Splitting ρκλ into maximally many stationary sets

Letκ >ω be a regular cardinal and λ >κ a cardinal. Solovay’s classical result for κ[So] led Menas [Me] to conjecture that a stationary subset ofP _κλ would split into λ^<κ stationary set of size κ⁺ (see[BT]), the conjecture implies that the size is (κ⁺)^<κ as well. Part of this work was done during the author’s stay at Boston University as one of the Japanese Overseas Research Fellows. He gratefully acknowledge Professor Akihiro Kanamori’s hospitality. He also wishes to thank members of the set theory seminar at Waseda University for their interest at the early stage.     

Luminescent Heteropolynuclear Complexes of 3,5‐Dimethylpyrazolate [Pt2Au2M2(Me2pz)8] (M=Ag,Cu) Showing the Synergistic Effect of Three Transition Elements in the Excited State

Swap the coins! The Pt₂Au₂, Pt₂Au₂Cu₂, and Pt₂Au₂Ag₂ complexes of 3,5‐dimethylpyrazolate exhibit yellow‐green, orange, and sky‐blue luminescence, respectively (see figure). The emission energies of Pt₂Au₂M₂ complexes can be controlled by the change of the third coinage metal ions M. The Pt₂Au₂M₂ complexes take the cis configuration with respect to the Au₂M₂ plane.

     

Yield process of mild steel in plane problems

The analysis of the yield process of mild steel in the plane problems is presented. The continuously distributed dislocations model of the edge component type is adapted with a new application technique as the method of solving the elastic-plane problems. Hahn's equation and the criterion of yield initiation proposed in the previous work [1] are employed as the constitutive relations of mild steel. Examples are taken for the bending of straight beams which is known to accompany the particular patterns with wedge-type plastic-zones. The calculated plastic-zone patterns exhibit close resemblance to the actually observed ones and the scale effect of the patterns given by the analysis is reconfirmed by the related pure bending experiments.     

Synthesis of the epimer of pericosine B from (-)-quinic Acid

Synthesis of the epimer of pericosine B from (-)-quinic acid was achieved. This synthesis involves some regioselective and stereoselective processes. The desired product showed lower cytotoxic activity in comparison with natural pericosine B against the P388 leukemia cell line. The result implies that the stereocenter of C-6 in natural pericosine B plays an important role in this activity.     

First total synthesis of antitumor natural product (+)- and (-)-pericosine A: determination of absolute stereo structure

The first total synthesis of (+)- and (-)-pericosine A has been achieved, enabling the revision and determination of the absolute configuration of this antitumor natural product as methyl (3S,4S,5S,6S)-6-chloro-3,4,5-trihydroxy-1-cyclohexene-1-carboxylate. Every step of this total synthesis proceeded well with excellent stereoselectivity. Structures of the intermediates in crucial steps were confirmed by detailed 2D NMR analysis.     

Eigenvalues and suspension structure of compact Riemannian orbifolds with positive Ricci curvature

Let M be a compact n-dimensional Riemannian orbifold of Ricci curvature ≥n−1. We prove that for 1 ≤k≤n, the k ^th nonzero eigenvalue of the Laplacian on M is equal to the dimension n if and only if M is isometric to the k-times spherical suspension over the quotient S ^{n − k} }Γ of the unit (n−k)-sphere by a finite group Γ⊂O(n−k+1) acting isometrically on S ^{n − k} ⊂ℝ ^{n − k +}. Received: 21 September 1998 / Revised version: 23 February 1999