• Journal of the Architectural Institute of Korea Structure & Construction
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• v.33 no.12
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• pp.37-44
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• 2017

Due to structural characteristics, construction costs and duration of a modular system would be saved by minimizing the schedule on the job site. As such, it is crucial to develop a connection that can guarantee stiffness while allowing for simple assembling. Particularly, the mid- to high-rise construction of the modular system necessitates the securing of the structural stability and seismic performance of multi-unit frames and connections, and thus, the stiffness of unit-assembled structures needs to be re-evaluated and designed. However, evaluating a frame consisting of slender members and reinforcing materials is a complicated process. Therefore, the present study aims to examine the structural characteristics of a modular unit connection based a method for reinforcing connection brackets and hinges while minimizing the loss of the cross section. Toward this end, the study modeled the beam-to-column connection of a modular system with the proposed connection, and produced a specimen which was used to perform a cycling loading test. The study compared the initial stiffness, the attributes of the hysteretic behavior, and the maximum flexural moment, and observed whether the model acquired the seismic performance, compared to the flexural strength of the steel moment frame connection that is required by the Korean Building Code. The test results showed that the proposed connection produced a similar initial stiffness value to that of the theoretical equation, and its maximum strength exceeded the theoretical strength. Furthermore, the model with a larger ceiling bracket showed higher seismic performance, which was further increased by the reinforcement of the plate.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.167-170
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• 1986

Let M be a von Neumann algebra and .alpha., .betha. be *-automorphisms of M satisfying the operator equation .alpha.+.alpha.$^{-1}$ =.betha.+.betha.$^{-1}$ This operator equation has been extensively studied and many important decomposition theorems have been obtained by several authors (for instance see [4], [5], [2], [1]). Originally, this operator equation arose in the paper of Van Daele on the new approach of the Tomita-Takesaki theory in the case of modular operators ([7]). In the case of one-parameter automorphism groups, this equation has produced a bounded and completely positive map which can play a role similar to the infinitesimal generator (for details see [6] and [1]). A recent and one of the most important applications of this equation has been in developing an anglogue of the Tomita-Takesaki theory for Jordan algebras by Haagerup [3]. One general result of this theory is the following.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.67-77
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• 2011

We find some Eisenstein series related to modulus 4 using a theta function identity of McCullough and Shen and residue theorem for elliptic functions.

• The Pure and Applied Mathematics
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• v.23 no.4
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• pp.389-389
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• 2016

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.8
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• pp.748-754
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• 2004

In this paper, we propose the Triple Modular Redundancy (TMR) control system equipped with a checkpoint strategy. In this system, faults in a single processor are masked and faults in two or more processors are detected at each checkpoint time. When faults are detected, the rollback recovery is activated to recover from faults. The conventional TMR control system cannot overcome faults in two or more processors. The proposed system can effectively cope with correlated and independent faults in two or more processors. We develop a reliability model for this TMR control system under correlated and independent transient faults, and derive the reliability equation. Then we investigate the number of checkpoints that maximizes the reliability.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.4
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• pp.101-105
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• 2005

Recently a new public key cryptosystem based on a diagonal matrix has been proposed by Zheng. This system uses eigenvalues as a long-term key and random numbers as session key generators. However, there are a couple of flaws in that system. In this paper, we propose a new algorithm in which those flaws are all fixed. Our scheme is based on modular equations over a composite and uses a matrix of Jordan form. We also analyze the security of it.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1045-1061
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• 2023

Using variational methods, Krasnoselskii's genus theory and symmetric mountain pass theorem, we introduce the existence and multiplicity of solutions of a parameteric local equation. At first, we consider the following equation $$\{-div[a(x,{\mid}{\nabla}u{\mid}){\nabla}u]\,=\,{\mu}(b(x){\mid}u{\mid}^{s(x)-2}-{\mid}u{\mid}^{r(x)-2})u\;in\;{\Omega},\\u\,=0\,on\;{\partial}{\Omega},$$ where Ω⊆ ℝ^N is a bounded domain, µ is a positive real parameter, p, r and s are continuous real functions on ${\bar{\Omega}}$ and a(x, ξ) is of type |ξ|^p(x)-2. Next, we study boundedness and simplicity of eigenfunction for the case a(x, |∇u|)∇u = g(x)|∇u|^p(x)-2∇u, where g ∈ L^∞(Ω) and g(x) ≥ 0 and the case $a(x,\,{\mid}{\nabla}u{\mid}){{\nabla}u}\,=\,(1\,+\,{\nabla}u{\mid}^2)^{\frac{p(x)-2}{2}}{\nabla}u$ such that p(x) ≡ p.

• Journal for History of Mathematics
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• v.20 no.1
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• pp.103-111
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• 2007

1997년 Coppersmith는 소인수분해를 모르는 법 N에 대한 합동방정식(modular equation)의 '작은 해'를 찾는 방법을 제안한다. 동시에 두 변수 다항식의 제한된 크기의 해를 찾는 방법도 격자이론을 이용하여 제안한다. 이러한 Coppersmith의 정리는 이후 암호학에서 매우 유용하게 사용되는데 특별히 RSA 암호체계에서 비밀 키를 찾아내거나 일부 비밀 키가 노출되었을 때 전체키를 복원하는 데에 중요한 역할을 한다. 본 논문에서는 Coppersmith의 정리를 살펴보고 이것이 RSA의 안전성에 어떠한 영향을 주었는지를 살펴본다.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.267-273
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• 2017

The objective of this note is to establish three results between q-products and combinatorial partition identities in a elementary way. Several closely related q-product identities such as (for example)continued fraction identities and Jacobis triple product identities are also considered.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.377-386
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• 2021

In this paper, we use theta-function identities involving parameters 𝑙_5,n, 𝑙'_5,n, and 𝑙'_5,4n to evaluate the Rogers-Ramanujan continued fractions $R(e^{-2{\pi}{\sqrt{n/20}}})$ and $S(e^{-{\pi}{\sqrt{n/5}}})$ for some positive rational numbers n.