The rhizome of Cyperus rotundus was assessed for its cytoprotective effects against ethanol induced gastric damage. Decoctions of Rhizoma Cyperi were given orally (1.25, 2.5, 4.0 g crude drug/kg) to rats 30 min before ethanol (40% v/v, 10 mL/kg) was administered. The decoction showed an ulcer inhibitory effect in a dose dependent manner. Moreover, the activity was also observed when the decoction was given subcutaneously (0.3–0.6 g/kg), suggesting that the herb possessed systemic effects on protecting the stomach. Compared with controls, gastric motility of the ethanol‐treated rats was delayed significantly by either oral (2.5–4.0 g/kg) or subcutaneous (0.3 g/kg) administration of the decoction. Pretreatment of rats with indomethacin (5 mg/kg) significantly reduced the gastric protective action of C. rotundus. Mucus content in the stomach was not affected by administration of the docoction. The findings in this study suggest that the protective action of C. rotundus is related to its inhibition of gastric motility and endogeneous prostaglandins may play an important role. © 1997 John Wiley & Sons, Ltd.

Abstract. This paper studies, using the Bochner technique, a sharp lower bound of the first eigenvalue of a subelliptic Laplace operator on a strongly pseudoconvex CR manifold in terms of its pseudo-Hermitian geometry. For dimensions greater than or equal to 7, the lower bound under a condition on the Ricci curvature and the torsion was obtained by Greenleaf. We give a proof for all dimensions greater than or equal to 5. For dimension 3, the sharp lower bound is proved under a condition which also involves a distinguished covariant derivative of the torsion.

In the paper, we provide an explicit formula for computing the Webster pseudo Ricci curvature, we also apply this formula to obtain a theorem on characterizing balls by using area and pseudo scalar curvature.

Let f : (C n+1 , 0) → (C, 0) be a holomorphic germ defining an isolated hypersurface singularity V at the origin. Let µ and ν and p g be the Milnor number, multiplicity and geometric genus of (V, 0), respectively. We conjecture that µ ≥ (ν − 1) n+1 and the equality holds if and only if f is a semi-homogeneous function. We prove that this inequality holds for n = 1, and also for n = 2 or 3 with additional assumption that f is a quasihomogeneous function. For n = 1, if V has at most two irreducible branches at the origin, or if f is a quasi-homogeneous function, then µ = (ν − 1) 2 if and only if f is a homogeneous polynomial. For n = 2, if f is a quasihomogeneous function, then µ = (ν − 1) 3 iff 6p g = ν(ν − 1)(ν − 2) iff f is a homogeneous polynomial after biholomorphic change of variables. For n = 3, if f is a quasi-homogeneous function, then µ = (ν − 1) 4 iff 24p g = ν(ν − 1)(ν − 2)(ν − 3) iff f is a homogeneous polynomial after biholomorphic change of variables.

This paper gives an explicit formula for calculating the Webster pseudo torsion for a strictly pseudoconvex pseudo-hermitian hypersurface. As applications, we are able to classify some pseudo torsion-free hypersurfaces, which include real ellipsoids.