On singularities arising from the contraction op the minimal section of a ruled surface

We will discuss the Gorenstein property of the singularity which is blown down from the minimal section of a ruled surface in terms of the extension class. In the case that the base field has positive characteristic, we find a new example (3.4) of Gorenstein singularity in connection with Theorem B.     

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.     

Stereocontrol of diene polymers by topochemical polymerization of substituted benzyl muconates and their crystallization properties

We report the stereocontrol of diene polymers by the topochemical polymerization of alkoxy-substituted benzyl muconates in the solid state. A monomer stacking structure is controlled by the weak intermolecular interactions in the monomer crystals, depending on the structure and position of the alkoxy-substituent. The translational and alternating types of molecular stacking structures in a column provide diisotactic and disyndiotactic polymers, respectively, by the solid-state polymerization under UV and γ-ray irradiation. On the other hand, the meso and racemo structures of the resulting polymers are determined by the molecular symmetry of the used muconate monomers. The various substituted benzyl ester polymers are transformed into the same ethyl ester polymers with the four types of tacticities. The structure and crystallization behavior of the substituted benzyl ester polymers as well as the ethyl ester polymers have been revealed in detail. We clarify the effects of the tacticity on the crystallization property of the stereoregular polymuconates. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4952–4965, 2006     

Enantiomeric purity determination of malic acid in apple juices by multi-beam circular dichroism detection

A multi-beam circular dichroism (CD) detector which is easily constructed by inserting inexpensive optics into a conventional photo-diode array detector has an advantage of simultaneous detection of the absorbance and CD. The enantiomeric purity determination of malic acid in beverages was performed by this detection system. Malic acid when complexed with Cu(II) was found to have an absorbance maximum at around 750 nm. The L-malic acid-Cu(II) complex showed a positive Cotton effect in its absorbance band and its anisotropy factor (delta epsilon/epsilon) was relatively large at about 1/170. This complex was retained on a reversed-phase column with the addition of racemic 2-hydroxy-3-methylbutyric acid to the mobile phase as the ligand. A plot of the relative peak areas between the CD and the absorption (delta abs/abs) versus optical purity showed good linearity with a correlation coefficient of 0.999, and the precision expressed as the relative standard deviation of the errors from the regression line was +/-2.7% (2sigma). The accuracy of the proposed method was assessed by capillary electrophoresis. Eight commercially available juice products were analyzed using this method. Five of them were thought to be adulterated with synthetic malic acid.     

C3 cyclopolymerization. I. Is the cyclopolymerization of 1,3-bis(p-vinylphenyl)-propane by means of radical or anionic initiators possible?

Polymerization of 1,3-bis(p-vinylphenyl) propane (St-C₃-St) was investigated by using radical and anionic initiators. Radical polymerization yielded linear polymer with pendant styryl groups in pertinent conditions without gelation. Anionic polymerization with n-butyllithium and sodium naphthalene produced insoluble polymers that, according to infrared (IR) spectroscopy, had no cyclized units. On the other hand, phenylmagnesium bromide gave soluble polymer in HMPA-benzene mixed solvent. Zero-valent nickel catalyst also gave soluble polymer. The soluble polymers could be analyzed by several spectroscopies, and it was confirmed that those obtained by anionic and coordination polymerization had no [3.3]paracyclophane units in the main chain. From these results it was concluded that cationic propagation could be assumed if the polymer Of St-C₃-St contained [3.3]paracyclophane units in the main chain.     

Identification and determination of sulphamethazine and N4-acetylsulphamethazine in meat by high-performance liquid chromatography with photodiode-array detection

A simple and selective method for the determination of sulphamethazine (SMT) and its metabolite, N4-acetylsulphamethazine (N4-AcSMT), in meat by high-performance liquid chromatography (HPLC) with photodiode-array detection was developed. The drugs were extracted from meat with 0.2% metaphosphoric acid-methanol (6:4), followed by a Bond-Elut C18 clean-up procedure. The HPLC separation was carried out on a Supersphere RP-18e column (125 X 4.0 mm I.D.) using 0.05 M sodium dihydrogenphosphate (pH 4.5)-acetonitrile (8:2) as the mobile phase at a flow-rate of 0.5 ml/min, and monitored with a photodiode-array detector. The recoveries of SMT and N4-AcSMT from meat fortified at 0.5 micrograms/g were 90.1-93.3 and 93.0-94.4%, respectively, with coefficients of variation of 1.9-3.2 and 1.5-2.7%. The limits of detection were 0.02 micrograms/g for each drug. SMT was found in ten samples of imported meat (12.5%) at levels ranging from 0.05 to 1.05 micrograms/g.     

Combinatorial synthesis of MUC1 glycopeptides: polymer blotting facilitates chemical and enzymatic synthesis of highly complicated mucin glycopeptides

The chemoselective polymer blotting method allows for rapid and efficient synthesis of glycopeptides based on a "catch and release" strategy between solid-phase and water-soluble polymer supports. We have developed a heterobifunctional linker sensitive to glutamic acid specific protease (BLase). The general procedure consists of five steps, namely (i) the solid-phase synthesis of glycopeptide containing BLase sensitive linker, (ii) subsequent deprotections and the release of the glycopeptide from the resin, (iii) chemoselective blotting of the glycopeptide intermediates in the presence of water-soluble polymers with oxylamino functional groups, (iv) sugar elongations using glycosyltransferases, and (v) the release of target glycopeptides from the polymer platform by selective BLase promoted hydrolysis. The combined use of the solid-phase chemical syntheses of peptides and the enzymatic syntheses of carbohydrates on water-soluble polymers would greatly contribute to the production of complicated glycopeptide libraries, thereby enhancing applicative research. We report here a high-throughput synthetic system for the various types of MUC1 glycopeptides exhibiting a variety of sugar moieties. It is our belief that this concept will become part of the entrenched repertoire for the synthesis of biologically important glycopeptides on the basis of glycosyltransferase reactions in automated and combinatorial syntheses.     

Micropore-free surface-activated carbon for the analysis of polychlorinated dibenzo-p-dioxins-dibenzofurans and non-ortho-substituted polychlorinated biphenyls in environmental samples

2,3,7,8-Substituted polychlorinated dibenzo-p-dioxins/polychlorinated dibenzofurans (PCDD/Fs) and non-ortho-substituted polychlorinated biphenyls (PCBs) account for almost all of the total toxic equivalents (TEQ) in environmental samples. Activated carbon columns are used to fractionate the samples for GC-MS analysis or bioassay. Micropore-free surface-activated carbon is highly selective for PCDD/Fs and non-ortho-PCBs and can improve the conventional activated carbon column clean-up. Along with sulfuric acid-coated diatomaceous earth columns, micropore-free surface-activated carbon provides a rapid, robust, and high-throughput sample preparation method for PCDD/Fs and non-ortho-PCBs analysis.