Real hypersurfaces in complex two-plane Grassmannians with commuting restricted Jacobi operators

In this paper, we have considered a new commuting condition, that is, $(R_\xi\phi) S = S (R_\xi\phi)$ \big(resp. (\Bar{R}_N\phi) S = S (\Bar{R}_N\phi)\big) between the restricted Jacobi operator~$R_\xi\phi$ (resp. \Bar{R}_N\phi), and the Ricci tensor $S$ for real hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$. In terms of this condition we give a complete classification for Hopf hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$

Singlet oxygen quenching by deoxygadusol and related mycosporine-like amino acids from phytoplankton Prorocentrum micans

Deoxygadusol (DG) and structurally related mycosporine-like amino acids, i.e. mycosporine glycine (MG) and mycosporine taurine (MT), were isolated from phytoplankton Prorocentrum micans and studied for the reactivity toward singlet oxygen. These water-soluble compounds with a cyclohexenone chromophore were all shown to be highly effective in quenching singlet oxygen

Lie Derivatives and Ricci Tensor on Real Hypersurfaces in Complex Two-plane Grassmannians

On a real hypersurface M in a complex two-plane Grassmannian Gz(Cm+z) we have the Lie derivation L and a diòerential operator of order one associated with the generalized Tanaka– Webster connection L(k). We give a classiûcation of real hypersurfaces M on Gz(Cm+z) satisfying L (k) S = L S, where epsilon is the Reeb vector ûeld on M and S the Ricci tensor of M

Ankle MRI for Anterolateral Soft Tissue Impingement: Increased Accuracy with the Use of Contrast-Enhanced Fat-Suppressed 3D-FSPGR MRI

OBJECTIVE: To validate the use of contrast-enhanced (CE) fat-suppressed three-dimensional (3D) fast gradient-recalled acquisition in the steady state with radiofrequency spoiling (FSPGR) magnetic resonance imaging (MRI) for the diagnosis of anterolateral soft tissue impingement of the ankle, as compared to the use of routine ankle MRI. MATERIALS AND METHODS: Contrast-enhanced fat-suppressed 3D-FSPGR MRI and routine MRI scans were retrospectively reviewed for 45 patients with arthroscopically proven anterolateral impingement. In addition, scans were reviewed in 45 control subjects with diagnoses other than impingement. Two radiologists independently reviewed the two sets of images in random order. Using areas (Az) under the receiver operating characteristic curve (ROC), we compared the depiction of anterolateral soft tissue impingement in the two sets of images. RESULTS: The overall accuracy for lesion characterization was significantly higher (p < 0.05) using the CE fat-suppressed 3D-FSPGR MR images (Az = 0.892 and 0.881 for reader 1 and 2, respectively) than using the routine MR images (Az = 0.763 and 0.745). The use of CE fat-suppressed 3D-FSPGR MRI enhanced impingement depiction in most cases. However, in cases with a thickened non-enhancing scar or joint effusion, the routine images better depicted a soft tissue mass that intruded into anterolateral gutter than the CE images. CONCLUSION: The use of CE fat-suppressed 3D-FSPGR MRI of the ankle allows a more accurate assessment of anterolateral soft tissue impingement of the ankle, as compared to the use of routine MRIope