• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.961-976
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• 2019

Let R be any commutative ring and S be any multiplicative closed set. We introduce an S-version of $\mathcal{F}$-Mittag-Leffler modules, called $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, and define the projective dimension with respect to these modules. We give some characterizations of $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, investigate the relationships between $\mathcal{F}$-Mittag-Leffler modules and $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, and use these relations to describe noetherian rings and coherent rings, such as R is noetherian if and only if $R_S$ is noetherian and every $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler module is $\mathcal{F}$-Mittag-Leffler. Besides, we also investigate the $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension of R, and prove that $R_S$ is noetherian if and only if its $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension is zero; $R_S$ is coherent if and only if its $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension is at most one.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.29 no.3
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• pp.515-518
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• 2019

The performance of Elliptic Curves Cryptosystem(ECC) is dominated by the modular multiplication since the elliptic curve scalar multiplication consists of the modular multiplication in projective coordinates. In this paper, we propose a new method that combines the Karatsuba-Ofman multiplication method and a new modular reduction algorithm in order to improve the performance of the modular multiplication for NIST p224 in the FIPS 186-4 standard. The proposed method leads to a running time improvement for computing the modular multiplication about 25% faster than the previous methods. The results also show that the method can reduce the arithmetic complexity by half when compared with traditional implementations on the standpoint of the modular reduction.

• Smart Structures and Systems
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• v.23 no.4
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• pp.359-371
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• 2019

As part of a structural health monitoring system, the relative geometric relationship between a ship and bridge has been recognized as important for bridge authorities and ship owners to avoid ship-bridge collision. This study proposes a novel computer vision method for the real-time geometric parameter identification of moving ships based on a single shot multibox detector (SSD) by using transfer learning techniques and monocular vision. The identification framework consists of ship detection (coarse scale) and geometric parameter calculation (fine scale) modules. For the ship detection, the SSD, which is a deep learning algorithm, was employed and fine-tuned by ship image samples downloaded from the Internet to obtain the rectangle regions of interest in the coarse scale. Subsequently, for the geometric parameter calculation, an accurate ship contour is created using morphological operations within the saturation channel in hue, saturation, and value color space. Furthermore, a local coordinate system was constructed using projective geometry transformation to calculate the geometric parameters of ships, such as width, length, height, localization, and velocity. The application of the proposed method to in situ video images, obtained from cameras set on the girder of the Wuhan Yangtze River Bridge above the shipping channel, confirmed the efficiency, accuracy, and effectiveness of the proposed method.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.279-286
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• 2019

Complex Grassmann manifolds $G_{n,k}$ are a generalization of complex projective spaces and have many important features some of which are captured by the $Pl{\ddot{u}}cker$ embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$ where $N=\(^n_k\)$. The problem of existence of cross sections of fibrations can be studied using the Gottlieb group. In a more generalized context one can use the relative evaluation subgroup of a map to describe the cohomology of smooth fiber bundles with fiber the (complex) Grassmann manifold $G_{n,k}$. Our interest lies in making use of techniques of rational homotopy theory to address problems and questions involving applications of Gottlieb groups in general. In this paper, we construct the Sullivan minimal model of the (complex) Grassmann manifold $G_{n,k}$ for $2{\leq}k<n$, and we compute the rational evaluation subgroup of the embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$. We show that, for the Sullivan model ${\phi}:A{\rightarrow}B$, where A and B are the Sullivan minimal models of ${\mathbb{C}}P^{N-1}$ and $G_{n,k}$ respectively, the evaluation subgroup $G_n(A,B;{\phi})$ of ${\phi}$ is generated by a single element and the relative evaluation subgroup $G^{rel}_n(A,B;{\phi})$ is zero. The triviality of the relative evaluation subgroup has its application in studying fibrations with fibre the (complex) Grassmann manifold.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.18 no.4
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• pp.135-141
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• 2008

The risk enlargement of cyber infringement and hacking is one of the latest hot issues. To solve the problem, the research for Security Risk Analysis, one of Information Security Technique, has been activating. However, the evaluation for Security Risk Analysis has many burdens; evaluation cost, long period of the performing time, participants’ working delay, countermeasure cost, Security Management cost, etc. In addition, pre-existing methods have only treated Analyzing Standard and Analyzing Method, even though their scale is so large that seems like a project. the Analyzing Method have no option but to include assessors’ projective opinion due to the mixture using that both qualitative and quantitative method are used for. Consequently, in this paper, we propose the Security Risk Analysis Methodology which manage the quantitative evaluation as a project and use Case-Based Reasoning Algorithm for define the period of the performing time and for select participants.

• Proceedings of the Korea Water Resources Association Conference
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• 2022.05a
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• pp.14-14
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• 2022

홍수시 하천의 유량측정은 매우 어렵고 위험하며 많은 노력과 비용이 드는 작업이다. 이러한 홍수시 유량측정을 위해 영상을 이용하여 하천의 표면유속을 측정하고 여기서 유량을 산정하는 기술은 하천 유량 측정의 자동화와 안전한 유량 측정을 위한 대안으로 크게 주목받고 있다. 그런데, 유속측정을 위해 20~40초 정도의 영상의 평균유속을 구하고자 하면, 방대한 양의 영상처리에 많은 시간이 소요되어 실시간 측정이나 분석이 어렵게 된다. 본 연구는 영상을 이용하여 홍수시 하천의 유량을 실시간으로 측정하기 위해 투영변환과 시공간영상 분석법을 적용하여 실용적인 표면영상유속계를 개발하기 위한 것이다. 이를 위해, 3차원 투영변환(11변수 변환)을 적용하여 측정선과 유속측정점의 위치를 영상내에 특정하고 이 부분만을 추출하여 시공간 영상(spatio-temporal images)으로 구성하고, 이 시공간 영상을 분석하여 유속과 유량을 산출하는 기법을 개발하였다. 즉, 하천의 주흐름 방향의 유속만을 산정하도록 하여 영상의 분석에 소요되는 계산량과 계산시간을 단축하였다. 또한, 시공간 분석과정도 기존의 CASTI (Correlation Analysis of Spatio-Temporal Images)를 훨씬 간단하고 빠르게 계산할 수 있도록 개량하였다. 그 결과 영상의 유속분석 및 유량산정에 소요되는 시간을 획기적으로 줄일 수 있었으며, 실시간으로 유량 측정이 가능하게 되었다.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1687-1695
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• 2023

In this paper, we study the Green ring r(𝔴⁰_n) of the weak Hopf algebra 𝔴⁰_n based on Taft Hopf algebra H_n(q). Let R(𝔴⁰_n) := r(𝔴⁰_n) ⊗_ℤ ℂ be the Green algebra corresponding to the Green ring r(𝔴⁰_n). We first determine all finite dimensional simple modules of the Green algebra R(𝔴⁰_n), which is based on the observations of the roots of the generating relations associated with the Green ring r(𝔴⁰_n). Then we show that the nilpotent elements in r(𝔴⁰_n) can be written as a sum of finite dimensional indecomposable projective 𝔴⁰_n-modules. The Jacobson radical J(r(𝔴⁰_n)) of r(𝔴⁰_n) is a principal ideal, and its rank equals n - 1. Furthermore, we classify all finite dimensional non-simple indecomposable R(𝔴⁰_n)-modules. It turns out that R(𝔴⁰_n) has n² - n + 2 simple modules of dimension 1, and n non-simple indecomposable modules of dimension 2.

• Structural Engineering and Mechanics
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• v.90 no.1
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• pp.97-106
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• 2024

This paper presents a significant contribution to aided design by conducting an analytical examination of geometric links with the aim of establishing criteria for assessing an analogy measure of the extrinsic geometric and kinematic characteristics of the Variable Compression Ratio (VCR) engine with a Geared Mechanism (GBCM) in comparison to the existing Fixed Compression Ratio (FCR) engine with a Standard-Reciprocating Crankshaft configuration. Employing a mechanical approach grounded in projective computational methods, a parametric study has been conducted to analyze the kinematic behavior and geometric transformations of the moving links. The findings indicate that in order to ensure equivalent extrinsic behavior and maintain consistent input-output performance between both engine types, precise adjustments of intrinsic geometric parameters are necessary. Specifically, for a VCR configuration compared to an FCR configuration, regardless of compression ratio and gearwheel radius, for the same crankshaft ratios and stroke lengths, it is imperative to halve lengths of connecting rods, and crank radius. These insights underscore the importance of meticulous parameter adjustment in achieving comparable performance across different engine configurations, offering valuable implications for design optimization.

• Journal of the Korean Association of Geographic Information Studies
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• v.13 no.2
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• pp.11-20
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• 2010

In this study, the effects of stand height growth on GIS-based viewshed analysis were investigated. DSM was created by combining stand height layers on DEM using map algebra functions. In developing the tree height layers, the digital forest-type maps, forest site maps and stand yield tables of Korea Forest Research Institute were used. The time horizon for viewshed analysis were 40 years. Two viewpoints in crossings of downtown for viewshed analyses were chosen using a projective mapping technique. The effects of tree height growth over time on visibility were measured in terms of the depth of blind areas and the area of visible regions. The results of viewshed analyses show that 17% of visible regions is reduced when we use DSM instead of DEM. As the tree height grows, the visibility gets worse and worse and the depth of blind area increases.

• Journal of The Korean Association of Information Education
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• v.18 no.4
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• pp.605-614
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• 2014

Many healing programs regard successful healing as the cure of the presenting physical and emotional problems. To heal present broken heart on a smart environment, we need to know states of mind. We also have to need psychoanalytic healing that cure mind caused. It is necessary to consider a more comprehensive view of healing that incorporates not only physical healing but mental healing. For this, we analyze through retrospective review from existing researches and healing programs. We obtain psychological and emotional factors about negative side effects on a smart environment. Throughout this study we draw upon factors of psychology and emotion to represent pictures by projective methods such as visual representation. That pictures is being used in developing the digital workbook for mind healing. We look at the possibility of psychological therapy from negative side effects causing converts into digital forms which have fixed scales on a smart environment.