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.     

Direct determination of benzamides in serum by column-switching high-performance liquid chromatography.

A column-switching high-performance liquid chromatographic method with fluorescence detection was developed for the simultaneous determination of four benzamide-type anti-psychotic drugs: sulpiride, tiapride, sultopride and metoclopramide in human serum. In this method, a TSKgel Super-ODS column was used as an analytical column, and a TSKgel G 2000SW was prepared as a pretreatment column. Under the optimized analytical conditions, four benzamide-type anti-psychotic drugs were eluted within 18 min. The detection limits (S/N = 3) for sulpiride, tiapride, sultopride and metoclopramide are 1 ng/ml, 4 ng/ml, 2 ng/ml and 0.5 ng/ml, respectively. Finally, the method was applied to the determination of sulpiride in human serum samples obtained after a single oral dose of sulpiride.     

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.     

Chloroprene as a source of fine chemicals: palladium-catalyzed synthesis of terminal allenes

[reaction: see text] Several functionalized terminal allenes were prepared in moderate to excellent yield by a palladium-catalyzed reaction of chloroprene (2-chloro-1,3-butadiene) with soft nucleophiles.     

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.     

A new route to methyl (R,E)-(-)-tetradeca-2,4,5-trienoate (pheromone of Acanthoscelides obtectus) utilizing a palladium-catalyzed asymmetric allene formation reaction

[reaction: see text] A formal total synthesis of the sex attractant of male dried bean beetle, methyl (R,E)-(-)-tetradeca-2,4,5-trienoate, was achieved by a new efficient route utilizing the Pd-catalyzed asymmetric allene synthesis reaction. It was found that the atropisomeric biaryl bisphosphine (R)-segphos showed better enantioselectivity than (R)-binap in the Pd-catalyzed reaction for preparing alkyl-substituted axially chiral allenes.     

Stereoselective syntheses of 4-hydroxy 4-substituted glutamic acids

The 4-hydroxy 4-substituted glutamic acid moiety is a common substructure of biologically important natural products such as monatin [(2S,4S)-2], lycoperdic acid (3), and dysiherbaine (4). To develop methodology for syntheses of these natural products, cycloadditions of nitrone 5 with 2-substituted 2-propen-1-ols 6 and 2-substituted acrylates 8 were investigated. Reactions of nitrone 5 with alcohols 6 in the presence of MgBr2OEt2 gave cycloadducts 7 in a highly stereoselective manner, whereas noncatalyzed reactions of 5 with acrylates 8 afforded adducts 9. Using the former reaction, syntheses of monatin [(2S,4S)-2], monatin derivative 18, and lycoperdic acid (3) were accomplished. The C4-epimer of monatin [(2S,4R)-2)] was also synthesized by employing the latter cycloaddition.     

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.     

Preparation of multisubstituted allenes from allylsilanes

[reaction: see text] A three-step route of converting allylsilanes to functionalized allenes was developed. Thermal decomposition of 1,1-dibromo-2-(silylmethyl)cyclopropanes, which were quantitatively prepared by treatment of allylsilane derivatives with CHBr3/KO(t)Bu, afforded substituted 2-bromo-1,3-butadienes with elimination of bromosilanes. The Pd-catalyzed reaction of the bromodienes with soft nucleophiles gave the allene derivatives. Previously inaccessible tri- and tetrasubstituted allenes can be prepared by this method as well.