• Korean Journal of Mathematics
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• v.6 no.2
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• pp.313-318
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• 1998

In this paper we prove two independent theorems concerning formality of a nilmanifold and a differential graded algebra using the well-known theorem of Deligne-Griffiths-Morgan-Sullivan. We first give a rational homotopy theoretic proof to the statement that a nilmanifold is formal if and only if it is a torus. And then we study some conditions with which formality of one dga implies formality of the other in an extension of dga's.

• Journal of the Korean School Mathematics Society
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• v.14 no.3
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• pp.325-337
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• 2011

There have been several studies regarding strict and formal proof in the field of geometry in middle school curriculum, and the level of proof has been gradually lowered along with the changes in the curriculum. In the 2011 Revised Middle School Math Curriculum, there have been efforts to eliminate the term 'proof' and instead to replace it with the new one, 'justification'. Therefore, this study intends to present specific and practical examples of justification by analyzing the current math textbook especially in the field of geometry. As a result, it identified that strict and practical proof has been sharply increased in the second year of middle school. It also witnessed the possibility of justification from the various examples presented in the first, second, and the third year of the middle school math textbook.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.55-70
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• 2008

This study is about the Data which is one of Euclid's writing. It dealt with the organization of contents, formal system and mathematical meaning. First, we investigated the organization of contents of the Data. Second, on the basis of this investigation, we analyzed the formal system of the Data. It contains the analysis of described method of definition, proposition, proof and the meaning of 'given'. Third, we explored the mathematical meaning of the Data which can be classified as algebraic point of view, geometric point of view and the opposite point of view to 'The Elements'.

• Nuclear Engineering and Technology
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• v.31 no.2
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• pp.157-171
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• 1999

In this work, an automatic software verification method for Nuclear Power Plant (NPP) protection system is developed. This method utilizes Colored Petri Net (CPN) for system modeling and Prototype Verification System (PVS) for mathematical verification. In order to help flow-through from modeling by CPN to mathematical proof by PVS, an information extractor from CPN models has been developed in this work. In order to convert the extracted information to the PVS specification language, a translator also has been developed. ML that is a higher-order functional language programs the information extractor and translator. This combined method has been applied to a protection system function of Wolsong NPP SDS2(Steam Generator Low Level Trip). As a result of this application, we could prove completeness and consistency of the requirement logically. Through this work, in short, an axiom or lemma based-analysis method for CPN models is newly suggested in order to complement CPN analysis methods and a guideline for the use of formal methods is proposed in order to apply them to NPP Software Verification and Validation.

• Journal of Korean Philosophical Society
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• v.147
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• pp.215-237
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• 2018

The purpose of this study is to illuminate the precise nature and the central line of Kant's proof of the causal principle stated in the Second Analogy of the 2nd. edition of the Critique of Pure Reason. The study argues for the following thesis: 1. The proof of the Second Analogy concerns only the causal principle called the "every-event-some-cause" principle, and not the causal law(s) called the "same-cause-same-event" principle. 2. The goal of the proof is to establish the possibility of knowledge of an temporal order of successive states of an object. 3. The proof is broadly an single transcendental argument in two steps. The 1st. step is an analytic argument that infers from the given perceptions of an oder of successive states of an objects to the conclusion that the causal principle is the necessary condition for the objectivity of dies perceived order. The 2nd. step is a synthetic argument that infers from the formal nature of time to the conclusion that the causal principle is a necessary condition for die possibility of objective alterations and of empirical knowledge of these alterations. 4. The poof involves not the 'non sequitur' assumed by P. F. Strawson, that is, Kant infers not directly from a feature of our perceptions to a conclusion regarding the causal relations of distinct states of affairs that supposedly correspond to these perceptions.

• Journal of Computing Science and Engineering
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• v.6 no.4
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• pp.310-319
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• 2012

Next generation wireless receivers demand low computational complexity algorithms with high computing power in order to perform fast signal detections and error estimations. Several signal detection and estimation algorithms have been proposed for next generation wireless receivers which are primarily designed to provide reasonable performance in terms of signal to noise ratio (SNR) and bit error rate (BER). However, none of them have been chosen for direct implementation as they offer high computational complexity with relatively lower computing power. This paper presents a low-complexity power-efficient algorithm that improves the computing power and provides relatively faster signal detection for next generation wireless multiuser receivers. Measurement results of the proposed algorithm are provided and the overall system performance is indicated by BER and the computational complexity. Finally, in order to verify the low-complexity of the proposed algorithm we also present a formal mathematical proof.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.4
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• pp.2219-2236
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• 2017

With cloud storage services, users can handle an enormous amount of data in an efficient manner. However, due to the widespread popularization of cloud storage, users have raised concerns about the integrity of outsourced data, since they no longer possess the data locally. To address these concerns, many auditing schemes have been proposed that allow users to check the integrity of their outsourced data without retrieving it in full. Yuan and Yu proposed a public auditing scheme with a deduplication property where the cloud server does not store the duplicated data between users. In this paper, we analyze the weakness of the Yuan and Yu's scheme as well as present modifications which could improve the security of the scheme. We also define two types of adversaries and prove that our proposed scheme is secure against these adversaries under formal security models.

• Asia pacific journal of information systems
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• v.16 no.4
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• pp.151-178
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• 2006

The objective of this research is to develop a formal framework and methodology to facilitate real-time data integration, thus enabling semantic interoperability among distributed and heterogeneous information systems. The proposed approach is based on the concepts of "ontology" and "semantic mediators." An ontology is developed and used to capture the intension (including structure, integrity rules and meta-properties) of the database schema. We also develop the agent communication protocol for semantic reconciliation, which is based on the theory of speech acts and agent communication language. This protocol is used by a set of semantic mediators, which automatically detect and resolve various semantic conflicts at the data- and schema-levels by referring to the ontology. A mediation-based query processing technique is developed to provide uniform and integrated access to the multiple heterogeneous information sources. Prototype tools are being implemented to provide proof of concept for this work.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.5
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• pp.1904-1919
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• 2015

Deniable authentication protocol allows a sender to deny his/her involvement after the protocol run and a receiver can identify the true source of a given message. Meanwhile, the receiver has no ability to convince any third party of the fact that the message was sent by the specific sender. However, most of the proposed protocols didn't achieve confidentiality of the transmitted message. But, in some special application scenarios such as e-mail system, electronic voting and Internet negotiations, not only the property of deniable authentication but also message confidentiality are needed. To settle this problem, in this paper, we present a non-interactive identity-based deniable authenticated encryption (IBDAE) scheme using pairings. We give the security model and formal proof of the presented IBDAE scheme in the random oracle model under bilinear Diffie-Hellman (BDH) assumption.

• Proceedings of the KSR Conference
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• 1998.05a
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• pp.408-418
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• 1998

This paper presents the implementation of comparator which is self-testing with respect to the faults caused by any single physical defect likely to occur in NMOS and CMOS integrated circuit. The goal is to use it for the fault-tolerant system. First, a new fault model for PLA(Programmable Logic Array) is presented. This model reflects several physical defects in VLSI circuits. It focuses on the designs based on PLA because VLSI chips are far too complex to allow detailed analysis of all the possible physical defects that can occur and of the effects on the operation of the circuit. Second, this paper shows that these design, which has been implemented with 2 level AND-ORor NOR-NOR circuit, are optimal in term of size. And it also presents a formal proof that a comparator implemented using NOR-NOR PLA, based on these design, is sol f-testing with respect to most single faults in the presented fault model. Finally, it discusses the application of the self-testing comparator as a building block for the implementation of the fault-tolerant system.