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.     

Probing for electrical inclusions with complex spherical waves

Let a physical body Ω in ?² or ?³ be given. Assume that the electric conductivity distribution inside Ω consists of conductive inclusions in a known smooth background. Further, assume that a subset Γ ? ?Ω is available for boundary measurements. It is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on Γ. More precisely: given a ball B with center outside the convex hull of Ω and satisfying (B? ∩ ?Ω) ? Γ, boundary measurements on Γ with explicitly given Dirichlet data are enough to determine whether B intersects the inclusion. An approximate detection algorithm is introduced based on the theory. Numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion‐free domain near Γ and is robust against measurement noise. © 2007 Wiley Periodicals, Inc.     

Crystallographic report: Bis{µ‐[O‐cyclopentyl(4‐methoxyphenyl)dithiophosphonato]1κ:S,2κ:S‐[O‐cyclopentyl(4‐methoxyphenyl)dithiophosphonato]‐1κ2S,S′}dicadmium(II)

The centrosymmetric title compound, [Cd₂{CH₃OC₆H₄P(OC₅H₉)S₂}₄], features an eight‐membered [? Cd? S? P? S? ]₂ ring owing to the presence of bridging dithiolate ligands. Tetrahedral coordination geometries for cadmium are completed by chelating ligands. Copyright © 2004 John Wiley & Sons, Ltd.     

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 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.

     

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.