Stability of homogeneous principal bundles with a classical groupas the structure group

Let G be a connected semisimple linear algebraic group defined over an algebraically closed field k and P ⊂ G a parabolic subgroup without any simple factor. Let H be a connected reductive linear algebraic group defined over the field k such that all the simple quotients of H are of classical type. Take any homomorphism π : P → H such that the image of p is not contained in any proper parabolic subgroup of H. Consider the corresponding principal H-bundle E_P(H) = (G × H)/P over G/P. We prove that E_P (H) is strongly stable with respect to any polarization on G/P.     

Oximato bridged RhIII2MII and RhIIIMI species (MII = Mn, Co, Ni; MI = Cu, Ag)

The reaction of [RhCl₂(HPhL)(PhL)] with M^II(ClO₄)₂·6H₂O in presence of alkali has furnished trinuclear [RhCl₂(PhL)₂]₂M(H₂O)₂·H₂O (HPhL is phenylazobenzaldoxime; M = Mn, Co, Ni). A similar reaction with M^I(PPh₃)₂NO₃ yielded binuclear [RhCl₂(PhL)₂]M(PPh₃)₂ (M = Cu, Ag). In these molecules the oximato group acts as a bridge between Rh^III (bonded at N) and M^II or M^I (bonded at O). In structurally characterized [Rh^IIICl₂(PhL)₂]₂Mn(H₂O)₂.H₂O the centrosymmetric distorted octahedral MnO₆ coordination sphere is spanned by four oximato oxygen atoms and two water molecules lying in trans position. In the lattice the neighbouring molecules are held together by H₂O⋯H₂O⋯H₂O hydrogen bonds generating infinite zigzag chains. The manganese atoms lie parallel to the C-axis, the shortest Mn...Mn distance being 7.992 ?. Magnetic exchange interactions if any are small as seen in room temperature magnetic moments. The manganese system displays a strong EPR signal near g = 2.00. In the complex [RhCl₂(PhL)₂]Cu(PPh₃)₂ the copper atom is coordinated to two oximato oxygen atoms and the two phosphorus atoms in a distorted tetrahedral geometry. The softness of the phosphine ligand is believed to sustain the stable coordination of hard oximato oxygen to soft Cu^I. The coordination sphere of the RhIII atom in both the complexes is uniformly trans-RhN₄Cl₂.     

Automorphisms of curves fixing the order two points of the Jacobian

Let X be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic different from two. If X admits a nontrivial automorphism σ that fixes pointwise all the order two points of Pic⁰(X), then we prove that X is hyperelliptic with σ being the unique hyperelliptic involution. As a corollary, if a nontrivial automorphisms of X fixes pointwise all the theta characteristics on X, then X is hyperelliptic with being its hyperelliptic involution.      

Novel and rapid palladium-assisted 6pi electrocyclic reaction affording 9,10-dihydrophenanthrene and its analogues

A novel methodology for the synthesis of 9,10-dihydrophenanthrene and its analogues has been developed via a palladium-assisted 6pi electrocyclic reaction followed by formaldehyde elimination.     

Synthesis, characterization, and study of octanuclear iron-oxo clusters containing a redox-active Fe4O4-cubane core

A one-pot synthetic procedure yields the octanuclear Fe(III) complexes Fe(8)(micro(4-)O)(4)(micro-pz(*))(12)X(40, where X = Cl and pz(*) = pyrazolate anion (pz = C(3)H(3)N(2)-) (1), 4-Cl-pz (2), and 4-Me-pz (3) or X = Br and pz(*) = pz (4). The crystal structures of complexes 1-4, determined by X-ray diffraction, show an Fe(4)O(4)-cubane core encapsulated in a shell composed of four interwoven Fe(micro-pz(*))(3)X units. Complexes 1-4 have been characterized by 1H NMR, infrared, and Raman spectroscopies. M?ssbauer spectroscopic analysis distinguishes the cubane and outer Fe(III) centers by their different isomer shift and quadrupole splitting values. Electrochemical analyses by cyclic voltammetry show four consecutive, closely spaced, reversible reduction processes for each of the four complexes. Magnetic susceptibility studies, corroborated by density functional theory calculations, reveal weak antiferromagnetic coupling among the four cubane Fe centers and strong antiferromagnetic coupling between cubane and outer Fe atoms of 1. The structural similarity between the antiferromagnetic Fe(8)(micro(4-)O)(4) core of 1-4 and the antiferromagnetic units contained in the minerals ferrihydrite and maghemite is demonstrated by X-ray and M?ssbauer data.     

A mixed-valence octanuclear iron-oxo pyrazolate: assessment of electronic delocalization by structural and spectroscopic analysis

A formally Fe(III)(7)Fe(II) complex, containing an inner Fe(4)O(4)-cubane and four peripheral Fe centers, is derived from the one-electron reduction of its Fe(III)(8) precursor. Spectroscopic analysis of the former reveals that the redox activity of this Fe(8) system is confined within its cubane core. The resulting (Fe(4)O(4))(3+)-cubane, which is valence-delocalized in the NMR, M?ssbauer, and IR spectroscopy time scales but valence-trapped in the X-ray photoelectron spectroscopy (XPS) time scale, is better described as a Robin-Day class-II system by the analysis of its near-infrared (NIR) intervalence charge transfer (IVCT) band profile.     

Physicochemical studies on pepsin-CTAB interaction: energetics and structural changes

The interaction between pepsin and CTAB has been elaborately studied with a number of techniques. The enzyme-induced interaction produced complexes, aggregates, and micelles of CTAB with distinct physicochemical features. It was found that at very low surfactant concentration (much below the critical micellar concentration (cmc) of pure CTAB), the surfactant got adsorbed both in monomeric and lower aggregated forms to the high-energy sites of the native biopolymer, leading to enhanced hydrophobicity of the combine, and hence, lowering of the interfacial (air/solution) tension. This was followed by the formation of a faintly turbid solution of the polymer-surfactant coacervate. The CTAB interacted unfolded pepsin along with the surfactant monomer remained adsorbed at the interface to decrease the interfacial tension (gamma) to a low level to produce a break in the gamma vs log [CTAB] plot prior to the normally observed extended cmc (cmce) in presence of polymers. The cac-like aggregation (as observed in tensiometry and viscometry) was not found in conductometry and microcalorimetry, whereas microcalorimetry evidenced the formation of the cmce of CTAB in the presence of the biopolymer. The CTAB influenced structural features of the pepsin were assessed from spectral, viscometric, and circular dichroism measurements.     

On abelian principal bundles

Let T be a complex torus and E _T a holomorphic principal T-bundle over a connected complex manifold M. We prove that the total space of E _T admits a K?hler structure if and only if M admits a K?hler structure and E _T admits a flat holomorphic connection whose monodromy preserves a K?hler form on T. If E _T admits a K?hler structure, then is isomorphic to . Received: 2 September 2005     

One-pot multicomponent synthesis of diversely substituted 2-aminopyrroles. A short general synthesis of rigidins A, B, C, and D

Privileged medicinal scaffolds based on the structures of tetra- and pentasubstituted 2-aminopyrroles were prepared via one-pot multicomponent reactions of structurally diverse aldehydes and N-(aryl-, hetaryl-, alkylsulfonamido)acetophenones with activated methylene compounds. This methodology was used in a four-step synthesis of alkaloids rigidins A, B, C, and D in overall yields of 61%, 58%, 60%, and 53%, respectively. Of these, rigidins B, C, and D were synthesized for the first time.