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.     

Collection of iron(III) from homogeneous aqueous solutions on membrane filters using Chromazurol B with Triton X-100.

A membrane filtration method was examined concerning the effective collection of iron(III) from a homogeneous aqueous solution with Chromazurol B (CAB), one of the triphenylmethane dyes, as a precipitating reagent in the presence of a non-ionic surfactant, polyethylene glycol mono[4-(1,1,3,3-tetramethylbutyl)phenyl]ether (Triton X-100). A formed blue Fe(III)-CAB complex was collected as a precipitate on a membrane filter by filtration under suction from a homogeneous aqueous solution in the pH range over about 2. The original solution was prepared at a concentration ratio of CAB to Fe(III) of to 10, and that of Triton X-100 to CAB of 10 to 100. It was then adjusted to a pH value of between 1.0 and 6.5. A linear relationship (r = 0.999) was obtained between the initial concentration and the found one of Fe(III) in the range of 2.0 x 10(-5) to 4.0 x 10(-4) mol dm(-3) at a fixed concentration ratio of CAB to Fe(III) of 3 and that of Triton X-100 to CAB of 20. This membrane filtration with CAB and Triton X-100 may be utilized for the separation of Fe(III) as a background species.     

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.     

Asymmetric interaction of optically active polymers with asymmetric small molecules. IV. Effect of hydrophobic groups on asymmetric interaction

In order to investigate the mechanism of the asymmetric interaction between optically active polymers and small molecules, optically active copolymers of N-acrylyl L-amino acids(N-acrylyl-L -phenylalanine, N-acrylyl-L -tryptophan, and N-acrylyl-L -leucine, respectively) and N,N′-hexamethylene diacrylylamide were synthesized, and interaction of these polymers with the optical isomers of phenylalanine and tryptophan was investigated. In the interaction of these acidic polymers with amino acids performed at pH 5.0, significant difference in amount of adsorption between the D and L isomers of amino acids were observed, and the L form of amino acids was adsorbed preferentially. The interaction between optically active small molecules was also investigated: these results showed a similarity to the results for interaction between optically active polymers and amino acids. In some instances of asymmetric interaction the influence of hydrophobic interaction between a polymer and substrate was clearly perceived. The stereoselective effects on the asymmetric interaction are discussed.     

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.     

XPS study of one-dimensional compounds: TiS3

X-Ray photoelectron spectra of TiS₃ with a one-dimensional structure were measured. TiS₃ may be regarded as Ti⁴⁺(S₂)^2?S^2? with pairs of S atoms (S₂) and isolated S atoms. The spectra of the sulfur core-levels are assigned by comparison with those of TiS₂, where all S atoms are largely separated. The binding energy of the S₂ pairs is found to be 1.4 eV higher than that of the isolated S atoms, which is consistent with the larger negative charge of the isolated atoms. The structures of the valence band of TiS₃ are discussed in terms of a molecular orbital scheme for the S₂ pairs.     

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 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.     

Capacitance-conductance detector for high-pressure liquid chromatography. Application to alkaloids and fatty acids

Summary A new type of detector for high-pressure liquid chromatography has been designed. This detector is equipped with a RC resonance circuit, and is similar to the capacitance detector previously reported. It is operated as a capacitance detector with nonpolar eluents; while with polar solvents, it behaves as a conductance detector. Electrolytes such as salts, acids and bases are sensitively detected. The detector was successfully used for the detection of fatty acids and alkaloids.

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Zusammenfassung Ein neuartiger Detektor für die Hochdruck-Flüssigchromatographie wurde entwickelt. Dieser ist mit einem Resonanzstromkreis ausgestattet und ähnelt dem kürzlich beschriebenen Kapazitanz-Detektor. Als solcher funktioniert er mit nichtpolaren Eluenten, während er sich mit polaren Lösungsmitteln wie ein Leitfähigkeitsdetektor verhält. Salze, Säuren und Basen werden empfindlich nachgewiesen. Das Gerät wurde zum Nachweis von Fettsäuren und Alkaloiden verwendet.

     

Stability and vibrational spectra of toroidal isomers of C 240

To study the thermodynamic and mechanical stability of toroidal isomers of C ₂₄₀, we use a semi-empirical tight-binding theory and calculate their electronic structure, cohesive energy and vibrational spectra within the harmonic approximation. From these, we deduce their free energy at temperatures up to 1500K. The results are also compared to the isomer with icosahedral symmetry. Finally, we discuss within this approach, their stability and abundance.