• 대한수학회지
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• 제59권3호
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• pp.571-594
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• 2022

Let D be an integral domain with quotient field K, Pic(D) be the ideal class group of D, and X be an indeterminate. A polynomial overring of D means a subring of K[X] containing D[X]. In this paper, we study almost Dedekind domains which are polynomial overrings of a principal ideal domain D, defined by the intersection of K[X] and rank-one discrete valuation rings with quotient field K(X), and their ideal class groups. Next, let ℤ be the ring of integers, ℚ be the field of rational numbers, and 𝔊f be the set of finitely generated abelian groups (up to isomorphism). As an application, among other things, we show that there exists an overring R of ℤ[X] such that (i) R is a Bezout domain, (ii) R∩ℚ[X] is an almost Dedekind domain, (iii) Pic(R∩ℚ[X]) = $\oplus_{G{\in}G_{f}}$ G, (iv) for each G ∈ 𝔊f, there is a multiplicative subset S of ℤ such that RS ∩ ℚ[X] is a Dedekind domain with Pic(RS ∩ ℚ[X]) = G, and (v) every invertible integral ideal I of R ∩ ℚ[X] can be written uniquely as I = XnQe11···Qekk for some integer n ≥ 0, maximal ideals Qi of R∩ℚ[X], and integers ei ≠ 0. We also completely characterize the almost Dedekind polynomial overrings of ℤ containing Int(ℤ).

• 대한수학회보
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• 제49권4호
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• pp.885-898
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• 2012

Let m, n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D : $R{\rightarrow}R$ be a skew derivation of R and $E(x)=D(x^{m+n+r})-D(x^m)x^{n+r}-x^mD(x^n)x^r-x^{m+n}D(x^r)$. We prove that if $E(x)=0$ for all $x{\in}L$, then D is a usual derivation of R or R satisfies $s_4(x_1,{\ldots},x_4)$, the standard identity of degree 4.

• 대한약학회:학술대회논문집
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• 대한약학회 2003년도 Proceedings of the Convention of the Pharmaceutical Society of Korea Vol.2-2
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• pp.65.2-65.2
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• 2003

88 selective COX-2 inhibitors belonging to three chemical classes (triaryl rings, diaryl cycloalkanopyrazoles, and diphenyl hydrazides) were studied using comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA). Partial least squares analysis produced statistically significant models with q values of 0.84 and 0.79 for CoMFA and CoMSIA, respectively. The key spatial properties were detected by careful analysis of the isocontour maps. The binding energies calculated from flexible docking correlated with inhibitory activities by the least-squares fit method. (omitted)

• 대한수학회논문집
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• 제38권1호
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• pp.55-67
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• 2023

In this paper we obtain a new structure of a k-annihilating ideal hypergraph of a reduced ring R, by determine the order and size of a hypergraph 𝒜𝒢_k(R). Also we describe and count the degree of every nontrivial ideal of a ring R containing in vertex set 𝒜(R, k) of a hypergraph 𝒜𝒢_k(R). Furthermore, we prove the diameter of 𝒜𝒢_k(R) must be less than or equal to 2. Finally, we determine the minimal dominating set of a k-annihilating ideal hypergraph of a ring R.

• 한국정밀공학회지
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• 제26권2호
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• pp.86-93
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• 2009

Elastomeric O-rings have been the most common seals due to their excellent sealing capacity, and availability in costs and sizes. One of the critical applications of O-ring seals is solid rocket motor joint seal where the operating hot gas must be sealed during the combustion. This has long been a design issue to avoid the system failure. For laterally constrained, squeezed and pressurized condition, deformed shape of O-ring was measured by computed tomography method and CCD laser sensor, compared with numerical calculations. As clearance gap changes, sealing performance had been evaluated on peak contact stresses at top, bottom and side contact surfaces. As clearance gap increases, peak contact stresses and contact widths in top and side contact surfaces increase, and the asymmetry of stress distributions is promoted due to pressure increase. It is suggested that peak stress of bottom contact surface can be approximated by simple superposition of peak ones due to squeeze and pressure. Under pressurized condition, sealing performance is dependent on not peak stresses of bottom and side contact surfaces but that of top.

• 대한수학회보
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• 제55권4호
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• pp.1189-1208
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• 2018

The aim of this paper is to study the class of ${\Lambda}$-constacyclic codes of length $2p^s$ over the finite commutative chain ring ${\mathcal{R}}_a=\frac{{\mathbb{F}_{p^m}}[u]}{{\langle}u^a{\rangle}}={\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}+{\cdots}+u^{a-1}{\mathbb{F}}_{p^m}$, for all units ${\Lambda}$ of ${\mathcal{R}}_a$ that have the form ${\Lambda}={\Lambda}_0+u{\Lambda}_1+{\cdots}+u^{a-1}{\Lambda}_{a-1}$, where ${\Lambda}_0,{\Lambda}_1,{\cdots},{\Lambda}_{a-1}{\in}{\mathbb{F}}_{p^m}$, ${\Lambda}_0{\neq}0$, ${\Lambda}_1{\neq}0$. The algebraic structure of all ${\Lambda}$-constacyclic codes of length $2p^s$ over ${\mathcal{R}}_a$ and their duals are established. As an application, this structure is used to determine the Rosenbloom-Tsfasman (RT) distance and weight distributions of all such codes. Among such constacyclic codes, the unique MDS code with respect to the RT distance is obtained.

• 대한수학회보
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• 제29권1호
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• pp.65-72
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• 1992

All rings are commutative, Noetherian with identity and of prime characteristic p, unless otherwise specified. First, we describe the definition of tight closure of an ideal and the properties about the tight closure used frequently. The technique used here for the tight closure was introduced by M. Hochster and C. Huneke [4,5, or 6]. Using the concepts of the tight closure and its properties, we will prove that if R is a complete local domain and F-rational, then R is Cohen-Macaulay. Next, we study the properties of R$^{+}$, the integral closure of a domain in an algebraic closure of its field of fractions. In fact, if R is a complete local domain of characteristic p>0, then R$^{+}$ is Cohen-Macaulay [8]. But we do not know this fact is true or not if the characteristic of R is zero. For the special case we can show that if R is a non-Cohen-Macaulay normal domain containing the rationals Q, then R$^{+}$ is not Cohen-Macaulay. Finally we will prove that if R is an excellent local domain of characteristic p and F-ratiional, then R is Cohen-Macaulay.aulay.

• 센서학회지
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• 제31권5호
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• pp.353-359
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• 2022

This study investigated via computational analysis the application utility of series-cascaded ring resonators based on silicon-on-insulator (SOI) slot optical waveguides in integrated optical biochemical sensors. The radii of the two rings in the series-cascaded ring resonators were 59.4 ㎛ and 77.6 ㎛ respectively, and the coupling distance was 0.5 ㎛. The series-cascaded ring resonators were computationally analyzed using FIMMProp and PICWave numerical software. The free spectral range (FSR), full width at half maximum (FWHM), sensitivity, and quality-factor (Q-factor) of the series-cascaded ring resonators were 12.2 nm, 0.134 nm, 4100 nm/RIU, and 11580, respectively, and the measurement range was calculated to be slightly smaller than 3×10^-3 RIU. Although the measurement range was smaller than that of the single ring resonator, upon considering other characteristic parameters, the series-cascaded ring resonators are found to be more effective as integrated sensors than single ring resonators.

• 한국광학회지
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• 제16권5호
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• pp.469-475
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• 2005

본 논문에서는 코히런트하게 결합되는 폴리머 마이크로링 공진기를 이용한 광학적 방식의 마이크로웨이브 대역통과 필터를 제안하고 구현하였다. 제안된 소자는 소형이며 구조가 간단하고, 열광학 및 전기광학 효과를 통한 중심주파수 변화가 용이하고, 그리고 다른 전기소자나 광소자와의 집적성 등이 뛰어나다. 특히, 이 공진기는 마이크로웨이브 신호를 수반하는 광신호를 효과적으로 필터링하기 위해 아주 작은 대역폭을 갖도록 설계되었다. 본 논문에서는 한 개의 링과 두 개의 링으로 구성된 공진기를 각각 제작하여 특성을 확인하였다. 링 공진기의 측정된 전달 특성을 이론적으로 fitting하였으며, 이로부터 제안된 마이크로웨이브 필터의 특성을 정확하게 예측하였다. 공진기의 링 수가 증가할수록 대역폭은 감소하고 롤오(roll-off) 특성이 향상되며 대역 소멸비가 증가함을 알 수 있었다. 측정된 대역통과 필터의 중심주파수는 $\~10GHz$였고 3-dB 대역폭은 $\~0GHz$였다. 그리고 Q값(quality factor)은 $\~10$이었고 통과대역의 소멸비는 약 25dB였다.

• 대한수학회논문집
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• 제20권3호
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• pp.427-436
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• 2005

Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and v be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple v-ideals $m=P_0\;{\supset}\;P_1\;{\supset}\;{\cdotS}\;{\supset}\;P_t=P$ and all the other v-ideals are uniquely factored into a product of those simple ones. It then was also shown by Lipman that the predecessor of the smallest simple v-ideal P is either simple (P is free) or the product of two simple v-ideals (P is satellite), that the sequence of v-ideals between the maximal ideal and the smallest simple v-ideal P is saturated, and that the v-value of the maximal ideal is the m-adic order of P. Let m = (x, y) and denote the v-value difference |v(x) - v(y)| by $n_v$. In this paper, if the m-adic order of P is 2, we show that $O(P_i)\;=\;1\;for\;1\;{\leq}\;i\; {\leq}\;{\lceil}\;{\frac{b+1}{2}}{\rceil}\;and\;O(P_i)\;=2\;for\;{\lceil}\;\frac{b+3}{2}\rceil\;{\leq}\;i\;\leq\;t,\;where\;b=n_v$. We also show that $n_w\;=\;n_v$ when w is the prime divisor associated to a simple v-ideal $Q\;{\supset}\;P$ of order 2 and that w(R) = v(R) as well.