• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.925-934
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• 2010

A crystallization of a closed connected PL manifold M is a special edge-colored graph representing M via a contracted triangulation. The regular genus of M is the minimum genus of a closed connected surface into which a crystallization of M regularly embeds. We disprove a conjecture on the regular genus of $\mathbb{S}\;{\times}\;\mathbb{S}^n$, $n\;{\geq}\;3$, stated in [J. Korean Math. Soc. 41 (2004), no. 3, p. 420].

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.363-379
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• 2014

In this paper, introducing various separation axioms on a bi-GTS, it has been observed that such separation axioms actually unify the well-known separation axioms on topological spaces. Several characterizations of such separation properties of a bi-GTS are established in terms of ${\gamma}_{{\mu}_i,{\mu}_j}$-closure operator, generalized cluster sets of functions and graph of functions.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.475-484
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• 2019

We study the set of critical exponents of discrete groups acting on regular trees. We prove that for every real number ${\delta}$ between 0 and ${\frac{1}{2}}\;{\log}\;q$, there is a discrete subgroup ${\Gamma}$ acting without inversion on a (q+1)-regular tree whose critical exponent is equal to ${\delta}$. Explicit construction of edge-indexed graphs corresponding to a quotient graph of groups are given.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1261-1277
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• 2021

An inertial manifold is often constructed as a graph of a function from low Fourier modes to high ones and one used to consider backward bounded (in time) solutions for that purpose. We here show that the proof of the uniqueness of such solutions is crucial in the existence theory of inertial manifolds. Avoiding contraction principle, we mainly apply the Arzela-Ascoli theorem and Laplace transform to prove their existence and uniqueness respectively. A non-self adjoint example is included, which is related to a differential system arising after Kwak transform for Navier-Stokes equations.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.71-90
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• 2023

We construct generalized Cauchy-Riemann equations of the first order for a pair of two ℝ-valued functions to deform a minimal graph in ℝ³ to the one parameter family of the two dimensional minimal graphs in ℝ⁴. We construct the two parameter family of minimal graphs in ℝ⁴, which include catenoids, helicoids, planes in ℝ³, and complex logarithmic graphs in ℂ². We present higher codimensional generalizations of Scherk's periodic minimal surfaces.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.31 no.3
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• pp.509-516
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• 2021

The transitive signature scheme is a technique that can be very useful when authenticating edges in a graph that is transitively closed. In other words, when there is an authentication value for an edge (i, j) and an authentication value for an edge (j, k), the authentication value for the edge (i, k) can also be calculated immediately without any separate authentication procedure through a transitive signature. In this paper, we propose the first identity-based transitive signature scheme. Our scheme is based on the lattice problem.

• Journal of Korea Water Resources Association
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• v.51 no.11
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• pp.989-998
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• 2018

Connectivity between water source and demand node can be served as a critical system performance indicator of the degree of water distribution network (WDN)' failure severity under abnormal conditions. Graph theory-based approaches have been widely applied to quantify the connectivity due to WDN's graph-like topological feature. However, most previous studies used undirected-unweighted graph theory which is not proper to WDN. In this study, the directed-weighted graph theory was applied for WDN connectivity analyses. We also proposed novel connectivity indicators, Source-to-Node Shortest Pathway (SNSP) and SNSP-Degree (SNSP-D) which is an inverse of the SNSP value, that does not require complicate hydraulic simulation of a WDN of interest. The proposed SNSP-D index was demonstrated in total 42 networks in J City, South Korea in which Pearson Correlation Coefficient (PCC) between the proposed SNSP-D and four other system performance indicators was computed: three resilience indexes and an energy efficiency metric. It was confirmed that a system representative value of the SNSP-D has strong correlation with all resilience and energy efficiency indexes (PCC = 0.87 on average). Especially, PCC was higher than 0.93 with modified resilience index (MRI) and energy efficiency indicator. In addition, a multiple linear regression analysis was performed to identify the system hydraulic characteristic factors that affect the correlation between SNSP-D and other system performance indicators. The proposed SNSP is expected to be served as a useful surrogate measure of resilience and/or energy efficiency indexes in practice.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1381-1388
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• 2018

Let ${\Delta}$ be a simplicial complex, $I_{\Delta}$ its Stanley-Reisner ideal and $K[{\Delta}]$ its Stanley-Reisner ring over a field K. Assume that ${\Gamma}(R)$ denotes the zero-divisor graph of a commutative ring R. Here, first we present a condition on two reduced Noetherian rings R and R', equivalent to ${\Gamma}(R){\cong}{\Gamma}(R{^{\prime}})$. In particular, we show that ${\Gamma}(K[{\Delta}]){\cong}{\Gamma}(K^{\prime}[{\Delta}^{\prime}])$ if and only if ${\mid}Ass(I_{\Delta}){\mid}={\mid}Ass(I_{{{\Delta}^{\prime}}}){\mid}$ and either ${\mid}K{\mid}$, ${\mid}K^{\prime}{\mid}{\leq}{\aleph}_0$ or ${\mid}K{\mid}={\mid}K^{\prime}{\mid}$. This shows that ${\Gamma}(K[{\Delta}])$ contains little information about $K[{\Delta}]$. Then, we define the squarefree zero-divisor graph of $K[{\Delta}]$, denoted by ${\Gamma}_{sf}(K[{\Delta}])$, and prove that ${\Gamma}_{sf}(K[{\Delta}){\cong}{\Gamma}_{sf}(K[{\Delta}^{\prime}])$ if and only if $K[{\Delta}]{\cong}K[{\Delta}^{\prime}]$. Moreover, we show how to find dim $K[{\Delta}]$ and ${\mid}Ass(K[{\Delta}]){\mid}$ from ${\Gamma}_{sf}(K[{\Delta}])$.

• Carbon letters
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• v.10 no.1
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• pp.5-8
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• 2009

We measured the non-carbon content of single-walled carbon nanotubes (SWCNTs) in SWCNT soot using thermogravimetric analysis. The weight increased percentage by the oxidation of metal in the raw soot is well obtained by TGA graph which was confirmed with ICP-AES, XRD, and XPS. This work will be very useful for the purity precise evaluation of SWCNT with UN-vis-NIR spectroscopy.

• Electronics and Telecommunications Trends
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• v.29 no.4
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• pp.30-38
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• 2014

최근의 플랫폼 기술동향은 웹 기반 혹은 단순 의사소통이 가능한 모바일 플랫폼에서 빅데이터와 인공지능기술이 접목되면서 심층 질의응답이 가능한 차세대 지능형 지식처리 플랫폼으로의 진화가 진행 중이다. 선진국에서는 국가 차원 혹은 글로벌 기업의 주도하에 대형 장기 프로젝트가 진행 중이다. 국가 주도의 프로젝트로는 미국의 PAL, 유럽의 Human Brain, 일본의 Todai 프로젝트가 대표적인 예이며, 글로벌 기업의 경우는 IBM의 Watson, Google의 Knowledge Graph, Apple의 Sir가 대표적인 예이다. 본고에서는 차세대 지능형 플랫폼의 핵심기술인 인간과 기계의 지식소통을 위한 빅데이터 기반의 지식처리 인공지능 소프트웨어 기술의 개념과 국내외 기술 및 산업, 지식재산권 동향 등을 살펴보고 산업계 활용방안 및 발전방향에 대해 논하고자 한다.