• Journal for History of Mathematics
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• v.24 no.3
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• pp.59-76
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• 2011

Starting from a collection V as a model which satisfies the axioms of NBG, we call the elements of V as sets and the subcollections of V as classes. We reconstruct the G$\ddot{o}$del's proof of the consistency of GCH and AC with the axioms of Zermelo-Fraenkel set theory by using Mostowski-Shepherdson mapping theorem, reflection principles in Tarski-Vaught theorem and Montague-Levy theorem and the fact that NBG is a conservative extension of ZF.

• The Journal of the Korea Contents Association
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• v.10 no.5
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• pp.10-19
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• 2010

Korean word spacing rules have exceptional cases which permit both spacing and no-spacing between words. The exceptional cases, however, do not mean that inconsistent spacing between words or word-phrases is legitimate in a document proof reading. This paper proposes a word spacing consistency check method using syllable and morpheme information, and evaluated it through experiment.

• Journal of Venture Innovation
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• v.1 no.2
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• pp.1-12
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• 2018

The applications of psychology principles in marketing areas were pervasived. As the importance of digital marketing has increased, the cases of applications of psychology principles in digital marketing areas also has increased. This study analnyzed digital marketing cases based on the psychology principles of social proof, scarcity and loss aversion, reciprocity, commitment and consistency, anchoring. Cases were analnyzed amomg USA and Korea in digital marketing areas. This attempt will facilitating interdisciplinary research. It also will improve customer engagement, increase customer life value, and develope virtuous circle of customer journey through optimal user interface and message strategies.

• The Transactions of the Korea Information Processing Society
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• v.6 no.11
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• pp.2965-2980
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• 1999

There are several models and the corresponding diagrams to express software system in many kinds of viewpoints, but these are supposed to be integrated and implemented into only one system. Therefore, the software modelers should have the models ensuring the consistency between information in software development life cycle. To support the robust models for modelers using OO modeling methods, i.e. UML, and CASE tools, the meta models of the software architecture and the consistency rules between the models are suggested in this thesis. Finally, the rules are implemented in the OO CASE tool, DEBUTO(Design By UML Tool). It supports UML1.1 notations and has visual modeling editors that enable users make their own software model.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.37-58
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• 2011

The development of recent Mathematical Logic is mostly originated in Hilbert's Proof Theory. The purpose of the plan so called Hilbert's Program lies in the formalization of mathematics by formal axiomatic method, rescuing classical mathematics by means of verifying completeness and consistency of the formal system and solidifying the foundations of mathematics. In 1931, the completeness encounters crisis by the existence of undecidable proposition through the 1st Theorem of G?del, and the establishment of consistency faces a risk of invalidation by the 2nd Theorem. However, relative of partial realization of Hilbert's Program still exists as a fruitful research program. We have tried to bring into relief through Curry-Howard Correspondence the fact that Hilbert's program serves as source of power for the growth of mathematical constructivism today. That proof in natural deduction is in truth equivalent to computer program has allowed the formalization of mathematics to be seen in new light. In other words, Hilbert's program conforms best to the concept of algorithm, the central idea in computer science.

• Journal of the Korean Statistical Society
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• v.36 no.4
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• pp.471-477
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• 2007

In this paper, we provide a new proof to correct the asymptotic normality for the estimate $\hat{C}_{pmk}\;of\;C_{pmk}$, which is one of the well-known definitions of the process capability index. Also we comment briefly on the correction of the limiting distribution for $\hat{C}_{pmk}$ and on the use of re-sampling methods for the inference of $C_{pmk}$. Finally we discuss the concept of asymptotic unbiasedness.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.467-478
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• 1999

This paper deals with the problem of change-point estimation where there is one level change in location with iid errors. A change-point estimator using rank average is proposed with the proof of its consistency. A comparison study of various change-point estimators is done by simulation on the mean the proportion and the variance when the errors are from the normal and the double exponential distributions.

• Korean Journal of Logic
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• v.15 no.1
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• pp.155-190
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• 2012

As far as Hilbert's Program is concerned, there seems to be important differences in the development of Wittgenstein's thoughts. Wittgenstein's main claims on this theme in his middle period writings, such as Wittgenstein and the Vienna Circle, Philosophical Remarks and Philosophical Grammar seem to be different from the later writings such as Wittgenstein's Lectures on the Foundations of Mathematics (Cambridge 1939) and Remarks on the Foundations of Mathematics. To show that differences, I will first briefly survey Hilbert's program and his philosophy of mathematics, that is to say, formalism. Next, I will illuminate in what respects Wittgenstein was influenced by and criticized Hilbert's formalism. Surprisingly enough, Wittgenstein claims in his middle period that there is neither metamathematics nor proof of consistency. But later, he withdraws his such radical claims. Furthermore, we cannot find out any evidences, I think, that he maintained his formerly claims. I will illuminate why Wittgenstein does not raise such claims any more.

• International Journal of Railway
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• v.5 no.2
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• pp.65-70
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• 2012

This paper introduced a novel railway system, Automatic Train Protection and Block (ATPB) briefly, which is proposed to improve the efficiency of existing regional train lines with low cost in Japan. The biggest superiority of ATPB system is a great use of universal and mature technologies, such as GPS and regular mobile telephone networks, so that there is nearly no increment of trackside equipments in the reconstruction. Then in order to guarantee the system safety, a formal model of ATPB is established and analyzed by formal method VDM++. Firstly, the specification is specified by VDM++ formally without ambiguity. Secondly, its internal consistency is proved by discharging the proof obligations. And finally, its satisfiability is checked by systematic testing, which executes specification and checks the outputs against corresponding inputs.