate ion caused the formation of a suspension of ion associate in the solution. Centrifugation of the solution led to the isolation of a liquid organic phase that extracted the azo dye at the bottom of the centrifuge tube. The volume of the new phase was ca. 5 microL. After the aqueous phase was discarded, the organic phase was dissolved with 1 mL of 2-methoxyethanol to measure the absorbance. Nitrogen as NO2- at concentrations from 1.5 to 30 microg L(-1) was determined with sufficient precision. When 0.2 mL of 2-methoxyethanol was applied to dissolve the organic phase, 0.3-4.8 microg NO2--N L(-1) was determined. The recovery tests for nitrite added to some river water and seawater were satisfactory. This method is very simple and rapid. It takes only 30 min from the dye formation to the measurement of the absorbance.     

Hamiltonian formulation of energy conservative variational equations by wavelet expansion

Hamiltonian formulation of various energy conservative evolution equations is given by means of wavelet expansion of solutions on the whole real axis R. The KdV equation, wave equations and Schrödinger equations are treated in a unified similar manner. A matrix representation of operators with respect to a nice wavelet base plays an important role in the formulation. Since the procedure is very concrete, our results can be used to efficiently compute numerical solutions of partial differential equations described in the text. In fact, we may also use symplectic schemes to solve derived Hamiltonian systems.     

Symmetry-Breaking Phenomena in an Optimization Problem for some Nonlinear Elliptic Equation

Let $\Omega$ be a bounded domain in ${\bf R^n}$ with Lipschitz boundary, $\lambda >0,$ and $1\le p \le (n+2)/(n-2)$ if $n\ge 3$ and $1\le p< +\infty$ if $n=1,2$. Let $D$ be a measurable subset of $\Omega$ which belongs to the class $ {\cal C}_{\beta}=\{D\subset \Omega \quad | \quad |D|=\beta\} $ for the prescribed $\beta\in (0, |\Omega|).$ For any $D\in{\cal C}_{\beta}$, it is well known that there exists a unique global minimizer $u\in H^1_0(\Omega)$, which we denote by $u_D$, of the functional \[\quad J_{\Omega,D}(v)=\frac12\int_{\Omega}|\nabla v|^2\, dx+\frac{\lambda}{p+1}\int_{\Omega}|v|^{p+1}\, dx -\int_{\Omega}\chi_Dv\,dx \] on $H^1_0(\Omega)$. We consider the optimization problem $ E_{\beta,\Omega}=\inf_{D\in {\cal C}_{\beta}} J_D(u_D) $ and say that a subset $D^*\in {\cal C}_{\beta}$ which attains $E_{\beta,\Omega}$ is an optimal configuration to this problem. In this paper we show the existence, uniqueness and non-uniqueness, and symmetry-preserving and symmetry-breaking phenomena of the optimal configuration $D^*$ to this optimization problem in various settings.