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41.
    
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)  相似文献   
42.
    
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.  相似文献   
43.
    
A novel and simple method that combines an online concentration technique with an enantioseparation technique for capillary electrophoresis—namely, cation‐selective exhaustive injection and sweeping cyclodextrin‐modified micellar electrokinetic chromatography (CSEI‐sweeping CD‐modified MEKC)—realizes the effective enantioseparation of cationic analytes while keeping a significant increase of detection sensitivity. This technique consists of a slight modification of the basic CSEI‐sweeping MEKC. The main idea is to simply add an anionic CD as a chiral selector into the micellar buffer including sodium dodecyl sulfate, but not to change any other buffers in order to preserve the online concentration mechanism. When applied to analysis of the street drug, methamphetamine, the method achieved not only a baseline enantioseparation but also limits of detection (LODs; S/N = 3) of 70–90 pg/mL (ppt) for each isomer. This translates to a more than 10 000‐fold improvement compared to the LODs by the usual injection method. The present technique, which was made from a slight modification of CSEI‐sweeping MEKC, would give an attractive approach that is applicable to almost any analytes for which CSEI‐sweeping MEKC is applicable; all that is required is the selection of an appropriate anionic CD to be added to the micellar buffer.  相似文献   
44.
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  相似文献   
45.
46.
    
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.  相似文献   
47.
    
Most previous studies on lossless image compression have focused on improving preprocessing functions to reduce the redundancy of pixel values in real images. However, we assumed stochastic generative models directly on pixel values and focused on achieving the theoretical limit of the assumed models. In this study, we proposed a stochastic model based on improper quadtrees. We theoretically derive the optimal code for the proposed model under the Bayes criterion. In general, Bayes-optimal codes require an exponential order of calculation with respect to the data lengths. However, we propose an algorithm that takes a polynomial order of calculation without losing optimality by assuming a novel prior distribution.  相似文献   
48.
Synchrotron x-ray diffraction reciprocal space mapping was performed on perfluoropentacene (PFP) thin films on SiO2 in order to determine the crystal structure of a novel, substrate-induced thin film phase to be monoclinic with unit cell parameters of a = 15.76 +/- 0.02 A, b = 4.51 +/- 0.02 A, c = 11.48 +/- 0.02 A, and beta = 90.4 +/- 0.1 degrees . Moreover, layered and co-deposited heterostructures of PFP and pentacene (P) were investigated by specular and grazing-incidence x-ray diffraction, atomic force microscopy, and Fourier-transform infrared spectroscopy. For a ca. three-monolayers-thick PFP film grown on a P underlayer, slightly increased lattice spacing was found. In contrast, co-deposited P/PFP films form a new mixed-crystal structure with no detectable degree of phase separation. These results highlight the structural complexity of these technically relevant molecular heterojunctions for use in organic electronics.  相似文献   
49.
Palytoxin, one of the most toxic non-peptide substances, formed an associated dimer of 5 nm length in aqueous solution.  相似文献   
50.
Three novel compounds, yoshinones A, B1, and B2, were isolated from the marine cyanobacterium Leptolyngbya sp., and their structures were elucidated by NMR spectral analysis. Yoshinone A, but not yoshinone B1 or B2, inhibited the differentiation of 3T3-L1 cells into adipocytes. In addition, yoshinone A did not exhibit cytotoxicity, suggesting that yoshinone A may be useful in studies on the treatment of obesity.  相似文献   
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