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.     

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.     

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.     

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.     

Application of intramolecular 1,3-dipolar cyclic addition of azide and olefin; construction of (pyrrolidine-2-ylidene)glycinate and glycinamides

Oxopropyl E-(pyrrolidine-2-ylidene)glycinamide (5c) and allyl E-(pyrrolidine-2-ylidene)glycinate (5d) were effectively synthesized from 2,3,5-tri-O-benzyl-4-O-tert-butyldimethylsilyl(TBDMS)-D-arabinal (7) using intramolecular 1,3-dipolar cyclic reaction of azide and olefin as a key reaction. These results proved this cyclic reaction should be applicable for the synthesis of various (pyrrolidine-2-ylidene)glycinate and glycinamide. In addition, the development of a synthetic route for the precursor of an unsaturated cyclic dehydro amino acid involved in azinomycins (carzinophilin) using relating glycinate, methyl E-(pyrrolidine-2-ylidene)glycinate (5a) was described.     

An application of activation analysis of aluminum in biological materials

The behavior of aluminum compounds in animals was made clear by using non-destructive neutron activation analysis instead of radiotracer method. Basic aluminum sucrose sulfate (BASS) and dried aluminum hydroxide gel (DAHG) were orally administered to rats. The residual BASS and DAHG on gastric walls of rats were determined by neutron activation analysis. It was obtained the following results that BASS was found at the longer time in the stomach. For reason, it is seemed that BASS is hydrolyzed in gastric juice. And it could not find the aluminum in liver, kidney and spleen.     

An intramolecular diels-alder approach to quassinoids—a stereoselective construction of a-aromatic klaineanone

Thermolysis of a benzocyclobutene derivative ($\text{20}$) prepared from norcamphor produced stereoselectively a tetracyclic compound ($\text{2}$), which was converted to a lactone ($\text{21}$) having correct stereochemistry at C₇, C₈, C₉, C₁₁, C₁₃, and C₁₄ positions of (±)-klaineanone.     

Medium-sized cyclophanes—XVII : Tetra-, hexa-, octa- and decahydropyrenes from [2.2]metacyclophane. Transannular dehydrogenation,isomerization, and disproportionation reactions by means of benzoyl peroxide,metal salts and sulfuric acids

[2.2]Metacyclophane (1) undergoes a variety of reactions according to the reagents and conditions. These include (1) substitution (path a), (2) transannular dehydrogenation (path b and c), (3) cycloisomerization (path d) and (4) transannular hydrogenation. A brief summary of these reactions is presented.The diversity of the reactions of 1 is further explored using benzoyl peroxide (BPO), cupric chloride, aluminum chloride, other metal salts, H₂SO₄ and FSO₃H. With BPO or cupric chloride, one-electron transfer mechanism is postulated. This involves a tautomeric ion pair formed by the intramolecular arylation with an aryl cation radical. A supporting evidence in favor of the mechanism is presented from experiments using various metal salts in different solvents.On the contrary, the reaction with aluminum chloride gives decahydropyrene (8) and octahydropyrene (11) together with cycloisomerization product 5 and dehydrogenation products 2, 3 and 4. When treated with AlCl₃HCl 1 gives similar products as above but the product ratios are quite different. The major product is 5 but only a trace amount of 8 is formed. The reaction with H₂SO₄ or FSO₃H also produce 2, 4, 5 and 11. Some mechanistic evidence in favor of the disproportionation reaction is presented.