On the Slowly Well Orderedness of εo

For α < ε₀, N_α denotes the number of occurrences of ω in the Cantor normal form of α with the base ω. For a binary number-theoretic function f let B(K; f) denote the length n of the longest descending chain (α₀, …, α_n–1) of ordinals <ε₀ such that for all i < n, Nα_i ≤ f (K, i). Simpson [2] called ε₀ as slowly well ordered when B (K; f) is totally defined for f (K; i) = K · (i+ 1). Let |n| denote the binary length of the natural number n, and |n|_k the k-times iterate of the logarithmic function |n|. For a unary function h let L(K; h) denote the function B (K; h₀(K; i)) with h₀(K, i) = K + |i| · |i|_h(i). In this note we show, inspired from Weiermann [4], that, under a reasonable condition on h, the functionL (K; h) is primitive recursive in the inverse h^–1 and vice versa.     

Ordinal diagrams for recursively Mahlo universes

In this paper we introduce a recursive notation system of ordinals. An element of the notation system is called an ordinal diagram following G. Takeuti [25]. The system is designed for proof theoretic study of theories of recursively Mahlo universes. We show that for each in KPM proves that the initial segment of determined by is a well ordering. Proof theoretic study for such theories will be reported in [9]. Received: 13 January, 1998     

Total Synthesis of Decahydroquinoline Poison Frog Alkaloids ent-cis-195A and cis-211A

The total synthesis of two decahydroquinoline poison frog alkaloids ent-cis-195A and cis-211A were achieved in 16 steps (38% overall yield) and 19 steps (31% overall yield), respectively, starting from known compound 1. Both alkaloids were synthesized from the common key intermediate 11 in a divergent fashion, and the absolute stereochemistry of natural cis-211A was determined to be 2R, 4aR, 5R, 6S, and 8aS. Interestingly, the absolute configuration of the parent decahydroquinoline nuclei of cis-211A was the mirror image of that of cis-195A, although both alkaloids were isolated from the same poison frog species, Oophaga (Dendrobates) pumilio, from Panama.     

Influence of N-Substituents on Photovoltaic Properties of Singly Bay-Linked Dimeric Perylene Diimides

The influence of N-substituents on the photovoltaic properties of singly bay-linked perylene diimides (diPDIs) was systematically investigated to understand the aromatic-aliphatic balance, which is beneficial for achieving high device performance in organic photovoltaic (OPV) systems. The synthesis of various N-substituted diPDIs was successfully achieved using a newly developed one-step procedure, resulting in sufficiently high yields. Detailed investigations of seven variants of diPDIs demonstrated that the primary alkyl substituents, particularly the 2-ethylhexyl group, induce the self-organized growth of thin films with high crystallinity. This is beneficial for enhancing the device performance of bulk heterojunction (BHJ) systems. The results presented herein reveal the important roles of alkyl side chains as hydrophobic solubilizing auxiliaries or primary determinants in the control of the active layer nanomorphology. This offers a valuable guideline that is essential for developing high-performance organic semiconductor materials for future practical applications.     

Di-, tri-, and tetra-arylterephthalic acids as novel clathrate host compounds

Novel terephthalic acid host compounds having aromatic substituent 1-4 have been prepared and their inclusion properties were investigated. These host compounds enclathrated several kinds of alcohols, ethers, ketones, amides, and sulfoxides. The X-ray structures of 1:1 2a/EtOH, 1:2 2b/DMF, 1:2 3/MeOH, and 1:1 4/EtOH complexes revealed complexation mode.     

Subterranean electrical structure of Kozu-shima volcanic island, Japan

Following the electric current injection experiment carried out in 2009, a VLF-MT (Very Low Frequency Magnetotelluric) survey has been conducted in Kozu-shima Island to obtain further information on the subterranean electrical structure that might help understanding the results of our monitoring of geoelectric potentials. A number of VAN-type pre-seismic geoelectric potential anomalies were observed in 1997-2000, even showing a remarkable "Selectivity". However, similar pre-seismic anomalies were not observed during the Izu-Island volcano-seismic swarm 2000. All these observations would require extremely high degree of heterogeneity in the subterranean electrical structure of the volcanic island and its possible time changes. Several correlations between the results of this survey and the volcanic geology of the island and ground water distribution were found. Further investigation is needed for a complete explanation of the observed phenomena.     

Derivatives of normal functions and $$\omega $$-models

In this note the well-ordering principle for the derivative \(\mathsf{g}^{\prime }\) of normal functions \(\mathsf{g}\) on ordinals is shown to be equivalent to the existence of arbitrarily large countable coded \(\omega \)-models of the well-ordering principle for the function \(\mathsf{g}\).     

Wellfoundedness proofs by means of non-monotonic inductive definitions II: First order operators

In this paper, we give two proofs of the wellfoundedness of a recursive notation system for Π_N-reflecting ordinals. One is based on distinguished classes, and the other is based on -inductive definitions.     

First total synthesis and absolute stereochemical assignment of vittarilide-A,an antioxidant extractive component isolated from Vittaria anguste-elongata Hayata

The first stereocontrolled synthesis of vittarilide-A and its C5-epimer was completed from d-glucuronolactone. Comparison with the spectroscopic properties reported for authentic material has given a clear indication as to the absolute stereochemistry of the natural vittarilide-A.