• 호남수학학술지
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• 제32권1호
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• pp.45-51
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• 2010

Let A be an abelian variety defined over a number field K and let L be a cyclic extension of K with Galois group G = <${\sigma}$> of order n. Let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and of A over L. Assume III(A/L) is finite. Let M(x) be a companion matrix of 1+x+${\cdots}$+$x^{n-1}$ and let $A^x$ be the twist of $A^{n-1}$ defined by $f^{-1}{\circ}f^{\sigma}$ = M(x) where $f:A^{n-1}{\rightarrow}A^x$ is an isomorphism defined over L. In this paper we compute [III(A/K)][III($A^x$/K)]/[III(A/L)] in terms of cohomology, where [X] is the order of an finite abelian group X.

• East Asian mathematical journal
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• 제24권2호
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• pp.139-144
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• 2008

Given an injective envelope E of a left R-module M, there is an associative Galois group Gal($\phi$). Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope E[$x^{-1}$] of an inverse polynomial module M[$x^{-1}$] as a left R[x]-module and we can define an associative Galois group Gal(${\phi}[x^{-1}]$). In this paper we extend the Galois group of inverse polynomial module and can get Gal(${\phi}[x^{-s}]$), where S is a submonoid of $\mathds{N}$ (the set of all natural numbers).

• 대한전기학회:학술대회논문집
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• 대한전기학회 2000년도 하계학술대회 논문집 C
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• pp.2095-2097
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• 2000

Applications of soft X-ray which corresponds to the wavelength of the order of 1 nm and to the photon energy of the order of 1 key respectively, requires intense sources. Only synchrotron sources were available recently. The development of a new laboratory-sized source of soft X-ray radiation is required for wide applications. This paper introduces the generation of soft X-ray using laser-induced plasma.

• 대한수학회보
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• 제44권2호
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• pp.225-231
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• 2007

Given an injective envelope E of a left R-module M, there is an associative Galois group Gal$({\phi})$. Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope $E[x^{-1}]$ of an inverse polynomial module $M[x^{-1}]$ as a left R[x]-module and we can define an associative Galois group Gal$({\phi}[x^{-1}])$. In this paper we describe the relations between Gal$({\phi})$ and Gal$({\phi}[x^{-1}])$. Then we extend the Galois group of inverse polynomial module and can get Gal$({\phi}[x^{-s}])$, where S is a submonoid of $\mathbb{N}$ (the set of all natural numbers).

• Journal of Plant Biology
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• 제13권2호
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• pp.15-20
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• 1970

The treatment of X-ray was manipulated with the large focus of X-ray which was produced the capacity of 90 kilovoltage and 30 milliamphere in the distance of 50 centimeter. The germination of each gruop irradiated with X-ray for 5, 6, and 7 seconds was more delayed in the growth of carrot seed than those of the control group. However the germination of each group irradiated with X-ray for 2, 3, and 4 seconds was rather accelerated than those of the control group. The irradiation of ultraviolet light was carried out in the distance of 20 centimeter by Toshiba germidicial lamp which appeared the wavelength of 2537A$^{\circ}$. The germination of each group irradiated with ultraviolet light for 9, 15, 20, and 40 minutes was more delayed than those of the control group, but the germination of carrot seed was accelerated by adequate dosage of ultraviolet light. Consuquently it was suggested for the author that the inhibited substance contained in carrot seed would be certain fatty substance, becasue the germination of carrot seed was more accelerated by the treatment of acetone than those of X-ray and ultraviolet light.

• 충청수학회지
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• 제36권4호
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• pp.289-296
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• 2023

When G is an abelian group, we use the notation M(G, n) to denote the Moore space. The space X is the wedge product space of Moore spaces, given by X = M(ℤ_q, n+ 2) ∨ M(ℤ_q, n+ 1) ∨ M(ℤ_q, n). We determine the self-homotopy classes group [X, X] and the self-homotopy equivalence group 𝓔(X). We investigate the subgroups of [M_j , M_k] consisting of homotopy classes of maps that induce the trivial homomorphism up to (n + 2)-homotopy groups for j ≠ k. Using these results, we calculate the subgroup 𝓔^dim_#(X) of 𝓔(X) in which all elements induce the identity homomorphism up to (n + 2)-homotopy groups of X.

• 한국의학물리학회지:의학물리
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• 제26권4호
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• pp.215-222
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• 2015

본 연구에서는 단일 비산란 그리드 및 다색광 x-선원을 이용하여 위상대조 x-선 영상을 용이하게 구현할 수 있는 새로운 방법을 제안한다. 제안된 신기법의 개념 입증을 위해 집속형 선형 그리드(200 lines/inch 선 밀도), 마이크로 초점 x-선관(${\sim}5{\mu}m$ 초점크기), CMOS형 평판형 검출기($48{\mu}m$ 픽셀 크기)로 실험장치를 구성하였으며, 한 번의 x-선 촬영($90kV_p$, 0.1 mAs)으로 감약대조 x-선 영상과 향상된 가시성을 지진 산란 x-선 영상 및 차분 위상대조 x-선 영상을 Fourier변조복원 기법을 적용하여 성공적으로 분리 획득하였다. 더 나아가, 감약대조 x-선 영상과 산란 x-선 영상을 합성함으로써 일반 감약대조 x-선 영상에서는 명확하게 볼 수 없는 샘플의 미세 구조를 보다 선명하게 나타냄을 확인하였다. 본 논문에서 제안한 단일 비산란 그리드 기반 위상대조 x-선 영상화 기법은 실험 구성 및 절차가 단순하고 새로운 대조도에 기반한 산란 및 위상대조 x-선 영상을 동시에 제공하기 때문에 차세대 x-선 영상화 신기법으로 다양한 응용분야에서 용이하게 적용될 수 있을 것으로 전망한다.

• 충청수학회지
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• 제32권4호
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• pp.509-524
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• 2019

Let Act(G, X) be the set of all continuous actions of a finitely generated group G on a compact metric space X. In this paper, we study the concepts of topologically stable points and continuous shadowable points of a group action T ∈ Act(G, X). We show that if T is expansive then the set of continuous shadowable points is contained in the set of topologically stable points.

• 대한수학회지
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• 제41권3호
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• pp.479-487
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• 2004

Let G be a finite group and N be a normal subgroup of G. We denote by ncc(N) the number of conjugacy classes of N in G and N is called n-decomposable, if ncc(N) = n. Set $K_{G}\;=\;\{ncc(N)$\mid$N{\lhd}G\}$. Let X be a non-empty subset of positive integers. A group G is called X-decomposable, if KG = X. In this paper we characterise the {1, 3, 4}-decomposable finite non-perfect groups. We prove that such a group is isomorphic to Small Group (36, 9), the $9^{th}$ group of order 36 in the small group library of GAP, a metabelian group of order $2^n{2{\frac{n-1}{2}}\;-\;1)$, in which n is odd positive integer and $2{\frac{n-1}{2}}\;-\;1$ is a Mersenne prime or a metabelian group of order $2^n(2{\frac{n}{3}}\;-\;1)$, where 3$\mid$n and $2\frac{n}{3}\;-\;1$ is a Mersenne prime. Moreover, we calculate the set $K_{G}$, for some finite group G.

• 대한수학회지
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• 제43권6호
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• pp.1183-1197
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• 2006

Let X be a smooth, closed, connected spin 4-manifold with $b_1(X)=0$ and signature ${\sigma}-(X)$. In this paper we use Seiberg-Witten theory to prove that if X admits a spin alternating $A_4$ action, then $b^+_2(X)$ ${\geq}$ |${\sigma}{(X)}$|/8+3 under some non-degeneracy conditions.