Non‐elementary speed‐ups in logic calculi

In this paper we show some non‐elementary speed‐ups in logic calculi: Both a predicative second‐order logic and a logic for fixed points of positive formulas are shown to have non‐elementary speed‐ups over first‐order logic. Also it is shown that eliminating second‐order cut formulas in second‐order logic has to increase sizes of proofs super‐exponentially, and the same in eliminating second‐order epsilon axioms. These are proved by relying on results due to P. Pudlák. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exact bounds on epsilon processes

In this paper we show that the lengths of the approximating processes in epsilon substitution method are calculable by ordinal recursions in an optimal way.     

Total synthesis of the proposed structures of hyacinthacines C2, C3, and their C5-epimers

Synthesis and structural confirmation of highly oxygenated pyrrolizidine alkaloids, hyacinthacines C₂ [(1S,2R,3R,5R,7S,7aR)-3,5-hydroxymethyl-1,2,7-trihydroxypyrrolizidine], C₃[(1S,2R,3R,5S,7R,7aR)-3,5-hydroxymethyl-1,2,7-trihydroxypyrrolizidine], and their C5-epimers were achieved on the basis of the highly divergent method employing (S)-(−)-2-pyrrolidone-5-carboxylic acid as the starting material.     

Corrosion analysis and monitoring of the environmental factors for the deterioration of chromium-bearing reinforcing steel in mortar

To understand environmental factors, Cl ion concentration and pH were monitored by inserting microelectrodes into artificial pores in the mortar. The corrosion behavior of reinforcing steels containing chromium were investigated with carbon steel (SM) by electrochemical impedance spectroscopy (EIS). From the EIS, the corrosion resistance of the Cr-bearing reinforcing steel was visibly higher than the SM reinforcing steel. Simultaneously, the Cl ion concentration in the mortar was obtained using Ag/AgCl microelectrodes, showing that this behavior is generally controlled by diffusion. Similarly, the pH in the mortar was obtained using W/WOx microelectrodes. With a 20-mm cover thickness, pH was limited to approximately pH 11, but with a 10-mm cover thickness, pH continued to decrease to around pH 9.5. Solutions were prepared simulating the condition in the pores in mortar and were used in EIS measurements. The charge transfer resistance, R _ct, in the simulated solutions showed good correspondence with that in the actual mortar. This is attributed to the fact that the corrosion of reinforcing steel was controlled by the solution conditions (mainly Cl concentration and pH) in mortar. Moreover, it was found that, as compared with SM, Cr-bearing steel could keep the passive film in severe condition, and have long incubation time until the passive film was destroyed.     

Consistency proof via pointwise induction

We show that the consistency of the first order arithmetic follows from the pointwise induction up to the Howard ordinal. Our proof differs from U. Schmerl [Sc]: We do not need Girard's Hierarchy Comparison Theorem. A modification on the ordinal assignment to proofs by Gentzen and Takeuti [T] is made so that one step reduction on proofs exactly corresponds to the stepping down in ordinals. Also a generalization to theories of finitely iterated inductive definitions is proved. Received May 30, 1996     

Synthesis,Characterization, and Properties of [4]Cyclo‐2,7‐pyrenylene: Effects of Cyclic Structure on the Electronic Properties of Pyrene Oligomers

A cyclic tetramer of pyrene, [4]cyclo‐2,7‐pyrenylene ([4]CPY), was synthesized from pyrene in six steps and 18 % overall yield by the platinum‐mediated assembly of pyrene units and subsequent reductive elimination of platinum. The structures of the two key intermediates were unambiguously determined by X‐ray crystallographic analysis. DFT calculations showed that the topology of the frontier orbitals in [4]CPY was essentially the same as those in [8]cycloparaphenylene ([8]CPP), and that all the pyrene units were fully conjugated. The electrochemical analyses proved the electronic properties of [4]CPY to be similar to those of [8]CPP. The results are in sharp contrast to those obtained for the corresponding linear oligomers of pyrene in which each pyrene unit was electronically isolated. The results clearly show a novel effect of the cyclic structure on cyclic π‐conjugated molecules.     

Spontaneous formation of dye-functionalized gold nanoparticles using reverse micellar systems

Detailed exploratory and mechanistic investigations on spontaneous formation of dye-functionalized gold nanoparticles (GNPs) using dye-based reverse micellar systems are described in this publication. The accumulated results from spectroscopic and microscopic investigations demonstrated that water molecules confined within nanoscopic enclosure of the self-assembled reverse micelles played critical role in the redox processes of aurate ions to produce GNPs, which are assumed to have approximately constant size distributions. The resulting dye-functionalized GNPs were found to offer their absorption and fluorescence emission tunability by changing the medium polarity as well as to exhibit excellent film-forming properties to give optically homogeneous polystyrene thin films. These key findings in addition to broad applicability of the self-assembling process with a variety of dye analogues have led to a conclusion that the protocol presented here serves as a versatile synthetic method to provide a potential convenience for future development of new organic-inorganic hybrid nanomaterials.