Complete homogeneous varieties: Structure and classification

Homogeneous varieties are those whose group of automorphisms acts transitively on them. In this paper we prove that any complete homogeneous variety splits in a unique way as a product of an abelian variety and a parabolic variety. This is obtained by proving a rigidity theorem for the parabolic subgroups of a linear group. Finally, using the results of Wenzel on the classification of parabolic subgroups of a linear group and the results of Demazure on the automorphisms of a flag variety, we obtain the classification of the parabolic varieties (in characteristic different from ). This, together with the moduli of abelian varieties, concludes the classification of the complete homogeneous varieties.

     

Chiral pyrimidine metallacalixarenes: synthesis, structure and host-guest chemistry

A set of enantiomerically pure cyclic multinuclear complexes with the formula cis-[a(2)PdL](n) (n+) [a(2)=(R,R)-1,2-diaminocyclohexane (R,R-dach), (S,S)-1,2-diaminocyclohexane (S,S-dach); n=4, 6; LH=2-hydroxypyrimidine (2-Hpymo), 4,6-dimethyl-2-hydroxypyrimidine (2-Hdmpymo) and 4-hydroxypyrimidine (4-Hpymo)] were obtained by reaction of cis-[a(2)Pd(H(2)O)(2)](2+) and LH in aqueous media. The polynuclear complexes were studied by (1)H NMR spectroscopy and X-ray crystallography. These studies revealed that the N1,N3-bridging mode exhibited by the pyrimidine moieties is ideally suited for formation of inorganic analogues of calixarenes (metallacalixarenes) in a self-assembly process. The most stable species are the tetranuclear metallacalix[4]arenes, which are obtained in all cases. Hexanuclear species, namely, [a(2)Pd(2-dmpymo)](6) (6+), were also isolated and fully characterised. (1)H NMR experiments show conversion of [a(2)Pd(2-dmpymo)](6) (6+) to [a(2)Pd(2-dmpymo)](4) (4+) on heating. Analogously to organic calixarenes, these systems are also capable of incorporating hard metal ions at the oxo surface. Additionally, investigations on the receptor properties of these metallacalixarenes towards mononucleotides showed that enantioselective recognition processes occur in aqueous media.     

Synthesis of indazol‐4,7‐dione derivatives as potential trypanocidal agents

The synthesis of new indazol‐4,7‐dione derivatives via 1,3‐dipolar cycloaddition of diazomethane with 2,3‐dimethyl‐1,4‐benzoquinone ( 2 ) and 1,4‐naphthoquinone ( 7 ) followed by N‐alkylation of the pyrazol nitrogen atom of the corresponding quinones ( 3 ) and ( 8 ) with methyl chloroacetate is described. A series of amides from esters ( 5 ) and ( 10 ) were also obtained. These compounds were tested in vitro as potential anti‐trypanosomal agents. Compounds ( 4 ) and ( 8 ) were found to have significant activity.     

Biosynthesis of the angiogenesis inhibitor borrelidin by Streptomyces parvulus Tü4055: cluster analysis and assignment of functions

The biosynthetic gene cluster for the angiogenesis inhibitor borrelidin has been cloned from Streptomyces parvulus Tü4055. Sequence analysis indicates that the macrolide ring of borrelidin is formed by a modular polyketide synthase (PKS) (borA1-A6), a result that was confirmed by disruption of borA3. The borrelidin PKS is striking because only seven rather than the nine modules expected for a nonaketide product are encoded by borA1-A6. The starter unit of the PKS has been verified as trans-cyclopentane-1,2-dicarboxylic acid (trans-1,2-CPDA), and the genes involved in its biosynthesis identified. Other genes responsible for biosynthesis of the nitrile moiety, regulation, and self-resistance were also identified.     

Novel mechanism for priming aromatic polyketide synthases

In this issue of Chemistry & Biology, a novel priming mechanism is proposed for aromatic polyketide biosynthesis, with an iterative type I polyketide synthase generating a starter unit primed for a type II polyketide synthase. This novel priming system participates in hedamycin biosynthesis, a DNA alkylating agent.     

X-ray crystal structure of tetraaquabis (xanthosinato)nickel(II) hexahydrate

The complex [Ni(XsH_–1)₂(H₂O)₄]·6H₂O (XsH_–1: xanthosinate) was isolated from the reaction of nickel carbonate with xanthosine in aqueous solution. The octahedral coordination is supported by the reflectance measurements. Single-crystal X-ray diffraction studies show that the crystals belong to the triclinic P1 space group, with a = 7.152(1), b = 8.830(1),c = 13.783(1) Å, = 82.024(1)°, = 86.155(1)°, = 70.900(1)°, and D = 1.643 mg/m³, forZ = 1. Nickel is six coordinate with four water molecules, and two N7 atoms from xanthosinato ligands. A complicated hydrogen-bonding network is present, all possible donors taking part in it.     

Synthesis,spectroscopic studies,and crystal structure of theophyllinium tetrabromopalladate(II)

The theophyllinium tetrabromopalladate(II), [Thph]₂PdBr₄, has been synthesized and its molecular structure has been determined by single crystal X-ray diffraction. The salt crystallizes in the monoclinic space group C2 with two formula units in a cell of dimensionsa=11.074(1),b=8.545(2),c=11.804(2) Å;=95.22(1)°,V=1112.3(4) ų,D _c=2.353 mg m^–3,D _exp=2.352 mg m^–3,M _w=788.4, (MoK)=84.5 cm^–1,F(000)=752. The structure has been refined by full-matrix least-squares techniques to a final value of theR factor of 0.058 based on 907 independent intensities. The compound consists of theophyllinium cations protonated at N(9). The [PdBr₄]^2– anion is planar, with distances Pd-Br(1)=2.441(12) and Pd-Br(2)=2.412(6) Å, and Br(1)-Pd-Br(2) and Br(1)-Pd-Br(3) angles of 90.34(14)° and 89.66(14)°, respectively. The¹H-NMR spectrum of [Thph]₂PdBr₄ in DMSO-d₆ (300 MHz) is consistent with the observed solid-state structure, and its thermal behavior shows two steps: (i) a dehalogenation process about 327°C and (ii) a rapid pyrolitic decomposition in the 340–575°C temperature range giving PdO as final product.     

Electron impact mass spectra of phosphine sulphides and selenides

An electron impact mass spectral study of phosphine sulphides and selenides established the effect of the heteroatom and the role of the ortho substituent in the fragmentation pattern.     

Fourier-Mukai transforms for Gorenstein schemes

We extend to singular schemes with Gorenstein singularities or fibered in schemes of that kind Bondal and Orlov's criterion for an integral functor to be fully faithful. We also prove that the original condition of characteristic zero cannot be removed by providing a counterexample in positive characteristic. We contemplate a criterion for equivalence as well. In addition, we prove that for locally projective Gorenstein morphisms, a relative integral functor is fully faithful if and only if its restriction to each fibre is also fully faithful. These results imply the invertibility of the usual relative Fourier-Mukai transform for an elliptic fibration as a direct corollary.