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.     

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.     

Diaminothiazoles and diaminothiophenes

Several 2,4-diaminothiazoles and 2,4-diaminothiophenes could be easily obtained by metallation using LDA from aminomethylthiomethylenecyanamides $\text{2}$ and aminomethylthiomethylenemalononitrile, respectively.     

Synthesis of Six-Membered Compounds by Environmentally Friendly Cyclization Using Indirect Electrolysis

[Ni(cyclam)](ClO(4))(2)-catalyzed indirect electroreduction of olefinic bromides produced six-membered compounds in low to high yields. The synthetic intermediate 49 of Ipecac and Corynanthe alkaloids was obtained in 88% yield in a highly stereoselective manner. Lactam 66, the synthetic precursor of tacamonine, was prepared in 49% yield as a mixture of two diastereoisomers. The electrolysis of the bromoacetates gave the debrominated compounds in good yields.     

Coprecipitation with metal hydroxides for the determination of beryllium in seawater by graphite furnace atomic absorption spectrometry

Coprecipitation first with magnesium hydroxide, next with tin(IV) hydroxide is developed for the determination of traces of beryllium in sea-water. To a 200-ml sample is added a sodium hydroxide solution to form magnesium hydroxide at pH 11.5, on which beryllium is quantitatively coprecipitated. The precipitate is separated by centrifugation and dissolved in 2 ml of 12 mol/l hydrochloric acid. The resulting solution (ca. 10 ml) is mixed with 2 mg of tin (IV) carrier and the pH is adjusted to 5.0 to collect the beryllium on tin (IV) hydroxide, leaving magnesium ions in the solution. The tin (IV) hydroxide is centrifuged, dissolved in 0.1 ml of 5 mol/l hydrobromic acid, and then diluted to 1 ml with water. Magnesium is so added as to be 500 g/ml for increasing the sensitivity about four times, and the beryllium in the solution is determined by graphite furnace atomic absorption spectrometry. The experiments with synthetic seawater samples showed that pg — g amounts of beryllium can be coprecipitated on the metal hydroxides and beryllium at the low ng/1 level can be determined with reasonable precision (RSD < 10%). The detection limit of the proposed method is 0.5 ng/l of beryllium in seawater.     

Phenotyping of erythrocyte acid phosphatase and esterase D by high field strength isoelectric focusing on cellulose acetate membrane

Phenotyping of erythrocyte acid phosphatase (EAP) and esterase D (ESD) by cellulose acetate membrane isoelectric focusing (CAM-IEF) under a nonequilibrium condition is described. In an attempt to improve the method of CAM-IEF, we shortened the electrode distance to provide a higher field strength at a given (low) voltage. Various carrier ampholytes for EAP typing and various chemical separators for ESD typing were also tested. Good separations were obtained after 30 min IEF for EAP typing and 25 min for ESD typing. When applied to blood stains and stored for various periods at room temperature, the stains up to 8 months old could still be phenotyped for EAP and those up to 4 weeks old for ESD. CAM-IEF is suitable for routine forensic work of EAP and ESD phenotyping.     

Selective formation of AAB- and ABC-type heterotrimeric alpha-helical coiled coils

The alpha-helical coiled coils have a representative amino acid sequence of (abcdefg)(n) heptad repeats. We previously reported that two peptides named IZ-2A and IZ-2W formed an (IZ-2A)(2)/IZ-2W heterotrimer with an Ala-Ala-Trp interaction in the hydrophobic core. In this paper, we describe the selective formation of AAB- and ABC-type heterotrimers. To increase the selectivity of the AAB-type heterotrimeric formation, Lys residues at the f position were mutated to either an Ala or a Gln residue to form IZ-2A(fA) or IZ-2W(fQ). Separately, both IZ-2A(fA) and IZ-2W(fQ) have a random structure at pH 7 and 20 degrees C. However, together IZ-2A(fA) and IZ-2W(fQ) form a 2:1 complex with a thermal transition midpoint (Tm) of 48 degrees C. This procedure was applied to prepare the ABC-type heterotrimer, in which two sets of Ala-Ala-Trp interactions were designed in the hydrophobic core. Interhelical interaction between the e and g positions and the alpha-helical propensity of the amino acid at the f position were also considered in the design. The resultant three peptides selectively formed the ABC-type heterotrimer with a Tm of 51 degrees C. Other peptide combinations had random coil properties.     

Studies of the polymerization of diallyl compounds. XXII. Polymerization of diallyl oxalate in the evolution of carbon dioxide at elevated temperatures

The polymerization of diallyl oxalate was conducted in the presence of radical initiators at a high temperature range of 80–180°C; a large decrease in degree of polymerization, an increase in residual unsaturation of the resulting polymer, and the evolution of carbon dioxide were observed with the elevation of temperature. These findings were reasonably interpreted by considering the dismutation of the uncyclized growing radical to yield the allyl radical, carbon dioxide, and polymer carrying a terminal double bond. The kinetics of the polymerization of diallyl oxalate in the evolution of carbon dioxide at elevated temperatures were also discussed in detail.     

Selective desorption and analysis of humic substances on suspended particles in river water

The elemental analysis and morphology of individual particles indicate that the dominant suspended particles in river water are kaolin covered with hydrated iron(III) oxide which strongly sorbs humic substances. Suspended particles, about 1 mg, collected from 250 ml of water by centrifugation, are treated with 0.7 ml of 0.1M sodium hydroxide to desorb humic substances. Approximately 60% of copper and 30% of lead on or in suspended particles exist as humic complexes.