Epsilon substitution method for theories of jump hierarchies

 We formulate epsilon substitution method for theories (H)_α0 of absolute jump hierarchies, and give two termination proofs of the H-process: The first proof is an adaption of Mints M, Mints-Tupailo-Buchholz MTB, i.e., based on a cut-elimination of a specially devised infinitary calculus. The second one is an adaption of Ackermann Ack. Each termination proof is based on transfinite induction up to an ordinal θ(α₀+ ω)0, which is best possible. Received: 19 April 1999 / Published online: 20 December 2001     

A novel photorearrangement of a cyclohexadiene derivative of C60

[reaction: see text] Photorearrangement of tetraalkoxycarbonyl-substituted cyclohexadiene derivatives of C(60) yields not only well-known bis(fulleroid) but also bis(methano)fullerene. Existence of a labile and structurally new intermediate is observed in the reaction mixture. The discovery of the compound suggests the existence of another possible pathway giving those two products other than the widely accepted [4 + 4]/[2 + 2 + 2] mechanism.     

Syntheses of dibenzo[c,e][1,2]diselenin and related novel chalcogenide heterocyclic compounds

Reaction of 2,2′-dilithio-1,1′-binaphthyl with selenium followed by air oxidation gives a mixture of dinaph-thoselenophene and dimer and oligomers of 2,2′-diseleno-1,1′-binaphthyl. 2,2′-Dilithio-1,1′-biphenyl reacts with selenium to afford dibenzo[c,e][1,2]diselenin. Structures of the dimeric 2,2′-diseleno-1,1′-binaphthyl and dibenzo[c,e][1,2]diselenin have been confirmed by X-ray crystallographic analyses. Similar reaction of 2,2′-dilithio-1,1′-binaphthyl with sulfur or tellurium gives a mixture of dinaphthothiophene and dinaphtho[2,1-c:-1′,2′-e][1,2]dithiin or a mixture of dinaphthotellurophene and oligomer of 2,2′-ditelluro-1,1′-binaphthyl, respectively. Dibenzotellurophene and oligomer of 2,2′-ditelluro-1,1′-biphenyl are obtained from reaction of 2,2′-dilithio-1,1′-biphenyl with tellurium.     

Adsorption-induced intramolecular dipole: correlating molecular conformation and interface electronic structure

The interfaces formed between pentacene (PEN) and perfluoropentacene (PFP) molecules and Cu(111) were studied using photoelectron spectroscopy, X-ray standing wave (XSW), and scanning tunneling microscopy measurements, in conjunction with theoretical modeling. The average carbon bonding distances for PEN and PFP differ strongly, that is, 2.34 A for PEN versus 2.98 A for PFP. An adsorption-induced nonplanar conformation of PFP is suggested by XSW (F atoms 0.1 A above the carbon plane), which causes an intramolecular dipole of approximately 0.5 D. These observations explain why the hole injection barriers at both molecule/metal interfaces are comparable (1.10 eV for PEN and 1.35 eV for PFP) whereas the molecular ionization energies differ significantly (5.00 eV for PEN and 5.85 eV for PFP). Our results show that the hypothesis of charge injection barrier tuning at organic/metal interfaces by adjusting the ionization energy of molecules is not always readily applicable.     

Curved Perylene Diimides Fused with Seven-Membered Rings

Curved perylene diimides fused with seven-membered rings have been synthesized using a regioselective bay-functionalization method and Pd-catalyzed intramolecular C−H/C−Br coupling reaction. X-Ray analysis and temperature-dependent NMR spectroscopy revealed the curved molecular structure with a certain degree of conformational flexibility. The curved and expanded π-conjugation altered the electronic properties while retaining the intrinsic properties of the parent perylene diimide. Despite the absence of solubilizing N-substituents, the curved perylene diimides showed sufficient solubility for application in solution-processed organic photovoltaic devices. The devices showed superior performance with a power conversion efficiency of up to 2.76% due to suppressed charge recombination. Our detailed investigations suggest that the introduction of a curved structure enables the removal of the bulky N-substituents, which is an effective way to achieve a thin-film morphology suitable for photoelectric conversion.     

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.