• 충청수학회지
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• 제26권4호
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• pp.853-867
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• 2013

In this paper we study the cardinality of the dot product set generated by two subsets of vector spaces over finite fields. We notice that the results on the dot product problems for one set can be simply extended to two sets. Let E and F be subsets of the d-dimensional vector space $\mathbb{F}^d_q$ over a finite field $\mathbb{F}_q$ with q elements. As a new result, we prove that if E and F are subsets of the paraboloid and ${\mid}E{\parallel}F{\mid}{\geq}Cq^d$ for some large C > 1, then ${\mid}{\Pi}(E,F){\mid}{\geq}cq$ for some 0 < c < 1. In particular, we find a connection between the size of the dot product set and the number of lines through both the origin and a nonzero point in the given set E. As an application of this observation, we obtain more sharpened results on the generalized dot product set problems. The discrete Fourier analysis and geometrical observation play a crucial role in proving our results.

• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.537-543
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• 2010

Let X be a regular $T_1$-space such that each single point set is a $G_{\delta}$ set. Denot 'hereditarily closure-preserving' by 'HCP'. To consider a question of closed maps of S. Lin in [6], we improve some results of Foged in [1], and prove the following propositions. Proposition 1. $D\;=\;\{x{\in}X\;:\;\mid\{F{\in}\cal{F}:x{\in}F\}\mid{\geq}{\aleph}_0\}$ is discrete and closed if $\cal{F}$ is a collection of HCP. Proposition 2. $\cal{H}\;=\;\{{\cup}\cal{F}'\;:\;F'$ is an fininte subcolletion of $\cal{F}_n\}$ is HCP if $\cal{F}$ is a collection of HCP. Proposition 3. Let (X,$\tau$) have a $\sigma$-HCP k-network. Then (X,$\tau$) has a $\sigma$-HCP k-network F = ${\cup}_n\cal{F}_n$ such that such tat: (i) $\cal{F}_n\;\subset\;\cal{F}_{n+1}$, (ii) $D_n\;=\;\{x{\in}X\;:\;\mid\{F{\in}\cal{F}_n\;:\;x{\in}F\}\mid\;{\geq}\;{\aleph}_0\}$ is a discrete closed set and (iii) each $\cal{F}_n$ is closed to finite intersections.

• 대한수학회논문집
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• 제32권3호
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• pp.661-676
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• 2017

Let T be a bounded linear operator acting on a complex Hilbert space ${\mathfrak{H}}$. In this paper we introduce the class, denoted ${\mathcal{Q}}(A(k),m)$, of operators satisfying $T^{m{\ast}}(T^{\ast}{\mid}T{\mid}^{2k}T)^{1/(k+1)}T^m{\geq}T^{{\ast}m}{\mid}T{\mid}^2T^m$, where m is a positive integer and k is a positive real number and we prove basic structural properties of these operators. Using these results, we prove that if P is the Riesz idempotent for isolated point ${\lambda}$ of the spectrum of $T{\in}{\mathcal{Q}}(A(k),m)$, then P is self-adjoint, and we give a necessary and sufficient condition for $T{\otimes}S$ to be in ${\mathcal{Q}}(A(k),m)$ when T and S are both non-zero operators. Moreover, we characterize the quasinilpotent part $H_0(T-{\lambda})$ of class A(k) operator.

• 대한수학회논문집
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• 제19권2호
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• pp.321-328
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• 2004

In this paper, we will prove the following: Let D be a nonempty of a normed linear space X and T : D -> X be a nonexpansive mapping. Let ${x_n}$ be a sequence in D and ${t_n}$, ${s_n}$ be real sequences such that (i) $0\;{\leq}\;t_n\;{\leq}\;t\;<\;1\;and\;{\sum_{n=1}}^{\infty}\;t_n\;=\;{\infty},\;(ii)\;(a)\;0\;{\leq}\;s_n\;{\leq}\;1,\;s_n\;->\;0\;as\;n\;->\;{\infty}\;and\;{\sum_{n=1}}^{\infty}\;t_ns_n\;<\;{\infty}\;or\;(b)\;s_n\;=\;s\;for\;all\;n\;{\geq}\;1\;and\;s\;{\in}\;[0,1),\;(iii)\;x_{n+1}\;=\;(1-t_n)x_n+t_nT(s_nTx_n+(1-s_n)x_n)\;for\;all\;n\;{\geq}\;1.$ Then, if the sequence {x_n} is bounded, then $lim_{n->\infty}\;$\mid$$\mid$x_n-Tx_n$\mid$$\mid$\;=\;0$. This result improves and complements a result of Deng [2]. Furthermore, we will show that certain conditions on D, X and T guarantee the weak and strong convergence of the Ishikawa iterative sequence to a fixed point of T.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2006년도 추계 학술발표회 논문집
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• pp.173-176
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• 2006

The one of the commonly reported failure mode of the RC beam strengthened with FRP was caused by the separation of the concrete cover, so called delamination. Therefore, ACI440 recommended that concrete cover delamination can be prevented in strengthened beams if bond length of FRP composite be exteneded over a point of cracking moment. In this study, the failure mode and the flexural performance of RC beam with different bond length of FRP are estimated. Each bonded length is calculated based on the point of cracking moment with addition or subtraction of specific length(=150mm). The results of this study show that mid-span debonding occurs in the specimen strengthened with CFRP strips which are bonded over the point of cracking moment, while concrete cover deliamination occurs at the termination point of CFRP in the specimen with less bonded length than the point of cracking moment region.

• 대한치과보철학회지
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• 제33권2호
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• pp.281-299
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• 1995

The purpose of this study was to evaluate the degree of occlusal contact under the fixed implant prosthesis of partially edentulous patients which was hased on occlusal concept of implant prosthesis. From the patients who have free-standing implant supported prosthesis of unilateral partially edentulous area, occlusal and occlusal contact point of th enatural tooth side and implant side of light closure and heavy closure were analyzed by T-scan system throuht pre-and post-adjustment and the degree of occlusal contact was estimated by Shimstock. The following results were obtained : 1. The occlusal force of natural tooth side(NF) from mid-sagittal axis was relatively constant at light and heavy closure through pre-and post-adjustment, but the occlusal force of implant side(IF) was decreased significantly at light closure(P<0.01) and heavy closure(P<0.05) of post-adjustment. 2. Natural tooth side-implant side moment(MIMoment) fo occlusal force from mid-sagittal axis was significant(p<0.05) through pre-and post-adjustment and the deviation from mid-sagittal axis was increased at light closure of post-adjustment, but was decreased at heavy closure of post-adjustment. 3. Comparing the NF and IF, IF was greater at heavy closure of pre-adjustment, and NF was greater at light closure of post-adjustment, and the NF and IF was relatively equally distributed at light closure of pre-adjustment and at heavy closure of post-adjustment. 4. The number of occlusal contact point of natural tooth side(NC) was relatively constant through pre-and post-adjustment, but the number of occlusal contact point of implant side(IC) was significantly decreased(P<0.05) at light closure of post-adjustment, and was not significant but was lesser at heavy closure of post-adjustment. 5. Difference of the NC and IC was greater at light closure of post-adjustment, but it was less at heavy closure of post-adjustment, and therefore occlusal contact point of natural tooth side and implant side was relatively equally distributed at heavy closure of postadjustment. 6. When bilaterally distribution of occlusal force and occlusal contact point was established, degree of occlusal contact of implant suporoted prosthesis with opoosing teeth at light clousre was $34.13{\pm}21.69{\mu}m$.

• 한국농림기상학회:학술대회논문집
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• 한국농림기상학회 2018년도 하계 학술발표초록집
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• pp.121-121
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• 2018

• 한국농림기상학회:학술대회논문집
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• 한국농림기상학회 2017년도 추계 학술발표초록집
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• pp.72-72
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• 2017

• 충청수학회지
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• 제23권4호
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• pp.617-623
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• 2010

Let p be a hyperbolic periodic point of f, and let ${\Lambda}(p)$ be a closed set which containing p. In this paper, we show that $C^1$-generically, if $f{\mid}_{{\Lambda}(p)}$ has the $C^1$-stably asymptotic average shadowing property, then it admits a dominated splitting.

• 대한방사선치료학회지
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• 제1권1호
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• pp.70-78
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• 1985

The intrauterine irradiation is essential to achieve adequate tumor dose to centeral tumor mass in radio therapy for uterine malignancy. The complications of pelvic organ are known to be directly related to radiation dose and physical parameters. The comparison study of currently using 2 systems was undertaken. The simulation films and medical records of 135 patients who was treated with intrauterine irradiation at one of general hospitals in Busan and Seoul between Jan. 1983 and June 1983, were critically analized and physical parameters of low dose rate system and remote controlled high dose rate system were measured. The physical parameters include distances between lateral walls of vaginal fornices, longitudinal and lateral angles of tandem to the body axis, the distance from the external os of uterine cervix to the central axis of ovoids, the radiation dose ratio to rectum and bladder to reference point A. Followings were summary of study results: 1. In distances between lateral walls of vaginal fornices the low dose rate system showed wide distribution and relatively larger distances. In low dose rate system 5.0-5.9 cm was $55.89\%$ 6.0-6.9 cm: $23.53\%$, 4.0-4.9cm: $10.29\%$, 3.0-3.9cm: $10.29\%$, and in high dose rate system 5.0-5.9cm was $80.59\%$, 4.0-4.9cm: $17.91\%$, $6.0\~6.9\;cm:\;1.5\%$. 2. In lateral angulation of tandem to body axis, the low does system revealed mid position (the position along body axis) $64.7\%$, Lt. deviation $19.13\%$ and Rt. deviation $16.17\%$. However the high dose rate system revealed mid position $49.26\%$ Lt. deviation $40.29\%$ and Rt. deviation $10.45\%$. 3. In longitudinal angulation of tandem to body axis the mid position was $11.77\%$ and anterior angulation $88.23\%$ in low dose rate system but in high dose rate system the mid position was $1.56\%$ and anterior angulation $98.44\%$. 4. Down ward displacement of ovoids below external os was only $2.94\%$ in low dose rate system and $67.69\%$ in high dose rate system. 5. The radiation dose ration to rectum to reference point A was $102.70\%$ in high dose rate system and $70.09\%$ in low dose rate system. The dose ratio to bladder to reference point A was $78.14\%$ in high dose rate system and $75.32\%$ in low dose rate system.