Equivariant cohomology and analytic descriptions of ring isomorphisms

In this paper we consider a class of connected closed $G$-manifolds with a non-empty finite fixed point set, each $M$ of which is totally non-homologous to zero in $M_G$ (or $G$-equivariantly formal), where $G={\Bbb Z}_2$. With the help of the equivariant index, we give an explicit description of the equivariant cohomology of such a $G$-manifold in terms of algebra, so that we can obtain analytic descriptions of ring isomorphisms among equivariant cohomology rings of such $G$-manifolds, and a necessary and sufficient condition that the equivariant cohomology rings of such two $G$-manifolds are isomorphic. This also leads us to analyze how many there are equivariant cohomology rings up to isomorphism for such $G$-manifolds in 2- and 3-dimensional cases.Comment: 20 pages, updated version with two references adde

Tverberg-type theorems for intersecting by rays

In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set

Knaster's problem for (Z2)k(Z_2)^k-symmetric subsets of the sphere S2k−1S^{2^k-1}

We prove a Knaster-type result for orbits of the group $(Z_2)^k$ in $S^{2^k-1}$, calculating the Euler class obstruction. Among the consequences are: a result about inscribing skew crosspolytopes in hypersurfaces in $\mathbb R^{2^k}$, and a result about equipartition of a measures in $\mathbb R^{2^k}$ by $(Z_2)^{k+1}$-symmetric convex fans

The Yuan-Tseh Lee Array for Microwave Background Anisotropy

The Yuan-Tseh Lee Array for Microwave Background Anisotropy (AMiBA) is the first interferometer dedicated to studying the cosmic microwave background (CMB) radiation at 3mm wavelength. The choice of 3mm was made to minimize the contributions from foreground synchrotron radiation and Galactic dust emission. The initial configuration of seven 0.6m telescopes mounted on a 6-m hexapod platform was dedicated in October 2006 on Mauna Loa, Hawaii. Scientific operations began with the detection of a number of clusters of galaxies via the thermal Sunyaev-Zel'dovich effect. We compare our data with Subaru weak lensing data in order to study the structure of dark matter. We also compare our data with X-ray data in order to derive the Hubble constant.Comment: accepted for publication in ApJ (13 pages, 7 figures); a version with high resolution figures available at http://www.asiaa.sinica.edu.tw/~keiichi/upfiles/AMiBA7/pho_highreso.pd

Lie transformation groups and differential geometry

SIGLETIB: RN 4586 (150) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

On the method of infinitesimal symmetrization and the formula of the volume of tetrahedons in spherical or hyperbolic spaces

SIGLETIB: RN 4586 (151) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Pressure distention compared with pharmacologic relaxation in vein grafting upregulates matrix metalloproteinase-2 and -9

ObjectiveAutogenous vein bypasses are a common and effective method to treat occlusive disease. During surgical preparation, veins are routinely pressure distended to overcome vasospasm and twists. Distention, however, is believed to promote vascular remodeling and contribute to decreased graft patency. Pharmacologic vasorelaxation with a combination of effective vasodilators has been suggested as an alternative to pressure distention. The extracellular matrix (ECM)-degrading matrix metalloproteinases (MMPs) have been implicated in vascular remodeling and neointima formation. The purpose of the present study was to compare the effects of pressure distention with pharmacologic vasorelaxation on graft remodeling and regulation of MMP-2 and MMP-9 in porcine vein grafts.MethodsCarotid artery bypass utilizing internal jugular veins was performed in eight female white pigs. Jugular veins were randomized to receive pressure distention (300 mm Hg for 2 minutes) or a combination of vasodilators (the α-adrenergic antagonist phenoxybenzamine, 10 μmol/L; the Rho-kinase inhibitor HA-1077 [fasudil], 50 μmol/L; and the calcium-channel blocker nicardipine, 1 μmol/L) for 30 minutes and then were grafted into the carotid arteries. Two weeks after surgery, vein graft samples were analyzed for vessel intimal and medial area, lumen diameter, and ECM composition. Molecular analysis using reverse transcription-polymerase chain reaction, Western immunoblotting, gelatin zymography, and reverse zymography were performed to study the expression and activation of MMP-2 and MMP-9, and tissue inhibitors of MMP (TIMP)-1 and TIMP-2.ResultsPressure distention irreversibly overstretched the porcine jugular vein and increased MMP-2 and MMP-9 proteolytic activity by 40% and 77%, respectively. Two weeks of vein grafting in the carotid arterial bed induced vessel wall thickening, ECM modification, and neointima formation, which were more pronounced in the distended grafts (P < .05) and accompanied by an increase in MMP expression and activity. Distended grafts demonstrated higher percentages of active MMP-9 (17.8% ± 1.0%) and higher activities of latent (35.5% ± 3.3%) and active MMP-2 (69.6% ± 8.8%) than the pharmacologically treated grafts. Protein expression of TIMP-1 and TIMP-2 was downregulated after arterial grafting, but the pharmacologically treated grafts expressed significantly more TIMP-1 protein (by 36.8% ± 4.1%) than the distended ones. The activities of TIMPs were markedly decreased after grafting, contributing to the upregulated MMP activity.ConclusionsPressure distention of vein grafts before implantation, compared with pharmacologic vasodilatation, stimulates neointima formation and augments MMP activities. Pharmacologic vasorelaxation may be clinically superior to distention in attenuating graft remodeling and possibly improving graft patency.Clinical RelevanceAutogenous vein bypasses are a common and effective method to treat occlusive disease. This study demonstrated that pressure distention, a common preparatory procedure in bypass surgery, upregulates extracellular matrix-degrading matrix metalloproteinases, which predisposes vein grafts to extensive remodeling and contributes to neointima formation and graft occlusion. The topical application of a combination of vasodilators to the vein graft before implantation may be clinically superior to pressure distention in attenuating graft remodeling and may possibly improve graft patency and reduce secondary surgical interventions