• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.205-215
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• 2011

Given a knot diagram D, we construct a semi-threading circle of it which can be an axis of D as a closed braid depending on knot diagrams. In particular, we consider semi-threading circles of minimal diagrams of a knot with respect to overpasses which give us some information related to the braid index. By this notion, we try to give another proof of the fact that, for every nontrivial knot K, the braid index b(K) of K is not less than the minimum number l(K) of overpasses of diagrams. Also, they are the same for a torus knot.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.175-183
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• 1996

Let $S_n,n$ = 1, 2,... denote the partial sums of not necessarily in-dependent random variables. Let N(c) = min${ n ; S_n > c}$, c $\geq$ 0. Theorem 2 states that N (c), (suitably normalized), tends to 0 in p-mean, 1 $\leq$ p < 2, as c longrightarrow $\infty$ under mild conditions, which generalizes earlier result by Gut(1974). The proof follows by applying Theorem 1, which generalizes the known result $E$\mid$S_n$\mid$^p$ = o(n), 0 < p< 2, as n .rarw..inf. to randomly indexed partial sums.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.143-159
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• 2020

We propose a consistent numerical method for elliptic interface problems with nonhomogeneous jumps. We modify the discontinuous bubble immersed finite element method (DB-IFEM) introduced in (Chang et al. 2011), by adding a consistency term to the bilinear form. We prove optimal error estimates in L² and energy like norm for this new scheme. One of the important technique in this proof is the Bramble-Hilbert type of interpolation error estimate for discontinuous functions. We believe this is a first time to deal with interpolation error estimate for discontinuous functions. Numerical examples with various interfaces are provided. We observe optimal convergence rates for all the examples, while the performance of early DB-IFEM deteriorates for some examples. Thus, the modification of the bilinear form is meaningful to enhance the performance.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.37 no.5
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• pp.311-318
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• 1988

An adaptive control problem for a plant with unmodelled dynamics is studied. The upper bounds of the output due to the unmodelled dynamics and measurement noise is assumed to be known. This problem was studied by Middleton et al. They used a modified form of the least square method in estimating the plant paramaters. In this paper, the bounds of the parameters are estimated by linear programming and the parameters are estimated by the projetion type algorithm incorporating the bounds of the parameters. The stability of the proposed adaptive control system can be proved in nearly the same way as the proof of Middleton. The performance of the proposed method is found to be much better than the method of Midlleton's with respect to the parameter convergence and plant output in computer simulations.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.724-729
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• 2001

This paper discusses the composition of the theory of reinforcement learning, which is applied in real-time learning, and evolutionary strategy, which proves its the superiority in the finding of the optimal solution at the off-line learning method. The individuals are reduced in order to learn the evolutionary strategy in real-time, and new method that guarantee the convergence of evolutionary mutations are proposed. It possible to control the control object varied as time changes. As the state value of the control object is generated, applied evolutionary strategy each sampling time because the learning process of an estimation, selection, mutation in real-time. These algorithms can be applied, the people who do not have knowledge about the technical tuning of dynamic systems could design the controller or problems in which the characteristics of the system dynamics are slightly varied as time changes. In the future, studies are needed on the proof of the theory through experiments and the characteristic considerations of the robustness against the outside disturbances.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.115-124
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• 2006

Functions of bounded variation were discovered by Jordan in 1881 while working out the proof of Dirichlet concerning the convergence of Fourier series. Here, we investigate Waterman's study with respect to bounded variation and its application on a closed bounded interval. The value of his study is whether Dirichlet-Jordan theorem holds in which function classes or not and summability method is what modifies its Fourier coefficients to make resulting series converge to the associated function. We have a view that the directions of future research with respect to bounded variation are two things; one is to find the function spaces which are larger than HBV and smaller than ${\phi}BV$, and the other is to find a fields of applications.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.13-33
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• 2022

The quaternionic Calabi conjecture was introduced by Alesker-Verbitsky, analogous to the Kähler case which was raised by Calabi. On a compact connected hypercomplex manifold, when there exists a flat hyperKähler metric which is compatible with the underlying hypercomplex structure, we will consider the parabolic quaternionic Monge-Ampère equation. Our goal is to prove the long time existence and C^∞ convergence for normalized solutions as t → ∞. As a consequence, we show that the limit function is exactly the solution of quaternionic Monge-Ampère equation, this gives a parabolic proof for the quaternionic Calabi conjecture in this special setting.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.244-262
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• 2022

In this paper, we analyze the hybridizable discontinuous Galerkin (HDG) method for second-order elliptic equations with nonlinear coefficients, which are used in many fields. We present the HDG method that uses a mixed formulation based on numerical trace and flux. Under assumptions on the nonlinear coefficient and H²-regularity for a dual problem, we prove that the discrete systems are well-posed and the numerical solutions have the optimal order of convergence as a mesh parameter. Also, we provide a matrix formulation that can be calculated using an iterative technique for numerical experiments. Finally, we present representative numerical examples in 2D to verify the validity of the proof of Theorem 3.10.

• Annual Conference of KIPS
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• 2021.11a
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• pp.334-336
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• 2021

허가형 블록체인 기반 데이터 공유 시스템은 분산 환경에서 신뢰 수준을 구축하고 일관된 메시지를 기록 및 공유함으로써 서비스의 상호 운용성을 가능하게 한다. 그러나 허가형 블록체인은 종종 탈중앙화, 보안 및 상호 운용성과 충돌한다. 이는 중앙 집중식 시스템으로 돌아가거나 데이터의 독점 및 남용 및 오용으로 이어질 수 있다. 따라서 CAP (Consistency, Availability, Partition tolerance)에 이론 검증에 따라 메시지 공유, 비잔틴 내결함성 및 메시지 일관성을 고려하고 적용해야 한다. 기존의 PBFT(Practical Byzantine Fault Tolerance) 합의 알고리즘는 노드의 증가시, 장애내성을 갖기위해 계산되어야 할 합의 처리시간이 증가하며, DPOS(Delegated Proof of Stake) 알고리즘은 보상, 리더 선출의 공정성 문제 등에 따라 허가형 블록체인에서의 적합한 방식이 연구되고 있다. 본 논문에서는 서비스의 상호 운용성과 과제에 대해 논의하고 허가된 블록체인의 합의 개선을 통한 데이터 공유 시스템을 제안한다.

• Journal of Digital Convergence
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• v.19 no.6
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• pp.233-238
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• 2021

Recently, blockchain technology accumulates and stores all transactions. Therefore, in order to verify the contents of all transactions, the data itself is compressed, but the scalability is limited. In addition, since a separate verification algorithm is used for each type of transaction, the verification burden increases as the size of the transaction increases. Existing blockchain cannot participate in the network because it does not become a block sink by using a server with a low specification. Due to this problem, as the time passes, the data size of the blockchain network becomes larger and it becomes impossible to participate in the network except for users with abundant resources. Therefore, in this paper, we are improved transaction as studied the zero knowledge proof algorithm for general operation verification. In this system, the design of zero-knowledge circuit generator capable of general operation verification and optimization of verifier and prover were also conducted.