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.     

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.     

Molecular shape of palytoxin in aqueous solution

Palytoxin, one of the most toxic non-peptide substances, formed an associated dimer of 5 nm length in aqueous solution.     

Probability Distribution on Full Rooted Trees

The recursive and hierarchical structure of full rooted trees is applicable to statistical models in various fields, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is not a random variable; as such, model selection to avoid overfitting is problematic. One method to solve this problem is to assume a prior distribution on the full rooted trees. This enables the optimal model selection based on Bayes decision theory. For example, by assigning a low prior probability to a complex model, the maximum a posteriori estimator prevents the selection of the complex one. Furthermore, we can average all the models weighted by their posteriors. In this paper, we propose a probability distribution on a set of full rooted trees. Its parametric representation is suitable for calculating the properties of our distribution using recursive functions, such as the mode, expectation, and posterior distribution. Although such distributions have been proposed in previous studies, they are only applicable to specific applications. Therefore, we extract their mathematically essential components and derive new generalized methods to calculate the expectation, posterior distribution, etc.