Existence,unicité et homogénéité de certains immeubles hyperboliques

Résumé. Dans ce travail, nous introduisons une classe d'immeubles hyperboliques de dimension 2 à allure locale prescrite. Nous prouvons l'existence et l'unicité de ces immeubles. Nous montrons que leur groupe d'automorphismes est transitif sur les chambres. Ces résultats permettent d'identifier des immeubles hyperboliques construits par les diverses méthodes utilisées jusqu'ici: “blueprints” de Ronan-Tits et immeubles de Kac-Moody, revêtements ramifiés d'immeubles euclidiens, polygones de groupes etc... Nos méthodes s'appliquent en fait à des complexes polygonaux hyperboliques beaucoup plus généraux que les seuls immeubles. Received: 3 April 2000; in final form: 25 September 2000 / Published online: 23 July 2001     

The Szegö kernel of a symplectic quotient

Suppose a compact Lie group acts on a polarized complex projective manifold (M,L). Under favorable circumstances, the Hilbert-Mumford quotient for the action of the complexified group may be described as a symplectic quotient (or reduction). This paper addresses some metric aspects of this identification, by analyzing the relationship between the Szegö kernel of the pair (M,L) and that of the quotient.     

On spacelike hypersurfaces with constant scalar curvature in the de Sitter space

We classify spacelike hypersurfaces of the de Sitter space with constant scalar curvature and with two principal curvatures. Moreover, we prove that if Mn is a complete spacelike hypersurface with constant scalar curvature n(n−1)R and with two distinct principal curvatures such that the multiplicity of one of the principal curvatures is n−1, then R<(n−2)c/n. Additionally, we prove several rigidity theorems for such hypersurfaces.     

Method development for the determination of 24S‐hydroxycholesterol in human plasma without derivatization by high‐performance liquid chromatography with tandem mass spectrometry in atmospheric pressure chemical ionization mode

We developed a highly sensitive and specific high‐performance liquid chromatography with tandem mass spectrometry method with an atmospheric pressure chemical ionization interface to determine 24S‐hydroxycholesterol, a major metabolite of cholesterol formed by cytochrome P450 family 46A1, in human plasma without any derivatization step. Phosphate buffered saline including 1% Tween 80 was used as the surrogate matrix for preparation of calibration curves and quality control samples. The saponification process to convert esterified 24S‐hydroxycholesterol to free sterols was optimized, followed by liquid–liquid extraction using hexane. Chromatographic separation of 24S‐hydroxycholesterol from other isobaric endogenous oxysterols was successfully achieved with gradient mobile phase comprised of 0.1% propionic acid and acetonitrile using L‐column2 ODS (2 μm, 2.1 mm id × 150 mm). This assay was capable of determining 24S‐hydroxycholesterol in human plasma (200 μL) ranging from 1 to 100 ng/mL with acceptable intra‐ and inter‐day precision and accuracy. The potential risk of in vitro formation of 24S‐hydroxycholesterol by oxidation from endogenous cholesterol in human plasma was found to be negligible. The stability of 24S‐hydroxycholesterol in relevant solvents and human plasma was confirmed. This method was successfully applied to quantify the plasma concentrations of 24S‐hydroxycholesterol in male and female volunteers.     

Structural study of a manganese(II) `picket‐fence' porphyrin complex

`Picket‐fence' porphyrin compounds are used in the investigation of interactions of hemes with dioxygen, carbon monoxide, nitric monoxide and imidazole ligands. (Cryptand‐222)potassium chlorido[meso‐tetra(α,α,α,α‐o‐pivalamidophenyl)porphyrinato]manganese tetrahydrofuran monosolvate (cryptand‐222 is 4,7,13,16,21,24‐hexaoxa‐1,10‐diazabicyclo[8.8.8]hexacosane), [K(C₁₈H₃₆N₂O₆)][Mn(C₆₄H₆₄N₈O₄)Cl]·C₄H₈O or [K(222)][Mn(TpivPP)Cl]·THF [systematic name for TpivPP: 5,10,15,20‐tetrakis(2‐tert‐butanamidophenyl)porphyrin], is a five‐coordinate high‐spin manganese(II) picket‐fence porphyrin complex. It crystallizes with a potassium cation chelated inside a cryptand‐222 molecule; the average K—O and K—N distances are 2.83 (4) and 2.995 (13) Å, respectively. All four protecting tert‐butyl pickets of the porphyrin are ordered. The porphyrin plane is nearly planar, as indicated by the atomic displacements and the dihedral angles between the mean planes of the pyrrole rings and the 24‐atom mean plane. The axial chloride ligand is located inside the molecular cavity on the hindered porphyrin side and the Mn—Cl bond is tilted slightly off the normal to the porphyrin plane by 3.68 (2)°. The out‐of‐plane displacement of the metal centre relative to the 24‐atom mean plane (Δ₂₄) is 0.7013 (4) Å, indicating a noticeable porphyrin core doming.     

IL-24重组载体的构建及其联合化疗药物对SKOV3细胞中TUBB3与ERCC-1基因表达的影响

通过基因重组技术将白介素24(IL-24)基因片段分别克隆成pc DNA3.0-OSP-1-IL-24和pc DNA3.0-IL-24载体,利用逆转录PCR(RT-PCR)测定2种载体的表达.将2种化疗药物紫杉醇(PTX)与顺铂(DDP)分别作用于正常SKOV3细胞及pc DNA3.0,pc DNA3.0-IL-24,pc DNA3.0-OSP-1和pc DNA3.0-OSP-1-IL-24稳定转染SKOV3细胞(卵巢癌细胞株),通过噻唑蓝(MTT)法检测化疗药物联合IL-24基因对细胞的杀伤效果及细胞的增殖能力,应用实时荧光定量PCR技术检测人β-微管蛋白3(TUBB3)与核苷酸切除修复交叉互补基因位1(ERCC1)基因在各组细胞中的表达.RT-PCR检测结果显示,通过基因重组技术克隆了pc DNA3.0-IL-24与pc DNA3.0-OSP-1-IL-24载体,IL-24基因能提高SKOV3细胞对化疗药物顺铂和紫杉醇的敏感性.其联合化疗药物对肿瘤药物的IC50值分别下降了10倍和6倍,TUBB3和ERCC1基因在IL-24基因转染的SKOV3细胞内的表达水平与在正常SKOV3细胞内相比,分别下降4倍和10倍多.上述结果表明,IL-24联合化疗药物可明显下调TUBB3与ERCC1基因的表达,该实验为临床治疗卵巢癌提供了重要的理论依据.     

Solitons and other solutions to a new coupled nonlinear Schrodinger type equation

In this paper, the first integral method combined with Liu's theorem is applied to integrate a new coupled nonlinear Schrodinger type equation. Using this combination, more new exact traveling wave solutions are obtained for the considered equation using ideas from the theory of commutative algebra. In addition, more solutions are also obtained via the application of semi-inverse variational principle due to Ji-Huan He. The used approaches with the help of symbolic computations via Mathematica 9, may provide a straightforward effective and powerful mathematical tools for solving nonlinear partial differential equations in mathematical physics.     

Free boundary minimal hypersurfaces with spherical boundary

We first prove that a compact embedded minimal annulus in meeting two concentric spheres perpendicularly along the boundaries is part of a plane. We also prove that an embedded minimal hypersurface lying outside of a ball is part of either a catenoid or a hyperplane if it is perpendicular to the sphere along the boundary and has only one end that is asymptotic to either a catenoid if , or a hyperplane if .     

Moufang sets of mixed type F4

Moufang sets were introduced by Jacques Tits in order to understand isotropic linear algebraic groups of relative rank one, but the notion is more general. We describe a new class of Moufang sets, arising from so‐called mixed groups of type ${\mathsf{F}}_4$ in characteristic 2, obtained as the fixed point set under a suitable involution.