• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.503-517
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• 2016

For positive integers d and n, let $[n]^d$ be the set of all vectors ($a_1,a_2,{\cdots},a_d$), where ai is an integer with $0{\leq}a_i{\leq}n-1$. A subset S of $[n]^d$ is called a Sidon set if all sums of two (not necessarily distinct) vectors in S are distinct. In this paper, we estimate two numbers related to the maximum size of Sidon sets in $[n]^d$. First, let $\mathcal{Z}_{n,d}$ be the number of all Sidon sets in $[n]^d$. We show that ${\log}(\mathcal{Z}_{n,d})={\Theta}(n^{d/2})$, where the constants of ${\Theta}$ depend only on d. Next, we estimate the maximum size of Sidon sets contained in a random set $[n]^d_p$, where $[n]^d_p$ denotes a random set obtained from $[n]^d$ by choosing each element independently with probability p.

• Earthquakes and Structures
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• v.5 no.5
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• pp.589-605
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• 2013

The effect of dead loads on dynamic responses of a uniform elastic beam subjected to moving loads is examined by means of a governing equation which takes into account initial bending stresses due to dead loads. First, the governing equation of beams which includes the effect of dead loads is briefly presented from the author's paper (1990, 1991, 2010). The effect of dead loads is considered by a strain energy produced by conservative initial stresses caused by the dead loads. Second, the effect of dead loads on dynamical responses produced by moving loads in simply supported beams is confirmed by the results of numerical computations using the Galerkin method and Wilson-${\theta}$ method. It is shown that the dynamical responses by moving loads are decreased remarkably on a heavyweight beam when the effect of dead loads is included. Third, an approximate solution of dynamic deflections including the effect of dead loads for a uniform beam subjected to moving loads is presented in a closed-form for the case without the additional mass due to moving loads. The proposed solution shows a good agreement with results of numerical computations with the Galerkin method and Wilson-${\theta}$ method. Finally it is clarified that the effect of dead loads on elastic uniform beams subjected to moving loads acts on the restraint of the transverse vibration for the both cases without and with the additional mass due to moving loads.

• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.71-74
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• 1983

The problems of the continuity of homomorphisms between Banach algebras have been studied widely for the last two decades to obtain various fruitful results, yet it is far from characterizing the calss of Banach algebras for which each homomorphism from a member of the class into a Banach algebra is conitnuous. For commutative Banach algebras A and B a simple proof shows that every homomorphism .theta. from A into B is continuous provided that B is semi-simple, however, with a non semi-simple Banach algebra B examples of discontinuous homomorphisms from C(K) into B have been constructed by Dales [6] and Esterle [7]. For non commutative Banach algebras the problems of automatic continuity of homomorphisms seem to be much more difficult. Many positive results and open questions related to this subject may be found in [1], [3], [5] and [8], in particular most recent development can be found in the Lecture Note which contains [1]. It is well-known that a$^{*}$-isomorphism from a $C^{*}$-algebra into another $C^{*}$-algebra is an isometry, and an isomorphism of a Banach algebra into a $C^{*}$-algebra with self-adjoint range is continuous. But a$^{*}$-isomorphism from a $C^{*}$-algebra into an involutive Banach algebra is norm increasing [9], and one can not expect each of such isomorphisms to be continuous. In this note we discuss an isomorphism from a commutative $C^{*}$-algebra into a commutative Banach algebra with dense range via separating space. It is shown that such an isomorphism .theta. : A.rarw.B is conitnuous and maps A onto B is B is semi-simple, discontinuous if B is not semi-simple.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.18 no.10
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• pp.909-916
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• 2005

The structural and electrical property of RF magnetron sputtered ZnO thin film have been studied as a function of RF power, substrate temperature, oxygen/argon gas ratio and film thickness at constant sputtering power, sputtering working pressure and target-substrate distance. To analyze a crystallo-graphic properties of the films, $\theta$/2$\theta$ mode X-ray diffraction, SEM, and AFM analyses. C-axis preferred orientation, resistivity and surface roughness highly depended on oxygen/argon gas ratio. The resistivity of ZnO thin film(6000 ${\AA}$) rapidly increased with increasing oxygen ratio and the resistivity value of $9 {\ast} 10^7 {\Omega}cm$ was obtained at a working pressure of 10 mTorr with the same oxygen/argon gas ratio. The surface roughness was also improved with increasing oxygen ratio and the ZnO films deposited with the same oxygen/argon gas ratio showed the excellent roughness value of 28.7 ${\AA}$. With increase of the substrate temperature, The C-axis preferred orientation of ZnO thin film increases and the resistivity decreases due to deviation from the stoichiometric ZnO due to oxygen deficiency.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.413-431
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• 2012

Let $C^r[0,t]$ be the function space of the vector-valued continuous paths $x:[0,t]{\rightarrow}\mathbb{R}^r$ and define $X_t:C^r[0,t]{\rightarrow}\mathbb{R}^{(n+1)r}$ and $Y_t:C^r[0,t]{\rightarrow}\mathbb{R}^{nr}$ by $X_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}),\;x(t_n))$ and $Y_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}))$, respectively, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n=t$. In the present paper, using two simple formulas for the conditional expectations over $C^r[0,t]$ with the conditioning functions $X_t$ and $Y_t$, we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form $${\exp}\{{\int_o}^t{\theta}(s,\;x(s))\;d{\eta}(s)\}{\psi}(x(t)),\;x{\in}C^r[0,t]$$ where ${\eta}$ is a complex Borel measure on [0, t] and both ${\theta}(s,{\cdot})$ and ${\psi}$ are the Fourier-Stieltjes transforms of the complex Borel measures on $\mathbb{R}^r$.

• East Asian mathematical journal
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• v.22 no.2
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• pp.249-257
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• 2006

Let n be a 2-step nilpotent Lie algebra which has an inner product <,> and has an orthogonal decomposition $n=\delta{\oplus}\varsigma$ for its center $\delta$ and the orthogonal complement $\varsigma\;of\;\delta$. Then Each element Z of $\delta$ defines a skew symmetric linear map $J_Z:\varsigma{\rightarrow}\varsigma$ given by $=$ for all $X,\;Y{\in}\varsigma$. Let $\gamma$ be a unit speed geodesic in a 2-step nilpotent Lie group H(2, 1) with its Lie algebra n(2, 1) and let its initial velocity ${\gamma}$(0) be given by ${\gamma}(0)=Z_0+X_0{\in}\delta{\oplus}\varsigma=n(2,\;1)$ with its center component $Z_0$ nonzero. Then we showed that $\gamma(0)$ is conjugate to $\gamma(\frac{2n{\pi}}{\theta})$, where n is a nonzero intger and $-{\theta}^2$ is a nonzero eigenvalue of $J^2_{Z_0}$, along $\gamma$ if and only if either $X_0$ is an eigenvector of $J^2_{Z_0}$ or $adX_0:\varsigma{\rightarrow}\delta$ is not surjective.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.7 no.4
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• pp.353-362
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• 1996

In this paper, SAR distribution is calculated according to the rabbit's head using approximation of its medium three layers model. Our experiment was classified 5 groups dependent on the power intensity of 2,450MHz microwave to measure EEG(Electroencephalograph) of rabbit, which was checked in left frontal lobe before and after irradiation of microwave. In results, mean total power of EEG was slightly decreased and mean composition percentages of $\theta$, $\delta$ and $\beta$ wave were increased after irradiation in observation. It means to decrease of elect- rophysiologic activity and trend of fast wave in brain after irradiation of its microwave. We analyzed the electrophysiological effect of the biobody quantitatively using measured EEG and estimated MPE (Maximum Permissible Exposure).

• Proceedings of the KIEE Conference
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• 1998.07d
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• pp.1447-1449
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• 1998

The c-axis orientation plays a very important role in controlling the main parameters of the perpendicular magnetic recording media, such as perepndicular magnetic anisotropy field $H_{K{\bot}}$, the ratio of coercive force $H_{C{\bot}}/H_{C//}$, the recording density $D_{50}$, and the dispersion of the c-axis orientation $\Delta\theta_{50}$, which is quite important for the performance as perpendicular recording media, as well as the magnetic properties of the film. In this study, the essential process requirement for preparing the Co-Cr films with the superior c-axis orientation, the dependence of $\Delta\theta_{50}$ and the magnetic properties on the film thickness $\delta$, and the effect of underlayer on the dispersion of c-axis orientation have been investigated for both the FTS and DCM system.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.23 no.3
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• pp.245-249
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• 2010

Two dimensional(2D) pair-photonic crystals (pair-PCs) have been fabricated by a multiple-exposure nanosphere lithography (MENSL) method using the self-assembled nanospheres as lens-mask patterns and the collimated laser beam as a multiple-exposing source. The arrays of the 2D pair-PCs exhibited variable lattice structures and shape the control of rotating angle (${\Theta}$), tilting angle (${\gamma}$) and the exposure conditions. In addition, the base period or filling factor of pair-PCs as well as their shapes could be changed by experimental conditions and nanosphere size. A 1.18-${\mu}m$-thick resist was spincoated on Si substrate and the multiple exposure was carried out at change of ${\gamma}$ and ${\Theta}$. Images of prepared 2D pair-PCs were observed by SEM. We believe that the MENSL method is a suitable useful tool to realize the pair-periodic arrays of large area.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.4
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• pp.131-140
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• 1993

A new model which requires one branch of main curves for the model calibration is developed based on the assumption that the weighting factor accounting for the pore blockage effect against air entry, $P_a({\theta})$, in Mualem's Model III-1 has a linear relation to the dimensionless pore radius r. The proposed model simulates experimental data more accurately than existing models which require one branch of main curves for the model calibration. Previous study showed that Model III-1 is the most appropriate model among domain models which require two branches of main curves for the model calibration. In comparison of the proposed model with Model III-1, both simulate hysteresis curves with almost the same accuracy. The proposed model can be applied efficiently in analyzing the unsaturated flow.