• Honam Mathematical Journal
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• v.32 no.1
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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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• v.24 no.2
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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).

• Proceedings of the KIEE Conference
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• 2000.07c
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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.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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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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• v.13 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.4
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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.

• Progress in Medical Physics
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• v.26 no.4
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• pp.215-222
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• 2015

In this work, we performed a proof-of-concept experiment for phase-contrast x-ray imaging (PCXI) based on a single antiscatter grid and a polychromatic x-ray source. We established a table-top setup which consists of a focused-linear grid having a strip density of 200 lines/inch, a microfocus x-ray tube having a focal-spot size of about $5{\mu}m$, and a CMOS-type flat-panel detector having a pixel size of $48{\mu}m$. By using our prototype PCXI system and the Fourier demodulation technique, we successfully obtained attenuation, scattering, and differential phase-contrast images of improved visibility from the raw images of several selected samples at x-ray tube conditions of $90kV_p$ and 0.1 mAs. Further, fusion image (e.g., the attenuation+the scattering) may have an advantage in displaying details of the sample's structures that are not clearly visible in the conventional attenuation image. Our experimental results indicate that single-grid-based approach seems a useful method for PCXI with great simplicity and minimal requirements on the setup alignment.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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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.