• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.187-204
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• 2018

Let $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}\;R_{\alpha}$ be a graded integral domain, H be the set of nonzero homogeneous elements of R, and ${\star}$ be a semistar operation on R. The purpose of this paper is to study the properties of $quasi-Pr{\ddot{u}}fer$ and UMt-domains of graded integral domains. For this reason we study the graded analogue of ${\star}-quasi-Pr{\ddot{u}}fer$ domains called $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. We study several ring-theoretic properties of $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. As an application we give new characterizations of UMt-domains. In particular it is shown that R is a $gr-t-quasi-Pr{\ddot{u}}fer$ domain if and only if R is a UMt-domain if and only if RP is a $quasi-Pr{\ddot{u}}fer$ domain for each homogeneous maximal t-ideal P of R. We also show that R is a UMt-domain if and only if H is a t-splitting set in R[X] if and only if each prime t-ideal Q in R[X] such that $Q{\cap}H ={\emptyset}$ is a maximal t-ideal.

• The Journal of Korean Academy of Prosthodontics
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• v.54 no.3
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• pp.291-297
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• 2016

Patients with $Sj{\ddot{o}}gren^{\prime}s$ syndrome usually suffer from teeth discoloration and attrition due to xerostomia. If the anterior teeth are badly worn, problems such as loss of anterior guidance, occlusal disharmony, and limited space for restoration may occur. However, ideal occlusion is obtained in both centric and eccentric relation by regaining the disocclusion of the posterior teeth through the anterior and lateral guidance using twin-stage method. In this case, rehabilitation was performed for a $Sj{\ddot{o}}gren^{\prime}s$ syndrome patient with maxillary and mandibular incisor's severe attrition and teeth discoloration by using twin-stage method.

• Journal of the Korean Institute of Traditional Landscape Architecture
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• v.36 no.3
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• pp.26-36
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• 2018

This study aims to examine the characteristics of landscape through the analysis of location and the landscape of Gugok while also conducting the empirical study through the literature review, field study, and digital analysis of the Okgung Gugok. Oksan Gugok is a set of songs set in Ogsan Creek(玉山川)or Jagyese Creek(紫溪川, 紫玉山), which flows in front of the Oksan Memorial Hall(李彦迪), which is dedicated to the Lee Eong-jeok (李彦迪). We first ascertained the location and configuration of Oksan Gogok. Second, we confirmed the accurate location of Oksan Gogok by utilizing the digital topographic map of Oksan Gogok which was submitted by Google Earth Pro and Geographic Information Center as well as the length of the longitude of the gravel measured by the Trimble Juno SB GPS. Through the study of the literature and the field investigation, The results of the study are as follows. First, Yi Eonjeok was not a direct composer of Oksan Gugok, nor did he produce "Oksan Gugokha(Music)". Lee Ia-sung(李野淳), the ninth Youngest Son of Tweo-Kye, Hwang Lee, visited the "Oksan Gugokha" in the spring of 1823(Sunjo 23), which was the 270th years after the reign of Yi Eonjeok. At this time, receiving the proposal of Ian Sung, Lee Jung-eom(李鼎儼), Lee Jung-gi(李鼎基), and Lee Jung-byeong(李鼎秉), the descendants of Ian Sung set up a song and created Oksan Gugok Music. And the Essay of Oksan Travel Companions writted by Lee Jung-gi turns out being a crucial data to describe the situation when setting up the Ok-San Gugok. Second, In the majority of cases, Gogok Forest is a forest managed by a Confucian Scholar, not run by ordinary people. The creation of "Oksan Bugok Music" can be regarded as an expression of pride that the descendants of Yi Eonjeok and Lee Hwang, and next generation of several Confucian scholars had inherited traditional Neo-Confucian. Third, Lee Jung-eom's "Oksan Donghaengki" contains a detailed description of the "Oksan Gugokha" process and the process of creating a song. Fourth, We examined the location of one to nine Oksan songs again. In particular, eight songs and nine songs were located at irregular intervals, and eight songs were identified as $36^{\circ}01^{\prime}08.60^{{\prime}{\prime}}N$, $129^{\circ}09^{\prime}31.20^{{\prime}{\prime}}E$. Referring to the ancient kingdom of Taojam, the nine-stringed Sainam was unbiased as a lower rock where the two valleys of the East West congregate. The location was estimated at $36^{\circ}01^{\prime}19.79^{{\prime}{\prime}}N$, $129^{\circ}09^{\prime}30.26^{{\prime}{\prime}}E$. Fifth, The landscape elements and landscapes presented in Lee Jung-eom's "Oksan Gugokha" were divided into form, semantic and climatic elements. As a result, Lee Jung-eom's Cho Young-gwan was able to see the ideal of mountain water and the feeling of being idle in nature as well as the sense of freedom. Sixth, After examining the appearance of the elements and the frequency of the appearance of the landscape, 'water' and 'mountain' were the absolute factors that emphasized the original curved environment at the mouth of Lee Jung-eom. Therefore, there was gugokga can gauge the fresh ideas(神仙思想)and retreat ever(隱居思想). This inherent harmony between the landscape as well as through the mulah any ideas that one with nature and meditation, Confucian tube.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.933-948
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• 2005

Let R be a commutative ring with identity and let M be an R-module. Then M is called a multiplication module if for every submodule N of M there exists an ideal I of R such that N = 1M. Let M be a non-zero multiplication R-module. Then we prove the following: (1) there exists a bijection: N(M)$\bigcap$V(ann$\_{R}$(M))$\rightarrow$Spec$\_{R}$(M) and in particular, there exists a bijection: N(M)$\bigcap$Max(R)$\rightarrow$Max$\_{R}$(M), (2) N(M) $\bigcap$ V(ann$\_{R}$(M)) = Supp(M) $\bigcap$ V(ann$\_{R}$(M)), and (3) for every ideal I of R, The ideal $\theta$(M) = $\sum$$\_{m(Rm :R M) of R has proved useful in studying multiplication modules. We generalize this ideal to prove the following result: Let R be a commutative ring with identity, P $\in$ Spec(R), and M a non-zero R-module satisfying (1) M is a finitely generated multiplication module, (2) PM is a multiplication module, and (3) P$^{n}$M$\neq$P$^{n+1}$ for every positive integer n, then $\bigcap$$^{$\_{n=1}$(P$^{n}$ + ann$\_{R}$(M)) $\in$ V(ann$\_{R}$(M)) = Supp(M) $\subseteq$ N(M).

• Journal of Astronomy and Space Sciences
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• v.32 no.4
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• pp.281-287
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• 2015

Two mini neutron monitors are installed at Concordia research station (Dome C, Central Antarctica, $75^{\circ}06^{\prime}S$, $123^{\circ}23^{\prime}E$, 3,233 m.a.s.l.). The site has unique properties ideal for cosmic ray measurements, especially for the detection of solar energetic particles: very low cutoff rigidity < 0.01 GV, high elevation and poleward asymptotic acceptance cones pointing to geographical latitudes > $75^{\circ}S$. The instruments consist of a standard neutron monitor and a "bare" (lead-free) neutron monitor. The instrument operation started in mid-January 2015. The barometric correction coefficients were computed for the period from 1 February to 31 July 2015. Several interesting events, including two notable Forbush decreases on 17 March 2015 and 22 June 2015, and a solar particle event of 29 October 2015 were registered. The data sets are available at cosmicrays.oulu.fi and nmdb.eu.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1167-1182
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• 2016

Let M be an R-module, where R is a commutative ring with identity 1 and let G(V,E) be a graph. In this paper, we study the graphs associated with modules over commutative rings. We associate three simple graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ to M called full annihilating, semi-annihilating and star-annihilating graph. When M is finite over R, we investigate metric dimensions in $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$. We show that M over R is finite if and only if the metric dimension of the graph $ann_f({\Gamma}(M_R))$ is finite. We further show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if M is a prime-multiplication-like R-module. We investigate the case when M is a free R-module, where R is an integral domain and show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if $$M{\sim_=}R$$. Finally, we characterize all the non-simple weakly virtually divisible modules M for which Ann(M) is a prime ideal and Soc(M) = 0.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.659-668
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• 2021

Let R be a semiprime ring with maximal right ring of quotients Q_mr(R), and let n₁, n₂, …, n_k be k fixed positive integers. Suppose that R is (n₁+n₂+⋯+n_k)!-torsion free, and that f : 𝜌 → Q_mr(R) is an additive map, where 𝜌 is a nonzero right ideal of R. It is proved that if [[…[f(x), x^n₁], …], x^n_k] = 0 for all x ∈ 𝜌, then [f(x), x] = 0 for all x ∈ 𝜌. This gives the result of Beidar et al. [2] for semiprime rings. Moreover, it is also proved that if R is p-torsion, where p is a prime integer with p = Σ^k_i=1 n_i and if f : R → Q_mr(R) is an additive map satisfying [[…[f(x), x^n₁], …], x^n_k] = 0 for all x ∈ R, then [f(x), x] = 0 for all x ∈ R.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2004.08a
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• pp.11-18
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• 2004

Asymmetric rolling, in which the circumferential velocities of the upper and lower rolls are different, can give rise to intense plastic shear strains and in turn shear deformation textures through the sheet thickness. The ideal shear deformation texture of fcc metals can be approximated by the <111> // ND and $\{001\}<110>$ orientations, among which the former improves the deep drawability. The ideal shear deformation texture for bcc metals can be approximated by the Goss $\{110\}<001>\;and\;\{112\}<111>$ orientations, among which the former improves the magnetic permeability along the <100> directions and is the prime orientation in grain oriented silicon steels. The intense shear strains can result in the grain refinement and hence improve mechanical properties. Steel sheets, especially ferritic stainless steel sheets, and aluminum alloy sheets may exhibit an undesirable surface roughening known as ridging or roping, when elongated along RD and TD, respectively. The ridging or roping is caused by differently oriented colonies, which are resulted from the <100> oriented columnar structure in ingots or billets, especially for ferritic stainless steels, that is not easily destroyed by the conventional rolling. The breakdown of columnar structure and the grain refinement can be achieved by asymmetric rolling, resulting in a decrease in the ridging problem.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.85-98
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• 2012

Let R be a commutative ring and I its proper ideal, let S(I) be the set of all elements of R that are not prime to I. Here we introduce and study the total graph of a commutative ring R with respect to proper ideal I, denoted by T(${\Gamma}_I(R)$). It is the (undirected) graph with all elements of R as vertices, and for distinct x, y ${\in}$ R, the vertices x and y are adjacent if and only if x + y ${\in}$ S(I). The total graph of a commutative ring, that denoted by T(${\Gamma}(R)$), is the graph where the vertices are all elements of R and where there is an undirected edge between two distinct vertices x and y if and only if x + y ${\in}$ Z(R) which is due to Anderson and Badawi [2]. In the case I = {0}, $T({\Gamma}_I(R))=T({\Gamma}(R))$; this is an important result on the definition.

• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.4
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• pp.737-744
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• 2018

The RSA cryptosystem is a one of the first public-key cryptosystems and is widely used for secure data transmission and electric signature. The security of the RSA cryptosystem is based on the difficulty of factoring large numbers.. Though many studies on finding methods for factoring large numbers are going on, the results of that are all experimental or probabilistic. We, in this paper, construct an algorithm for finding large prime factors of integers without factoring integers using properties of the structure of semigroup of imaginary quadratic order and non-invertible ideal, then propose our methods foe deterministic attack against RSA cryptosystem.