• Journal for History of Mathematics
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• v.12 no.2
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• pp.25-39
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• 1999

In Euclidean plane geometry, areas of polygons can be computed through a finite process of cutting and pasting. The Hilbert's third problem is that a theory of volume can not be based on the idea of cutting and pasting. This problem was solved by Dehn a few months after it was posed. The purpose of this article is not only to study Hilbert's third Problem and its proof but also to provide basis for the secondary school mathematics.

• The Mathematical Education
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• v.43 no.1
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• pp.87-96
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• 2004

For finding the optimal strategy in Blackout game which was introduced in the homepage of popular mono "Beautiful mind", we develope a mathematical proof and an algorithm with a software. We only use the concept of basis and knowledge of basic linear algebra. This process can be extended to the fullsize Go table problem and shows why we have to study mathematics at the college level.

• Journal of the Korean Statistical Society
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• v.26 no.2
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• pp.231-243
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• 1997

In this paper we investigate weak convergence of the intergral processes whose index set is the non-compact infinite time interval. Our first goal is to develop the empirical central limit theorem as random elements of [0, .infty.) for an integral process which is constructed from iid variables. In developing the weak convergence as random elements of D[0, .infty.), we will use a result of Ossiander(4) whose proof heavily depends on the total boundedness of the index set. Our next goal is to establish the empirical central limit theorem for the Kaplan-Meier integral process as random elements of D[0, .infty.). In achieving the the goal, we will use the above iid result, a representation of State(6) on the Kaplan-Meier integral, and a lemma on the uniform order of convergence. The first result, in some sense, generalizes the result of empirical central limit therem of Pollard(5) where the process is regarded as random elements of D[-.infty., .infty.] and the sample paths of limiting Gaussian process may jump. The second result generalizes the first result to random censorship model. The later also generalizes one dimensional central limit theorem of Stute(6) to a process version. These results may be used in the nonparametric statistical inference.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.2
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• pp.151-160
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• 2011

Typically, it is hard to find a closed form solution of option pricing formula under an asset governed by a change point process. In this paper we derive a closed-form solution of the valuation function for an American perpetual put option under an asset having a change point. Structural changes are formulated through a change-point process with a Markov chain. The modified smooth-fit technique is used to obtain the closed-form valuation function. We also guarantee the optimality of the solution via the proof of a corresponding verification theorem. Numerical examples are included to illustrate the results.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.2
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• pp.96-103
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• 2011

Rotor grip is used as a component of rotor system in unmanned helicopter. Instead of usual machining, hot forging process has been considered to improve its proof stress against repeated loading conditions and crash in the farm-field. Die design and forming analysis have been performed according to the conditions such as billet volume, flash, cavity filling, and the distribution of damage during the forming by using FE analysis. In the results of analysis, the possibility of structural failure in the model has not been found because its maximum effective stress is much lower than yield strength of the titanium alloy. In the forging die design, flash has been allowed because of low production in the industrial field. Preform design was studied by using FE-analysis, and its optimal dimension was obtained in the hot forging of rotor grip with titanium alloy.

• Smart Structures and Systems
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• v.12 no.1
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• pp.1-22
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• 2013

Magnetic nanoparticle based bioseparation in microfluidics is a multiphysics phenomenon that involves interplay of various parameters. The ability to understand the dynamics of these parameters is a prerequisite for designing and developing more efficient magnetic cell/bio-particle separation systems. Therefore, in this work proof-of-concept experiments are combined with advanced numerical simulation to design and optimize the capturing process of magnetic nanoparticles responsible for efficient microfluidic bioseparation. A low cost generic microfluidic platform was developed using a novel micromolding method that can be done without a clean room techniques and at much lower cost and time. Parametric analysis using both experiments and theoretical predictions were performed. It was found that flow rate and magnetic field strength greatly influence the transport of magnetic nanoparticles in the microchannel and control the capturing efficiency. The results from mathematical model agree very well with experiments. The model further demonstrated that a 12% increase in capturing efficiency can be achieved by introducing of iron-grooved bar in the microfluidic setup that resulted in increase in magnetic field gradient. The numerical simulations were helpful in testing and optimizing key design parameters. Overall, this work demonstrated that a simple low cost experimental proof-of-concept setup can be synchronized with advanced numerical simulation not only to enhance the functional performance of magneto-fluidic capturing systems but also to efficiently design and develop microfluidic bioseparation systems for biomedical applications.

• ETRI Journal
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• v.9 no.1
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• pp.84-96
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• 1987

The equality relation is very important in mechanical theorem proving procedures. A proposed inference rule called RHU-resolution is intended to extend the hyperparamodulation[23, 9] by introducing a bidirectional proof search that simultaneously employs a forward reasoning and a backward reasoning, and generalize it by incorporating beneflts of extended hyper steps with a preprocessing process, that includes a subsumption check in an equality graph and a high level planning. The forward reasoning in RHU-resolution may replace the role of the function substitution link.[9] That is, RHU-deduction without the function substitution link gets a proof. In order to control explosive generation of positive equalities by the forward reasoning, we haue put some restrictions on input clauses and k-pd links, and also have included a control strategy for a positive-positive linkage, like the set-of-support concept, A linking path between two end terms can be found by simple checking of linked unifiability using the concept of a linked unification. We tried to prevent redundant resolvents from generating by preprocessing using a subsumption check in the subsumption based eauality graph(SPD-Graph)so that the search space for possible RHU-resolution may be reduced.

• Journal of Educational Research in Mathematics
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• v.14 no.2
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• pp.143-156
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• 2004

Lakatos's mathematical philosophy implies that the mathematical knowledge is quasi-empirical and provides the context where mathematics grows and develops. So, it is educationally significant. But, it is not easy to apply Lakatos's methodology to teaching elementary mathematics, because Lakatos's logic of the mathematical discovery is based on the proofs and refutations but elementary mathematics does not contain any proof. This study is to develop the schemes that apply Lakatos's methodology to teaching elementary mathematics and to provide the teaching examples. I devised the teaching process and the curriculum development method. And I developed the teaching examples.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.4 no.6
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• pp.1042-1062
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• 2010

Cooperative spectrum sensing (CSS) is an effective technology for alleviating the unreliability of local spectrum sensing due to fading/shadowing effects. Unlike most existing solutions, this paper considers the use of CSS technology in decentralized networks where a fusion center is not available. In such a decentralized network, some attackers may sneak into the ranks of cooperative users. On the basis of recent advances in bio-inspired consensus algorithms, an attack-proof, decentralized CSS scheme is proposed in which all secondary users can maintain cooperative sensing by exchanging information locally instead of requiring centralized control or data fusion. Users no longer need any prior knowledge of the network. To counter three potential categories of spectrum sensing data falsification (SSDF) attacks, some anti-attack strategies are applied to the iterative process of information exchange. This enables most authentic users to exclude potentially malicious users from their neighborhood. As represented by simulation results, the proposed scheme can generally ensure that most authentic users reach a consensus within the given number of iterations, and it also demonstrates much better robustness against different SSDF attacks than several existing schemes.

• Proceedings of the KIEE Conference
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• 2000.07c
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• pp.2020-2022
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• 2000

The cross-linked polyethylene(herein after XLPE) insulated power cable emit the methane($CH_4$)gas in the course of chemical cross-linking process. The general stranded conductor easily discharge this methane gas through the gap of each stranded wires. But the special stranded conductor that filled with semi-conducting rubber compound to prevent water penetration which is applied to water proof type of cable(22.9kV CN/CV-W), disturb the methane gas emission. The pre-mold type cable joint shall be expanded gradually by emit of gas left in XLPE insulation. For example, sometimes the corona problem outbreak on a new power distribution line, resulted from the gap between the sleeve and semi-conductive layer of cable joint. If above mentioned problem especially happened on the way of operating. We have to shut down the line and try to discharge the methane gas in cable joint. In this point, we would like to explain the mechanism of methane gas & cable joint and our test result briefly. At last, we are pleased to introduce the solution for preventing reoccurrence of this problem.